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Field Manual 3-34.331 TOPOGRAPHIC SURVEYING 16 January 2001

TOC Chap1 2 3 4 5 6 7 8 9 10 11 AppA AppB AppC AppD Gl Bib

Chapter 8

## NAVSTAR GPS

This chapter provides a general overview of the NAVSTAR GPS. The NAVSTAR GPS is a passive, satellite-based navigation system that is operated and maintained by DOD. Its primary mission is to provide passive global positioning/navigation for air-, land-, and sea-based strategic and tactical forces.

SECTION I - GPS OVERVIEW

8-1. A GPS receiver is a simple range-measurement device. Distances are measured between the receiver antenna and the satellites, and the position is determined from the intersections of the range vectors. These distances are determined by a GPS receiver, which precisely measures the time it takes a signal to travel from the satellite to the station. This measurement process is similar to that used in conventional-pulsing marine-navigation systems and in phase-comparison EDM land-surveying equipment.

### OPERATING AND TRACKING MODES

8-2. There are two, general operating modes from which GPS-derived positions can be obtained absolute and relative (or differential) positioning. Within each of these two modes, range measurements to the satellites can be performed by tracking either the phase of the satellite's carrier signal or PRN codes that are modulated on the carrier signal. In addition, GPS positioning can be performed with the receiver operating in a static or dynamic (kinematic) environment. This variety of operational options results in a wide range of accuracy levels that can be obtained from the NAVSTAR GPS. Accuracies can range from 100 meters down to less than 1 centimeter. Increasing the accuracy to less than 1 centimeter requires additional observation time and can be achieved in real time. The selection of a particular GPS operating and tracking mode (for example, absolute, differential, code, carrier, static, kinematic, or combinations thereof) depends on the user's application. Topographic surveying typically requires differential positioning using carrier-phase tracking. Absolute modes are rarely used for geodetic surveying except when worldwide reference control is being established.

ABSOLUTE POSITIONING

8-3. Absolute positioning is the most common military and civil application of NAVSTAR GPS for real-time navigation. When operating in this passive, real-time navigation mode, ranges to NAVSTAR GPS satellites are observed by a single receiver positioned on a point for which a position is desired. This receiver may be positioned to be stationary over a point (static) or in motion (kinematic [such as on a vehicle, aircraft, missile, or backpack]). Two levels of absolute-positioning accuracy may be obtained SPS and PPS. With specialized GPS receiving equipment, data-processing refinements, and long-term static observations, absolute-positional coordinates can be determined to accuracy levels of less than 1 meter. These applications are usually limited to worldwide geodetic-reference surveys.

8-4. The SPS user is able to achieve real-time, 3D (point-positional) absolute positioning. The SPS is the GPS signal that DOD authorizes to civil users. This level of accuracy is due to the deliberate degradation of the GPS signal by DOD for national security reasons. DOD degradation of the GPS signal is referred to as selective availability (S/A). DOD has also implemented antispoofing (AS), which denies the SPS user the more accurate precision code (P-code).

8-5. Using the PPS requires DOD authorization for a decryption device that is capable of deciphering the encrypted GPS signals. Army topographic surveyors are authorized users; however, actual use of the equipment has security implications. Real-time, 3D absolute-positional accuracies of 16 to 20 meters are attainable through the PPS.

DIFFERENTIAL POSITIONING

8-6. Differential positioning is a process of measuring the differences in coordinates between two receiver points, each of which is simultaneously observing/measuring satellite code ranges and/or carrier phases from the NAVSTAR GPS constellation. This process measures the difference in ranges between the satellites and two or more ground observing points. The range measurement is performed by a phase-difference comparison, using either the carrier or code phase. The basic principle is that the absolute-positioning errors at the two receiver points will be about the same for a given instant. The resultant accuracy of these coordinate differences is at the meter level for code-phase observations and at the centimeter level for carrier-phase tracking. These coordinate differences are usually expressed as 3D baseline vectors, which are comparable to conventional survey azimuth/distance measurements. DGPS positioning can be performed in the static or the kinematic mode.

### SYSTEM CONFIGURATION

8-7. The NAVSTAR GPS consists of three distinct segments the space segment (satellites), the control segment (tracking and monitoring stations), and the user segment (air-, land-, and sea-based receivers).

SPACE SEGMENT

8-8. The space segment consists of all GPS satellites in orbit. The first generation of satellites were Block I or developmental. Several of these satellites are still operational. A full constellation of Block II or production satellites is now in orbit. The full constellation consists of 24 Block II operational satellites (21 primary with 3 active on-orbit spares). There are four satellites in each of six orbital planes inclined at 55� to the equator. The satellites are at altitudes of 10,898 nautical miles and have 11-hour, 56-minute orbital periods. The three spares are transparent to the user on the ground (the user is not able to tell which are operational satellites and which are spares). A procurement action for Block IIR (replacement) satellites is underway to ensure full system performance through the year 2025.

CONTROL SEGMENT

8-9. The control segment consists of five tracking stations that are located throughout the world (Hawaii, Colorado, Ascension Island, Diego Garcia Island, and Kwajalein Island). The information obtained from tracking the satellites is used in controlling and predicting their orbits. Three of the stations (Ascension, Diego Gracia, and Kwajalein) are used for transmitting information back to the satellites. The master control station is located at Colorado Springs, Colorado. All data from the tracking stations are transmitted to the master control station where they are processed and analyzed. Ephemerides, clock corrections, and other message data are then transmitted back to the three stations that are responsible for subsequent transmittal back to the satellites. The master control station is also responsible for the daily management and control of the GPS satellites and the overall control segment.

USER'S SEGMENT

8-10. The user's segment represents the ground-based receiver units that process the satellite signals and arrive at a user's position. This segment consists of both military and civil activities for an unlimited number of applications in a variety of air-, land-, and sea-based platforms.

### BROADCAST FREQUENCIES AND CODES

8-11. Each NAVSTAR satellite transmits signals on two L-band frequencies (designated as L1 and L2). The L1 carrier frequency is 1,575.42 megahertz and has a wavelength of about 19 centimeters. The L2 carrier frequency is 1,227.60 megahertz and has a wavelength of about 24 centimeters. The L1 signal is modulated with a P-code and a coarse-acquisition code (code). The L2 signal is modulated with a P-code only. Each satellite carries precise atomic clocks to generate the timing information needed for precise positioning. A navigation message is also transmitted on both frequencies. This message contains ephemerides, clock corrections and coefficients, the health and status of satellites, almanacs of all GPS satellites, and other information.

PSEUDORANDOM NOISE

8-12. Modulated C/A- and P-codes are referred to as PRN codes. These PRN codes are actually a sequence of very precise "time marks" that permit the ground receivers to compare and compute the time of transmission between a satellite and a ground station. The range to the satellite can be derived from this transmission time. This is the basis behind GPS range measurements. C/A-code pulse intervals are about every 300 meters in range. The more accurate P-code pulse intervals are about every 30 meters.

PSEUDORANGES

8-13. A pseudorange is the time delay between the satellite clock and the receiver clock, as determined from C/A- or P-code pulses. This time difference equates to the range measurement but is called a pseudorange since at the time of the measurement, the receiver clock is not synchronized to the satellite clock. In most cases, an absolute real-time, 3D navigational position can be obtained by observing at least four simultaneous pseudoranges.

SPS

8-14. The SPS uses the less precise C/A-code pseudoranges for real-time GPS navigation. Due to deliberate DOD degradation of the C/A-code accuracy, 100 meters in horizontal and 156 meters in vertical accuracy levels result. These accuracy levels are adequate for most civil applications where only approximate real-time navigation is required.

PPS

8-15. The PPS is the fundamental military real-time navigational use of the GPS. Pseudoranges are obtained using the higher pulse rate (higher accuracy) P-code on both frequencies (1 and 2). Real-time, 3D accuracies at the 16-meter level can be achieved with the PPS. The P-code is encrypted to prevent unauthorized civil or foreign use. This encryption requires a special decryption code to obtain this 16-meter accuracy.

CARRIER-PHASE MEASUREMENTS

8-16. Carrier-frequency tracking measures the phase differences between the Doppler-shifted satellite and receiver frequencies. The phase differences are continuously changing due to the changing satellite earth-orbit geometry. However, such effects are resolved in the receiver and subsequent data postprocessing. When carrier-phase measurements are observed and compared between two stations (differential mode), 3D baseline-vector accuracy (below the centimeter level) between the stations is attainable. New receiver technology and processing techniques have allowed for carrier-phase measurements to be used in real-time centimeter positioning.

### BROADCAST EPHEMERIS DATA

8-17. Each NAVSTAR GPS satellite periodically broadcasts data concerning clock corrections, system/satellite status and, most critically, its position or ephemeris data. There are two basic types of ephemeris data broadcast and precise.

BROADCAST EPHEMERIDES

8-18. Broadcast ephemerides are predicted satellite positions that are broadcast within the navigation message, which is transmitted from the satellites in real time. The ephemerides can be acquired in real time by a receiver that is capable of acquiring either the C/A- or P-code. The broadcast ephemerides are computed by using the past tracking data of the satellites. The satellites are tracked continuously by the monitor stations to obtain more recent data to use for orbit predictions. The data are analyzed by the master control station, and new parameters for the satellite orbits are transmitted back to the satellites. This upload is performed daily and the newly predicted orbital elements are transmitted every hour by the navigational message. Broadcast ephemerides are adequate to obtain needed accuracies for most survey applications.

PRECISE EPHEMERIDES

8-19. Precise ephemerides are based on actual tracking data that are postprocessed to obtain more accurate satellite positions. These ephemerides are delayed for processing but are more accurate than the broadcast ephemerides because they are based on actual tracking data and not predicted data. Civilian users can obtain this information from the NGS or private sources that maintain their own tracking networks and provide the information for a fee.

SECTION II - ABSOLUTE POSITIONING

8-20. Absolute positioning involves the use of only one passive receiver at one station location to collect data from multiple satellites to determine the station's location. It is not sufficiently accurate for precise surveying and positioning uses. However, it is the most widely used GPS-positioning method for real-time navigation and location.

### ABSOLUTE-POSITIONING ACCURACIES

8-21. Absolute-positioning accuracies are dependent on the user's authorization. The SPS user can obtain real-time, 3D accuracies of 100 meters. The lower level of accuracies achievable using the SPS is due to the intentional degradation of the GPS signal by DOD S/A. The PPS user (usually a DOD-approved user) can use a decryption device to achieve a 3D accuracy in the range of 10 to 16 meters with a single-frequency receiver. Accuracy to less than 1 meter can be obtained from absolute GPS measurements when special equipment and postprocessing techniques are employed.

8-22. By using broadcast ephemerides, the user is able to use pseudorange values in real time to determine absolute-point positions with an accuracy of between 3 meters in the best of conditions and 80 meters in the worst of conditions. By using postprocessed (precise) ephemerides, the user can expect absolute point positions with an accuracy of near 1 meter in the best of conditions and 40 meters in the worst of conditions.

### PSEUDORANGING

8-23. When a GPS user performs a GPS navigational solution, only an approximate range (or pseudorange) to selected satellites is measured. In order to determine the user's precise GPS location, the known range to the satellite and the position of those satellites must be known. By pseudoranging, the GPS user measures an approximate distance between the antenna and the satellite without any corrections for errors in synchronization between the clock of the transmitter and the clock of the receiver. This measurement correlates by correlation of a satellite-transmitted code and a reference code that is created by the receiver. The distance the signal has traveled is equal to the velocity of the transmission of the satellite multiplied by the elapsed time of transmission. The satellite-signal velocity changes that are due to tropospheric and ionospheric conditions must be considered.

8-24. The accuracy of the positioned point is a function of the range-measurement accuracy and the geometry of the satellites (reduced to spherical intersections with the earth's surface). A description of the geometrical magnification of uncertainty in a GPS-determined point position is the dilution of precision (DOP). Repeated and redundant range observations will generally improve range accuracy. However, the DOP remains the same. In a static mode (the GPS antenna stays stationary), range measurements to each satellite can be continuously remeasured over varying orbital locations of the satellite(s). The varying satellite orbits cause varying positional intersection geometry. In addition, simultaneous range observations to numerous satellites can be adjusted using weighting procedures that are based on the elevation and the pseudorange-measurement reliability.

8-25. Four pseudorange observations are needed to resolve a GPS 3D position. Three pseudorange observations are needed for a two-dimensional (2D) (horizontal) location. There are often more than four pseudorange observations due to the need to resolve the clock biases contained in both the satellite and the ground-based receiver. In computing the X, Y, and Z coordinates of a point, a fourth unknown parameter (clock bias) must also be included in the solution.

### ABSOLUTE-POSITIONING ERROR SOURCES

8-26. There are numerous sources of measurement errors that influence GPS performance. The sum of all systematic errors or biases contributing to the measurement error is referred to as a range bias. The observed GPS range (without removal of biases) is referred to as a biased range or pseudorange. Principal contributors to the final range error that also contribute to overall GPS error are ephemeris error, satellite-clock and electronics inaccuracies, tropospheric and ionospheric refraction, atmospheric absorption, receiver noise, and multipath effects. Other errors include those induced by DOD S/A and AS. In addition to these major errors, the GPS also contains random observation errors (such as unexplainable and unpredictable time variation). These errors are impossible to model and correct. The following paragraphs discuss errors associated with absolute GPS-positioning modes. Many of these errors are either eliminated or significantly minimized when the GPS is used in a differential mode, because the same errors are common to both receivers during simultaneous observing sessions.

EPHEMERIS ERRORS AND ORBIT PERTURBATIONS

<>8-27. Satellite-ephemeris errors are errors in the prediction of a satellite's position, which may then be transmitted to the user in the satellite data message. Ephemeris errors are satellite dependent and are very difficult to correct completely and compensate for, because the forces acting on the predicted orbit of a satellite are difficult to measure directly. The previously stated accuracy levels are subject to the equipment's condition and performance. Ephemeris errors produce equal error shifts in the calculated absolute-point positions.

CLOCK STABILITY

8-28. The GPS relies very heavily on accurate time measurements. GPS satellites carry rubidium and cesium time standards that are usually accurate to 1 part in 10 trillion and 1 part in 100 trillion, respectively, while most receiver clocks are actuated by a quartz standard accurate to 1 part in 100 million. A time offset is the difference between the time as recorded by the satellite clock and the time recorded by the receiver. A range error that is observed by the user as a result of time offsets between the satellite and receiver clock is a linear relationship and can be approximated.

8-29. Unpredictable transient situations that produce high-order departures in clock time can be stored for short periods of time. In a plane survey, departure is defined as the difference between the castings of the two ends of the line, which may be either plus or minus. Predictable time drift of the satellite clocks is closely monitored by ground-control stations. Through close monitoring of the time drift, the ground-control stations are able to determine second-order polynomials that accurately model the time drift. These second-order polynomials, determined to model the time drift, are included in the broadcast message in an effort to keep this drift to within 1 millisecond. The time synchronization between the GPS satellite clocks is kept to within 20 nanoseconds through the broadcast-clock corrections as determined by the ground-control stations and the synchronization of GPS standard time to the universal time, coordinated (UTC) to within 100 nanoseconds. Random time drifts are unpredictable, thereby making them impossible to model.

8-30. GPS receiver-clock errors can be modeled in a manner similar to GPS-satellite-clock errors. In addition to modeling the satellite-clock errors and in an effort to remove them, an additional satellite should be observed during operation to solve for an extra clock offset parameter along with the required coordinate parameters. This procedure is based on the assumption that the clock bias is independent at each measurement epoch. Rigorous estimation of the clock terms is more important for point positioning than for differential positioning. Many of the clock terms cancel each other when the position equations are formed from observations during a differential-survey session.

IONOSPHERIC DELAYS

8-31. GPS signals are electromagnetic signals and as such are nonlinearly dispersed and refracted when transmitted through a highly charged environment like the ionosphere. Dispersion and refraction of the GPS signal are referred to as ionospheric range effects, because dispersion and refraction of the signal result in an error in the GPS range value. Ionospheric range effects are frequency dependent.

8-32. The error effect of ionosphere refraction on GPS range values is dependent on sunspot activity, the time of day, and satellite geometry. GPS operations conducted during periods of high sunspot activity or with satellites near the horizon produce range results with the most amount of ionospheric error. GPS operations conducted during periods of low sunspot activity, during the night, or with a satellite near the zenith will produce range results with the least amount of ionospheric error.

8-33. Resolution of ionospheric refraction can be accomplished by using a dual-frequency receiver (a receiver that can simultaneously record both L1 and L2 frequency measurements). During a period of uninterrupted observation of the L1 and L2 signals, these signals can be continuously counted and differenced. The resultant difference shows the variable effects of the ionosphere delay on the GPS signal. Single-frequency receivers used to determine an absolute or differential position typically rely on ionospheric models that predict the effects of the ionosphere. Recent efforts have shown that significant ionospheric-delay removal can be achieved using single-frequency receivers.

TROPOSPHERIC DELAYS

8-34. GPS signals in the L-band level are refracted and not dispersed by the troposphere. Tropospheric conditions that cause refraction of the GPS signal can be modeled by measuring the dry and wet components.

MULTIPATH EFFECTS

8-35. Multipath describes an error that affects positioning and occurs when the signal arrives at the receiver from more than one path. Multipath normally occurs near large reflective surfaces, such as a building or structure with a reflective surface, a chain-link fence, or antenna arrays. Multipath is caused by the reflection of the GPS signal off of a nearby object, which produces a false signal at the GPS antenna. GPS signals received as a result of multipath give inaccurate GPS positions when processed. Newer receiver and antenna designs and thorough mission planning can minimize multipath effects as an error source. The averaging of GPS signals over a period of time can also reduce multipath effects.

RECEIVER NOISE

8-36. Receiver noise includes a variety of errors associated with the ability of the GPS receiver to measure a finite time difference. These errors include signal processing, clock/signal synchronization and correlation procedures, receiver resolution, and signal noise.

S/A AND AS

8-37. S/A purposely degrades the satellite signal to create position errors by dithering the satellite clock and offsetting the satellite orbits. The effects of S/A can be eliminated by using differential techniques. AS is implemented by interchanging the P-code with a classified, encrypted P-code called a Y-code. This denies users who do not possess an authorized decryption device. Manufacturers of civil GPS equipment have developed techniques, such as squaring or cross correlation, to make use of the P-code when it is encrypted.

### USER EQUIVALENT RANGE ERROR

8-38. The previously described error sources or biases are principal contributors to the overall GPS range error. This total error budget is often summarized as the user equivalent range error (UERE). As mentioned previously, errors can be removed or at least effectively suppressed by developing models of their functional relationships in terms of various parameters that can be used as a corrective supplement for the basic GPS information. Differential techniques also eliminate many of these errors. Table 8-1 lists significant sources for errors and biases and correlates them to the segment source.

Table 8-1. GPS Range-Measurement Accuracy

Segment Source | Error Source | Absolute Positioning | Differential Positioning (P-code) (m)
--- | --- | --- | ---
C/A-code Pseudorange (m) | P-code Pseudorange (m)
Space | Clock stability | 3.0 | 3.0 | Negligible
Orbit perturbations | 1.0 | 1.0 | Negligible
Other | 0.5 | 0.5 | Negligible
Control | Ephemeris predictions | 4.2 | 4.2 | Negligible
Other | 0.9 | 0.9 | Negligible
User | Ionosphere | 3.5 | 2.3 | Negligible
Troposphere | 2.0 | 2.0 | Negligible
Receiver noise | 1.5 | 1.5 | 1.5
Multipath | 1.2 | 1.2 | 1.2
Other | 0.5 | 0.5 | 0.5
1s UERE | �12.1 | �6.5 | �2.0

### ACCURACIES

8-39. The absolute value of range accuracies obtainable from the GPS are largely dependent on which code (C/A or P) is used to determine positions. These range accuracies (for example, UERE), when coupled with the geometrical relationships of the satellites during the position determination (for example, DOP), result in a 3D ellipsoid that depicts uncertainties in all three coordinates. Given the changing satellite geometry and other factors, GPS accuracy is time/location dependent. Error propagation techniques are used to define nominal accuracy statistics for a GPS user.

DOP

8-40. The final positional accuracy of a point (determined by using absolute GPS-S techniques) is directly related to the geometric strength of the configuration of satellites observed during the survey session. GPS errors resulting from satellite-constellation geometry can be expressed in terms of DOP. In mathematical terms, DOP is a scalar quantity used in an expression of a ratio of the positioning accuracy. It is the ratio of the standard deviation of one coordinate to the measurement accuracy. DOP represents the geometrical contribution of a certain scalar factor to the uncertainty (for example, standard deviation) of a GPS measurement. DOP values are a function of the diagonal elements of the covariance matrices of the adjusted parameters for the observed GPS signal. DOP values are used in point formulations and determinations. DOP is a scalar quantity of the contribution of the configuration of satellite-constellation geometry to the GPS accuracy. DOP can also be a measure of the strength of the satellite-constellation geometry. The more satellites that can be observed and used in the final solution, the better the solution. Since DOP can be used as a measure of geometrical strength, it can also be used to selectively choose four satellites in a particular constellation that will provide the best solution.

Geometric DOP

8-41. The main form of DOP used in absolute GPS positioning is the geometric DOP (GDOP). GDOP is a measure of accuracy in a 3D position and time. The final positional accuracy equals the actual range error multiplied by the GDOP.

Positional DOP

8-42. Positional DOP (PDOP) is a measure of the accuracy in 3D position. The PDOP values are generally developed from satellite ephemerides before conducting a survey. When developed before a survey, PDOP can be used to determine the adequacy of a particular survey schedule. This is valid for rapid-static or kinematic surveys but is less valid for a long-duration static survey.

8-43. PDOP represents position recovery at an instant in time and is not representative of a whole session of time. A PDOP error is generally given in units of meters of error per 1-meter error in a pseudorange measurement. When using pseudorange techniques, PDOP values in the range of 4 to 5 meters of error per 1-meter error are considered very good, while PDOP values greater than 10 meters of error per 1-meter error are considered very poor. For static surveys, it is generally desirable to obtain GPS observations during a time of rapidly changing GDOP or PDOP.

8-44. When the values of PDOP or GDOP are viewed over time, peak or high values (greater than 10 meters of error per 1-meter error) can be associated with satellites in a constellation of poor geometry. The higher the PDOP or GDOP, the poorer the solution for that instant in time. This is critical in determining the acceptability of real-time navigation and photogrammetric solutions. Poor geometry can be the result of satellites orbiting near each other or being in the same plane or at similar elevations.

Horizontal DOP

8-45. Horizontal DOP (HDOP) is a measurement of the accuracy in a 2D horizontal position. The HDOP statistic is most important in evaluating GPS-Ss intended for horizontal control. HDOP is the RMS error determined from the final variance-covariance matrix divided by the standard error of the range measurements. HDOP roughly indicates the effects of satellite-range geometry on a resultant position.

Vertical DOP

8-46. Vertical DOP (VDOP) is a measurement of the accuracy in the standard deviation of a vertical height. Table 8-2 indicates generally accepted DOP values for a baseline solution.

Table 8-2. Acceptable DOP Values

Measurement | DOP Value | Comment
--- | --- | ---
GDOP and PDOP | Less than 10 meters of error per 1-meter error (optimally 4 to 5 meters of error per 1-meter error) | In static GPS surveying, it is desirable to have a GDOP/PDOP that changes during the time of the GPS-S session. The lower the GDOP/PDOP, the better the instantaneous point-position solution.
HDOP and VDOP | 2 meters of error per 1-meter error | This DOP value results in the best constellation of four satellites.

ACCURACY COMPARISONS

8-47. It is important that GPS-accuracy measures clearly identify the statistic from which they were derived. A 100-meter or positional variance-covariance matrix is meaningless unless it is identified as being either one dimensional (1D), 2D, or 3D, along with the applicable probability level. For example, a PPS 16-meter 3-deviation accuracy is, by definition, a spherical error probable (SEP) (50 percent). This 16-meter SEP equates to a 28-meter 3D, 95 percent confidence spheroid. If transformed to 2D accuracy, the SEP equates roughly to a 10-meter circular error probable (CEP), a 12-meter root-mean-square (RMS), a 2-meter 2-deviation RMS, or a 36-meter 3-deviation RMS. Table 8-3 shows additional information on GPS-measurement statistics. In addition, absolute GPS point-positioning accuracies are defined relative to an earth-centered coordinate system/datum. This coordinate system will differ significantly from local or construction datums. Nominal GPS accuracies may also be published as design or tolerance limits, and accuracies achieved can differ significantly from these values.

Table 8-3. Representative GPS Error-Measurement Statistics for Absolute-Point Positioning

Error-Measure Statistic | Probability % | Relative Distance (ft)1 | GPS Precise- Positioning Service (m)2 | GPS Standard- Positioning Service (m)2
--- | --- | --- | --- | ---
1D Measures | sN or sE |  | sN or sE | sU
Probable error | 50.00 | 0.6745 s | �4.0 | �9.0 | �24.0 | �53.0
Average error | 57.51 | 0.7979 s | <�5.0 | �11.0 | �28.0 | �62.0
1s standard error/deviation3 | 68.27 | 1.0000 s | �6.3 | �13.8 | �35.3 | �78.0
90% probability (map accuracy standard) | 90.00 | 1.6450 s | �10.0 | �23.0 | �58.0 | �128.0
95% probability/confidence | 95.00 | 1.9600 s | �12.0 | �27.0 | �69.0 | �153.0
2 s standard error/deviation | 95.45 | 2.0000 s | �12.6 | �27.7 | �70.7 | �156.0
99% probability/confidence | 99.00 | 2.5760 s | �16.0 | �36.0 | �91.0 | �201.0
3 s standard error (near certainty) | 99.73 | 3.0000 s | �19.0 | �42.0 | �106.0 | �234.0
2D Measures4 | Circular Radius | Circular Radius
1 s standard error circle5 | 39.00 | 1.0000 sc | 6.0 | 35.0
CEP6 | 50.00 | 1.1770 sc | 7.0 | 42.0
1-deviation RMS (1DRMS)3, 7 | 63.00 | 1.4140 sc | 9.0 | 50.0
Circular map accuracy standard | 90.00 | 2.1460 sc | 13.0 | 76.0
95% 2D positional confidence circle | 95.00 | 2.4470 sc | 15.0 | 86.0
2-deviation RMS (2DRMS)8 | 98.00 | 2.8300 sc | 17.8 | 100.0
99% 2D positional confidence circle | 99.00 | 3.0350 sc | 19.0 | 107.0
3.5 s circular near-certainty error | 99.78 | 3.5000 sc | 22.0 | <123.0
3-deviation RMS (3DRMS) | 99.90 | 4.2400 sc | 27.0 | 150.0
3D Measures | Spherical Radius | <Spherical Radius
1 s spherical standard error9 | 19.90 | 1.0000 ss | 9.0 | 50.0
SEP10 | 50.00 | 1.5400 ss | 13.5 | 76.2
Mean radial spherical error (MRSE)11 | 61.00 | 1.7300 ss | 16.0 | 93.0
90% spherical accuracy standard | 90.00 | 2.5000 ss | 22.0 | 124.0
95% 3D confidence spheroid | 95.00 | 2.7000 ss | 24.0 | 134.0
99% 3D confidence spheroid | 99.00 | 3.3700 ss | 30.0 | 167.0
Spherical near-certainty error | 99.89 | 4.0000 ss | 35.0 | 198.0
1Valid for 2- and 3-deviation only if sN = sE = s U. (s minimum/s maximum) generally must be �0.2. Relative distance used unless otherwise indicated. 2Representative accuracy based on 1990 Federal Radio Navigation Plan (FRNP) simulations for PPS and SPS (FRNP estimates shown in bold italics) and that sN � s E. SPS may have significant short-term variations from these nominal values.
3Statistic used to define USACE hydrographic survey depth and positioning criteria.
4The 1990 FRNP also proposes SPS maintain, at minimum, a 2D confidence of 300 meters @ 99.99 percent probability.
5 sC 0.5 ( s N + s E) approximates standard error ellipse.
6CEP 0.589 ( s N + s E) � 1.18 s C.
71DRMS ( s N2 + s E2).
82DRMS 2 ( s N2 + s E2).
9 sS 0.333 ( s N + s E + s U).
10SEP 0.513 ( s N + s E + s U).
11MRSE ( s N2 + s E2 + s U2).

LEGEND:

sc = approximate standard error ellipse
ss = nominal standard error

NOTES:

>1. Most commonly used statistics are shown in bold-face type.
2. Estimates are not applicable to differential GPS positioning. Circular/spherical error radii do not have � signs.
3. Absolute positional accuracies are derived from GPS-simulated user range errors/deviations and the resultant geocentric-coordinate solution (X-Y-Z) covariance matrix, as transformed to a local datum (N-E-U or f -l -h). GPS accuracy will vary with GDOP and other numerous factors at time(s) of observation. The 3D covariance matrix yields an error ellipsoid. Transformed ellipsoidal dimensions given (for example, s N, sE, or s U) are only average values observed under nominal GDOP conditions. Circular (2D) and spherical (3D) radial measures are only approximations to this ellipsoid, as are probability estimates.

ROOT-MEAN-SQUARE ERROR MEASURES

8-48. Two-dimensional GPS positional accuracies are normally estimated using a RMS radial-error statistic. A 1-sigma (sigma is denoted bys RMS error equates to the radius of a circle with a 63 percent probability that the position is within the circle. A circle of twice this radius (2 s) represents about a 97 percent probability. This 97 percent probability circle, or 2 s RMS, is the most common positional-accuracy statistic used in GPS surveying. In some instances, a 3 s RMS (99 or more percent probability) is used. This RMS error statistic is also related to the positional variance-covariance matrix. An RMS error statistic represents the radius of a circle and, therefore, is not preceded by a � sign.

PROBABLE ERROR MEASURES

8-49. Three-dimensional GPS-accuracy measurements are commonly expressed by SEP. The SEP represents the radius of a sphere with a 50 percent confidence or probability level. This spheroid radial measure only approximates the actual 3D ellipsoid representing the uncertainties in the geocentric coordinate system. In 2D horizontal positioning, a CEP statistic is commonly used, particularly in military targeting. The CEP represents the radius of a circle containing a 50 percent probability of position confidence.

SECTION III - DIFFERENTIAL PRECISE POSITIONING

8-50. Absolute positioning does not provide the accuracies needed for most survey-control projects due to existing and induced errors. To eliminate the errors and obtain higher accuracies, the GPS can be used in a differential-positioning mode. The terms "relative" and "differential" used throughout this manual have similar meaning. Relative is used when discussing one thing in relation to another. Differential is used when discussing the method of positioning one thing in relation to another. Differential positioning requires that at least two receivers be set up at two stations (usually one is known) to collect satellite data simultaneously to determine coordinate differences. This method positions the two stations relative to each other (hence the term relative positioning) and can provide the accuracies required for basic land surveying.

### CODE-PSEUDORANGE TRACKING

8-51. Differential positioning (using code pseudoranges) is performed similarly to code-pseudorange tracking for absolute positioning. Code-pseudorange tracking effectively eliminates or minimizes some of the major uncertainties. This pseudorange process results in the absolute coordinates of the user on the earth's surface. Errors in range are directly reflected in resultant coordinate errors. Differential positioning is not as concerned with the absolute position of the user as with the relative difference between two user positions, which are simultaneously observing the same satellites. Since errors in the satellite position and atmospheric-delay estimates are effectively the same at both receiving stations, the errors cancel each other to a large extent.

8-52. For example, if the true pseudorange distance from a known control point to a satellite is 100 meters and the observed or measured pseudorange distance is 92 meters, then the pseudorange error or correction is 8 meters for that particular satellite. A pseudorange correction (PRC) can be generated for each satellite being observed. If a second receiver is observing at least four of the same satellites and is within a reasonable distance, it can use these PRCs to obtain a relative position to the known control point since the errors will be similar. Thus, the relative distance (coordinate difference) between the two stations is reasonably accurate regardless of poor absolute coordinates. In effect, the GPS-observed baseline vectors are no different from azimuth/distance observations. As with a total station, any type of initial-coordinate reference can be input to start the survey.

8-53. The GPS coordinates will not coincide with the user's local-project datum coordinates. Since differential-survey methods are concerned only with relative coordinate differences, disparities with the global reference system used by the NAVSTAR GPS are not significant for topographic purposes. Therefore, GPS coordinate differences can be applied to any type of local-project reference datum (for example, NAD 27 or NAD 83).

### CARRIER-PHASE TRACKING

8-54. Differential positioning (using carrier phases) uses a formulation of pseudoranges. The process becomes more complex when the carrier signals are tracked so that range changes are measured by phase resolution. In carrier-phase tracking, an ambiguity factor is added, which must be resolved to obtain a derived range. Carrier-phase tracking provides for a more accurate range resolution due to the short wavelength (about 19 centimeters for L1 and 24 centimeters for L2) and the ability of a receiver to resolve the carrier phase down to about 2 millimeters. This technique has primary application to engineering, topographic, and geodetic surveying and may be employed with either static or kinematic surveys. There are several techniques that use the carrier phase to determine a station's position. These include static, rapid-static, kinematic, stop-and-go kinematic, pseudokinematic, and on-the-fly (OTF) kinematic/Table 8-4 lists these techniques and their required components, applications, and accuracies.

Table 8-4. Carrier-Phase Tracking

Technique | Requirements | Applications | Accuracy
Static (postprocessing) | L1 or L1/L2 GPS receiver 386/486 computer for postprocessing 45-minute to 1-hour minimum observation time1 | Control surveys (high-accuracy) | Subcentimeter level
Rapid static (postprocessing) | L1/L2 GPS receiver 5- to 20-minute observation time1 | Control surveys (medium- to high-accuracy) | Subcentimeter level
Kinematic2 (postprocessing) | L1 GPS receiver with kinematic survey option 386/486 PC for postprocessing | Continuous topographic surveys Location surveys | Centimeter level
Stop-and-go kinematic2 (postprocessing) | L1 GPS receiver 386/486 PC for postprocessing | Control surveys (medium-accuracy) | Centimeter level
Pseudokinematic2 (postprocessing) | L1 GPS receiver 386/486 computer for postprocessing | Control surveys (medium-accuracy) | Centimeter level
OTF/RTK kinematic3 (real-time or postprocessing) | Real-time processing: Internal or external processor (a PC with dual communication ports) Minimum 4800 baud radio/modem data-link set Postprocessing: L1/L2 GPS receiver
386/486 PC

Hydro surveys
(real-time, high-accuracy)

Location surveys

Control surveys
(medium-accuracy)

Photo control surveys

Continuous topographic surveys

Subdecimeter level

1Dependent on the satellite constellation and the number of satellites in view. 2An initialization period is required, and loss of satellite lock is not tolerated. 3No static initialization is necessary, integers are gained while moving, and loss of satellite lock is tolerated.

STATIC

8-55. Static surveying is the most widely used differential technique for control and geodetic surveying. It involves long observation times (1 to 2 hours, depending on the number of visible satellites) to resolve the integer ambiguities between the satellite and the receiver. Accuracies of less than a centimeter can be obtained from this technique.

RAPID STATIC

8-56. Rapid-static surveying measures baselines and determines positions in the centimeter level with a short observation time (5 to 20 minutes). The observation time is dependent on the length of the baseline and the number of visible satellites. When moving from one station to the next, loss of satellite lock (also referred to as loss of lock) can occur since each baseline is processed independently.

KINEMATIC

8-57. Kinematic surveying allows the user to rapidly and accurately measure baselines, while moving from one point to the next. The data are collected and postprocessed to obtain accurate positions to the centimeter level. This technique permits only partial loss of lock during observation and requires a brief period of static initialization. The OTF technology, both real-time and postprocessed, could eventually replace standard kinematic procedures for short baselines.

STOP-AND-GO KINEMATIC

8-58. Stop-and-go kinematic surveying involves collecting data for a few minutes (1 to 2 minutes) at each station (after a period of initialization) to gain the integers. This technique does not allow for loss of lock during the survey. If loss of lock occurs, a new period of initialization must take place. This technique can be performed with two fixed or known stations to provide redundancy and improve accuracy.

PSEUDOKINEMATIC

8-59. Pseudokinematic surveying is similar to standard kinematic and static procedures combined. The differences are no static initialization, a longer period of time at each point (about 1 to 5 minutes) (each point must be revisited after about one hour), and loss of lock is acceptable. Pseudokinematic surveying is less acceptable for establishing baselines, because the positional accuracy is less than that for kinematic or rapid-static surveying.

OTF/RTK

8-60. OTF/RTK kinematic surveying uses GPS technology to allow positioning to less than a decimeter in real time. This technique determines the integer number of carrier wavelengths from the GPS antenna to the GPS satellite, transmitting them while in motion and without static initialization. The basic concept behind OTF/RTK kinematic surveying is kinematic surveying without static initialization (integer initialization is performed while moving) and allowances for loss of lock. Other GPS techniques that can achieve this kind of accuracy require static initialization while the user is not moving and do not allow for loss of lock while in motion.

### VERTICAL MEASUREMENTS

8-61. The GPS is not recommended for third-order or higher vertical-control surveys or as a substitute for standard differential leveling. It is practical for small-scale topographic mapping or similar projects.

ELEVATION DETERMINATION

8-62. The height component of GPS measurements is the weakest plane because of the orbital geometry of the X, Y, and Z position determination. Thus, GPS-ellipsoidal height differences are usually less accurate than the horizontal components. GPS-derived elevation differences do not meet third-order standards (as obtained by using conventional levels) and must be used with caution.

TOPOGRAPHIC MAPPING

8-63. GPS positioning, whether in the absolute or differential positioning mode, can provide heights (or height differences) of surveyed points. The height or height difference obtained from the GPS is in terms of height above or below the WGS-84 ellipsoid. Ellipsoid heights are not the same as orthometric heights or elevations. Orthometric heights or elevations are obtained from conventional differential leveling. This distinction between ellipsoid heights and orthometric elevations is critical to many engineering and construction projects. GPS users must exercise extreme caution in applying GPS height determinations to projects that are based on orthometric elevations.

8-64. The GPS uses WGS 84 as the optimal mathematical model best describing the shape of the true earth at sea level, based on an ellipsoid of revolution. The WGS-84 ellipsoid adheres very well to the shape of the earth in terms of horizontal coordinates but differs somewhat with the established MSL definition of orthometric height. The difference between ellipsoidal height (as derived by the GPS) and conventional leveled (orthometric) heights is required over an entire project area to adjust GPS heights to orthometric elevations. The NGS has developed geoid modeling software (for example, GEOID93, GEOID96, and GEOID99) to be used to convert ellipsoidal heights to approximate orthometric elevations. These converted elevation values should be used with extreme caution because they are easy to mess up.

8-65. Static- or kinematic-GPS-S techniques can be used effectively on a regional basis for the densification of low-accuracy vertical control for topographic mapping. Existing BM data (orthometric heights) and corresponding GPS-derived ellipsoidal values for at least three stations in a small project area can be used in tandem in a minimally constrained adjustment program to reasonably model the geoid. More than three correlated stations are required for larger areas to ensure proper modeling from the BM data. Corresponding GPS data can then be used to derive the unknown orthometric heights of the remaining stations that were occupied during the GPS-observation period.

GEOID HEIGHTS

8-66. The impact of the GPS on geodetic-control surveys has been immense. In the past, surveyors relied on line-of-sight instrumentation to develop coordinates. With the GPS, ground-station intervisibility is no longer required, and much longer lines can be surveyed. Different instruments and survey methods were used to measure horizontal and vertical coordinates, leading to two different networks with little overlap. The GPS, on the other hand, is a 3D system.

8-67. The heights obtained from the GPS are in a different height system than those historically obtained with geodetic leveling. GPS data can be readily processed to obtain ellipsoidal heights. This is the height above or below a simple ellipsoid model of the earth. Geodetic leveling takes into consideration a height called orthometric height (often known as the height above the MSL). These heights are found on topographic maps, stamped on markers, or stored in innumerable digital and paper data sets. To transform between these height systems requires the geoid height. These height systems are related by the following equation:

h = H + N

where
h= ellipsoidal height
H= orthometric height
N= geoid height

### DIFFERENTIAL ERROR SOURCES

8-68. Error sources encountered when using DGPS techniques are the same as for absolute positioning. In addition to these error sources, the receiver must maintain satellite lock on at least three satellites for 2D positioning and four satellites for 3D positioning. When loss of lock occurs, a cycle slip (discontinuity of an integer number of cycles in the measured carrier-beat phase as recorded by the receiver) may occur. In GPS absolute surveying, if satellite lock is not maintained, positional results will not be formulated. In GPS static surveying, if satellite lock is not maintained, positional results may be degraded resulting in incorrect formulations. In GPS static surveying, if the observation period is long enough, postprocessing software may be able to average out loss of lock and cycle slips over the duration of the observation period and formulate adequate positional results. If this is not the case, reoccupation of the stations may be required. In all differential-surveying techniques, if loss of lock does occur on some of the satellites, data processing can continue easily if a minimum of four satellites have been tracked. Generally, the more satellites tracked by the receiver, the more insensitive the receiver is to loss of lock. Cycle slips can usually be compensated.

### DIFFERENTIAL ACCURACIES

8-69. There are two levels of accuracy obtainable from the GPS when using differential techniques. The first level is based on pseudorange formulations, while the other is based on carrier-beat-phase formulations.

PSEUDORANGE FORMULATIONS

8-70. Pseudorange formulations can be developed from either the C/A-code or the more preciseP-code. Pseudorange accuracies are generally accepted to be 1 percent of the period between successive code epochs. Use of the P-code, where successive epochs are 0.1 millisecond apart, produces results that are about 1 percent of 0.1 millisecond (about 1 nanosecond). Multiplying this value by the speed of light gives a theoretical-resultant range measurement of around 30 centimeters. If using pseudorange formulations with the C/A-code, results can be ten times less precise (a range-measurement precision of around 3 meters). Point-positioning accuracy for a differential pseudorange solution is generally found to be in the range of 0.5 to 10 meters. These accuracies are largely dependent on the type of GPS receiver being used.

CARRIER-BEAT-PHASE FORMULATIONS

8-71. Carrier-beat-phase formulations can be based on either the L1, the L2, or both carrier signals. Accuracies achievable using carrier-beat-phase measurement are generally accepted to be 1 percent of the wavelength. Using the L1 frequency, where the wavelength is around 19 centimeters, a theoretical-resultant range measurement that is 1 percent of 19 centimeters (about 2 millimeters). The L2 carrier can only be used with receivers that employ a cross correlation, squaring, or another technique to get around the effects of AS.

8-72. The final positional accuracy of a point, that was determined using DGPS survey techniques, is directly related to the geometric strength of the configuration of satellites observed during the survey session. GPS errors resulting from satellite-constellation geometry can be expressed in terms of DOP. Positional accuracy for a differential carrier-beat-phase solution is generally in a range of 1 to 10 millimeters.

8-73. In addition to GDOP, PDOP, HDOP, and VDOP, the quality of the baselines produced by the DGPS (static or kinematic) through carrier-phase recovery can be defined by a quantity called relative DOP (RDOP). Multiplying the uncertainty of a double-difference measurement by RDOP yields the relative position error for that solution. The values of RDOP are measured in meters of error in relative position per error of one cycle in the phase measurement. The knowledge of an RDOP, or an equivalent value, is extremely important to the confidence one assigns to a baseline recovery. RDOP represents position recovery over a whole session of time and is not representative of a position recovery at an instant in time. When carrier-phase recovery is used, RDOP values around 0.1 meter per cycle are considered acceptable.

SECTION IV - PRECISE-POSITIONING SURVEY PLANNING

8-74. Using differential carrier-phase surveying to establish control for military projects requires operational and procedural specifications. These specifications are a project-specific function of the control being established. To accomplish these surveys in the most efficient and cost-effective manner and to ensure that the required accuracy is obtained, detailed survey planning is essential. This section defines GPS-S design criteria and other specifications that are required to establish control for topographic-survey projects.

### PROJECT-CONTROL ACCURACY

8-75. The first step in planning a control survey is to determine the ultimate accuracy requirements. Survey accuracy requirements are a direct function of the project's functional needs, that is, the basic requirements needed to support the planning, engineering design, maintenance, and operation. This is true forGPS or conventional surveying to establish project control. Most military activities require relative accuracies (accuracies between adjacent control points) ranging from 1:1,000 to 1:50,000, depending on the nature and scope of the project. Few topographic projects demand positional accuracies higher than 1:50,000 (second-order, Class I).

FUNCTIONAL REQUIREMENTS

8-76. Functional requirements must include planned and future design and mapping activities. Specific control density and accuracy are derived from these functional requirements. Control density within a given project is determined from factors such as planned construction, site-plan and master-plan mapping scales, and artillery/aviation-survey positioning requirements. The relative accuracy for project control is also determined based on such things as mapping scales, design needs, and project type. Most site-plan mapping for design purposes is performed and evaluated relative to the American Society of Photogrammetry and Remote Sensing (ASPRS) standards. These standards apply to photogrammetric mapping, plane-table mapping, and total-station mapping. Network control must be of sufficient relative accuracy to enable other users to reliably connect any supplemental mapping work.

MINIMUM ACCURACY REQUIREMENTS

8-77. Project control surveys should be planned, designed, and executed to achieve the minimum accuracy demanded by the functional requirements. To most efficiently use resources, control surveys should not be designed or performed to achieve accuracy levels that exceed the project requirements. For instance, if a third-order, Class I accuracy standard (1:10,000) is required for most topographic-project survey control, field-survey criteria should be designed to meet this minimum standard.

ACHIEVABLE GPS ACCURACY

8-78. GPS-S methods are capable of providing significantly higher relative positional accuracies with only minimal field observations, as compared with conventional triangulation or a traverse. Although a GPS-S may be designed and performed to support lower-accuracy project-control requirements, the actual results could be several magnitudes better than the requirement. Although higher accuracy levels are relatively easy to achieve with the GPS, it is important to consider the ultimate use of the control on the project when planning and designing GPS control networks. GPS-S adequacy evaluations should be based on the project's accuracy standards, not those theoretically obtainable with the GPS.

### NETWORK-DESIGN FACTORS

8-79. Many factors need to be considered when designing a GPS network and planning any subsequent observation procedures. These factors are described below.

PROJECT SIZE AND REQUIRED DENSITY OF CONTROL

8-80. The extent of the project will affect the GPS-S network shape. The type of GPS-S scheme used will depend on the number and spacing of points to be established as specified in the project requirements. In addition, maximum baseline lengths between stations and/or existing control are also prescribed. Often, a combination of GPS-S and conventional-survey densification is the most effective approach.

ABSOLUTE GPS REFERENCE DATUMS

8-81. Coordinate data for baseline observations are referenced and reduced relative to the WGS-84 ECEF coordinate system (X, Y, and Z). For all practical purposes, this system is not directly referenced to, but is closely related to, GRS 80 upon which NAD 83 is related (for CONUS work). Data reduction and adjustment are normally performed using the WGS-84 ECEF coordinate system, with baseline-vector components measured relative to the ECEF coordinate system. The baseline-vector components are denoted by delta [] X, Y, and Z.

8-82. If the external network being connected and adjusted to is a part of or belongs to NAD 83, the baseline coordinates may be directly referenced on the GRS-80 ellipsoid since they are nearly equal. All supplemental control that is established is therefore referenced to the GRS-80/NAD-83 coordinate system.

8-83. If a GPS-S is connected to NAD-27 stations that were not adjusted to NAD-83 datum, then these fixed points may be transformed to NAD-83 coordinates using Corpscon, and the baseline reductions and adjustments are performed relative to the GRS-80 ellipsoid. This method is recommended only if resurveying is not a viable option.

8-84. Alternatively, baseline connections to NAD-27 project control may be reduced and adjusted directly on that datum with resultant coordinates on the NAD 27. Geocentric coordinates on NAD-27 datum may be computed using transformation algorithms. Conversions of final adjusted points on NAD-27 datum to NAD 83 may also be performed using Corpscon.

8-85. Ellipsoid heights that are referenced to the GRS-80 ellipsoid differ significantly from the orthometric elevations. This difference (geoidal separation) can usually be ignored for horizontal control. Datum systems other than NAD 27/NAD 83 will be used outside CONUS (OCONUS) locations. Selected military operational requirements in CONUS may also require non-NAD datum references. It is recommended that GPS baselines be directly adjusted on the specific-project datum.

CONNECTIONS TO EXISTING CONTROL

8-86. For most static and kinematic GPS horizontal-control work, at least two existing control points should be connected for referencing and adjusting a new GPS-S. Table 8-5 shows GPS-S design, geometry, connection, and observing criteria. Existing points may be part of the NGRS or in-place project control that has been adequately used for years. Additional points may be connected if practical. In some instances, a single existing point may be used to generate spurred baseline vectors for supplemental construction control.

Table 8-5. GPS-S Design, Geometry, Connection, and Criteria

Criterion | Classification Order
--- | ---
2nd, I | 2nd, II | 3rd, I | 3rd, II
Relative accuracy:
ppm | 20 | 50 | 100 | 200
1 part in | <50k | 20k | >10k | 5k
NGRS network (local project network) (W/F/P) | Yes | Yes | Yes | Yes
Baseline observation check required over existing control | Yes | W/F/P | W/F/P |
Number of connections with existing network (NGRS or local project control):
Minimum | 2 | 2 | 2 | 2
Optimum | 3 | 3 | 2 | 2
New point spacing not less than (m) | 1,000 | 500 | 200 | 100
Maximum distance from network to nearest control point in project (km) | 50 | 50 | 50 | 50
Minimum network control quadrant location (relative to project center) | 2 | N/R | N/R | N/R
Master of fiducial stations required | W/F/P | No | No | No
Loop closure criteria:
Maximum number of baselines/loop | 10 | 20 | 20 | 20
Maximum loop length not to exceed (km) | 100 | 200 | N/R | N/R
Loop misclosure not less than (ppm) | 20 | 50 | 100 | 200
Single spur baseline observations: |  |  |  |
Allowed per order/class | No | No | Yes | Yes
Required number of sessions/baseline | NA | NA | 2 | 2
Required tie to NGRS | NA | NA | No | No
Field-observing criteria (static GPS-Ss):
Required antenna phase height measurement per session | 2 | 2 | 2 | 2
Meteorological observations required | No | No | No | No
Two frequency L1/L2 observations required: |  |  |  |
< 50-km lines | No | No | No | No
> 50-km lines | Yes | Yes | Yes | Yes
Recommended minimum observation time (per session) (min) | 60 | 45 | 30 | 30
Minimum number of sessions per GPS baseline | 1 | 1 | 1 | 1
Satellite quadrants observed (minimum number) | 3 W/F/P | N/R | N/R | N/R
Minimum obstruction angle above horizon (deg) | 15 | 15 | 15 | 15
Maximum HDOP/VDOP during session | N/R | N/R | N/R | N/R
Photograph and/or pencil rubbing required | A/R | No | No | No
Kinematic GPS surveying:
Allowable per survey class | Yes | Yes | Yes | Yes
Required tie to NGRS | W/F/P | W/F/P | No | No
Measurement time/baseline (follow manufacturer's specifications) | A/R | >A/R | A/R | A/R
Minimum number of reference points | 2 | 2 | 1-2 | 1
Preferred references | 2 | 2 | 2 | 1
Maximum PDOP | 15 | >15 | 15 | 15
Minimum number of observations from each reference station | 2 | 2 | 2 | 2
Adjustment and data submittal criteria:
Approximate adjustments allowed | Yes
Contract acceptance criteria:
Type of adjustment | Free (unconstrained)
Evaluation statistic | Relative distance accuracies
>Error-ellipse sizes | (not used as criteria)
Histogram | (not used as criteria)
Reject criteria:
Statistic | Normalized residual
Standard | �3 � SEUW
Optimum/nominal weighting:
Horizontal | �5 + 2 ppm
Vertical | >�10 + 2 ppm
>Optimum variance of unit weight | Between 0.5 and 1.5
GPS station/session data recording format | Field-survey book or form
Final station descriptions | Standard DA form
Written project/adjustment report required | Yes
LEGEND: W/F/P = where feasible and practical N/R = no requirement for this specification (usually indicates variance with provisional FGCC GPS specifications) A/R = as required in specific project instructions or manufacturer's operating manual SEUW = standard error of unit weight

Connections With Existing Project Control

8-87. The first choice for referencing new GPS-Ss is the existing project control. This is true for most surveying methods and has considerable legal basis. Unless a newly authorized project is involved, long-established project-control reference points should be used. If the project is currently on a local datum, then a supplemental tie to the

Connections With the NGRS

8-88. Connections with the NGRS (for example, National Ocean Service/ NGS control on NAD 83) are preferred where prudent and practical. As with conventional surveying, such connections to the NGRS are not mandatory. In many instances, connections with the NGRS are difficult and may add undue cost to a project with limited resources. When existing project control is known to be of poor accuracy, then ties (and total readjustment) to the NGRS may be warranted. Sufficient project funds should be programmed to cover the additional costs of these connections, including data submittal and review efforts if such work is intended to be included in the NGRS.

Mixed NGRS and Project-Control Connections

8-89. NGRS-referenced points should not be mixed with existing project control. This is especially important if existing project control was poorly connected with the older NGRS (NAD 27) or if the method of this original connection is uncertain. Since NGRS control has been readjusted to NAD 83 (including subsequent high-precision HARNs readjustments of NAD 83) and most project control has not, problems may result if these schemes are mixed indiscriminately. If a decision is made to establish or update control on an existing project and connections with the NGRS (for example, NAD 83) are required, then all existing project-control points must be resurveyed and readjusted. Mixing different reference systems can result in different datums, causing adverse impacts on subsequent construction or boundary references. It is far more preferable to use "weak" existing project control for a reference rather than end up with a mixture of different systems or datums.

Accuracy of Connected Reference Control

8-90. Connections should be made to control stations with a higher order of accuracy than is required. This is usually the case where NGRS control is readily available. However, when only existing project control is available, connection and adjustment will have to be performed using that reference system, regardless of its accuracy. GPS-baseline measurements should be performed over existing control to assess its accuracy and adequacy for adjustments or to configure partially constrained adjustments.

Connection Constraints

8-91. Table 8-5 indicates that a minimum of two existing stations are necessary to connect GPS static and kinematic surveys reliably. It is often prudent to include additional NGRS and/or project points, especially if the existing network is not reliable. Adding additional points will provide redundant checks on the surrounding network. This allows for the elimination of these points if the final constrained adjustment indicates a problem with one or more of the fixed points. This table also indicates the maximum-allowable distance that GPS baselines should extend from the existing network. Federal Geodetic Control Subcommittee (FGCS) GPS standards (FGCC 1988) require connections to be spread over different quadrants relative to the survey project. Other GPS standards suggest an equilateral distribution of fixed control on the proposed survey area.

LOCATION FEASIBILITY AND FIELD RECON

8-92. A good advance recon of all marks within the project area is crucial to an expedient and successful GPS-S. The site recon should be completed before the survey is started. Surveyors should prepare a site sketch and a brief description of how to reach the point, since the individual performing the site recon may not be the one that returns to occupy the known or unknown station.

Project Sketch

8-93. A project sketch should be developed before any site recon is performed. The sketch should be on a 1:50,000-scale map or another suitable drawing. Drawing the sketch on a map will assist the planner in determining site selections and travel distances between stations.

Station Descriptions and Recovery Notes

<8-94. Station descriptions for all new monuments will be developed as the monuments are established. The format for these descriptions is discussed in Chapter 3. Recovery notes should be written for existing NGRS network stations and project-control points. Estimated travel times to all stations should be included in the description. Include road-travel, walking, and GPS-receiver breakdown and setup time. These times can be estimated during the initial recon. A site sketch should also be made. DA Form 1959 can be used for description/recovery notes.

Way-Point Navigation

8-95. Way-point navigation (optional on some receivers) allows the user to enter the geodetic position (usually latitude and longitude) of points of interest along a particular route. The GPS antenna (fastened to a vehicle or range pole) and receiver can then provide the user with navigational information. This information may include the distance and bearing to the point of destination (stored in the receiver), the estimated time to the destination, and the speed and course of the user. This information can then be used to guide the user to the point of interest. Way-point navigation may also be helpful in the recovery of control stations that do not have descriptions. If a user has the capability of real-time code-phase positioning, the way-point-navigational accuracy can be in the range of 0.5 to 10 meters.

Site-Obstruction/Visibility Sketches

8-96. Record the azimuth and vertical angle of all obstructions during the site recon. The azimuths and vertical angles should be determined with a compass and an inclinometer, because obstructions such as trees and buildings cause the GPS signal being transmitted from the GPS satellite to be blocked. It is also important to know the type of obstruction to determine if multipath might be a problem. The obstruction data are needed to determine if the survey site is suitable for GPS surveying. Obstruction data should be plotted in a station-visibility diagram as shown in Figure 8-1. GPS surveying requires that all stations have an unobstructed view 15� above the horizon and satellites below 10� should not be observed.

Figure 8-1. Sample Station-Visibility Diagram

Suitability for Kinematic Observations

8-97. Obstruction-free projects may be suitable for kinematic- rather than static-GPS surveys. The use of kinematic observations increases productivity 5 to 10 times over static procedures, while still providing adequate accuracy levels. On many projects, a mixture of static- and kinematic-GPS observations may prove to be the most cost-effective.

On-Site Physical Restrictions and >Existing Control

8-98. The degree of difficulty in occupying points due to on-site physical restrictions (such as travel times, site access, multipath effects, and satellite visibility) should be anticipated. The need for redundant observations must also be considered. Additional GPS baselines may need to be observed between existing NGRS control to verify accuracy and/or stability.

Satellite-Visibility Limitations

8-99. There are at least four or five satellites in view at all times for most of CONUS. However, some areas may have less visibility when satellite maintenance is being performed or when there are unhealthy satellites. Satellite-visibility charts of the GPS-satellite constellation are important for optimizing network configuration and observation schedules.

Station-Intervisibility Requirements

8-100. Project specifications may dictate station-intervisibility requirements for azimuth reference. These requirements may constrain the minimum station spacing.

MULTIPLE/REPEAT BASELINE CONNECTIONS

8-101. Table 8-5 lists recommended criteria for baseline connections between stations, repeat baseline observations, and multiple station occupations so that extensive redundancy will result from the collected data. Many of these standards were developed by the FGCS for performing high-precision geodetic-control surveys.

LOOP REQUIREMENTS

8-102. A loop (traverse) provides the mechanism for performing field-data validation as well as final-adjustment accuracy analysis. Since loops of GPS baselines are comparable to traditional EDME/taped traverse routes, misclosures and adjustments can be handled similarly. Most GPS-S networks (static or kinematic) end up with one or more interconnecting loops that are either internal from a single fixed point or external through two or more fixed network points. Loops should be closed off at the spacing indicated in and meet the criteria specified in Table 8-5 based on the total loop length.

8-103. GPS control surveys may be conducted by forming loops between two or more existing points, with adequate cross-connections where feasible. Such alignment techniques are usually most practical on site plans or navigational projects that require control to be established along a linear path. Loops should be formed every 10 to 20 baselines, preferably closing on existing control. Connections to existing control should be made as opportunities exist and/or as often as practical.

8-104. When establishing control over such areas as relatively large military installations, perform a series of redundant baselines to form interconnecting loops. When densifying second- and third-order control for site-plan design and construction, extensive cross-connecting-loop and network configurations (recommended by the FGCS for geodetic surveying) are not necessary.

8-105. On all projects, consider the maximum use of combined static- and kinematic-GPS observations. Both may be configured to form pseudotraverse loops for subsequent field-data validation and final adjustment.

### NETWORK DESIGN AND LAYOUT

8-106. A wide variety of survey configurations may be used to densify project control using GPS surveying. Unlike conventional triangulation and EDM traverse surveying, the shape or geometry of the GPS-network design is not as significant. The following guidelines for planning and designing proposed GPS-Ss are intended to support lower-order (second-order, Class I, or 1:50,000 or less accuracy) military control surveys where relative accuracies at the centimeter level or better are required over a small project area. Newly established GPS control may or may not be incorporated into the NGRS. This depends on the adequacy of the connection to the existing NGRS network or whether the connection was tied only internally to existing project control.

8-107. When developing a network design, it is important to obtain the most economical coverage within the prescribed project-accuracy requirements. The optimum network design, therefore, provides a minimum amount of baseline/loop redundancy without an unnecessary amount of observation. Obtaining this optimum design (cost versus accuracy) is difficult and changes constantly due to evolving GPS technology and satellite coverage.

8-108. Planning a GPS-S scheme is similar to planning for conventional triangulation or traversing. The type of survey design used is dependent on the GPS technique and the user's requirements.

GPS NETWORKING

8-109. A GPS network is proposed when established survey control is to be used in precise-network densification (1:50,000 to 1:100,000). For lower-order work, elaborate network schemes are unnecessary and less work-intensive GPS-S methods may be used. The surveyor should devise a survey network that is geometrically sound. The networking method is practical only with static-, pseudokinematic-, and kinematic-survey techniques. Figure 8-2 shows a step-by-step example of how to design a GPS-S network.

Figure 8-2. GPS-Network Design

GPS TRAVERSING

8-110. GPS traversing should be used when the user has only two or three receivers and the required accuracies are 1:5,000 to 1:50,000. Traversing with GPS is similar to conventional methods. Open-end traverses are not recommended when 1:5,000 accuracies or greater are required. The GPS does not provide sufficient point-positioning accuracies, so surveyors must have a minimum of one fixed (or known) control point, although three are preferred.

8-111. A >fixed control point is a station with known latitude, longitude, and height or easting, northing, and height. This point may or may not be part of the NGRS. If only one control point is used and the station does not have a known height, the user will be unable to position the unknown stations.

8-112. When performing a loop traverse, surveyors should observe a check angle or check azimuth using conventional-survey techniques to determine if the known station has been disturbed. If azimuth targets are not visible and a check angle cannot be observed, a closed traverse involving one or more control points is recommended. Again, a check angle or check azimuth should be observed from the starting control station. If a check angle is not performed, the survey can still be completed. However, if the survey does not meet specified closure requirements, the surveyor will be unable to assess what control point may be in error. If a check angle or check azimuth cannot be observed, a third control point should be tied into the traverse to aid in determining the cause of misclosure (Figure 8-3).

Figure 8-3. GPS-Traversing Schemes

GPS SPUR SHOTS

8-113. GPS spurs shots are acceptable when the user has only two receivers or only a few control points are to be established. Spur lines should be observed twice during two independent observation sessions. Once the first session is completed, the receivers at each station should be turned off and the tripod elevations changed. This procedure is similar to performing a forward and backward level line. It is important that the tripods be moved in elevation and replumbed over the control station between sessions. If this step is not implemented, the two baselines cannot be considered independent. Spur shots are most applicable to static-survey and relative-positioning (code-phase) techniques.

### GPS-S TECHNIQUES

8-114. After a GPS network has been designed and laid out, a GPS-S technique needs to be considered. The most efficient technique should be chosen to minimize time and cost, while meeting the accuracy requirements of a given survey project. Once a technique is chosen, the equipment requirements, observation schedules, sessions designations, and planning functions can be determined.

GENERAL EQUIPMENT REQUIREMENTS

8-115. The type of GPS instrumentation used on a project depends on the accuracy requirements, the GPS-S technique, the project size, and economics. Dual-frequency receivers are recommended for baselines that exceed 50 kilometers. The length of the baseline may vary depending on the amount of solar activity during the observation period. Using a dual-frequency receiver permits the user to solve for possible ionospheric and tropospheric delays, which can occur as the signal travels from the satellite to the receiver antenna.

Receivers

8-116. A minimum of two receivers is required to perform a DGPS survey. The actual number used on a project will depend on the project size and the number of available instruments and operators. Using more than two receivers will often increase productivity and field-observation efficiency. Some kinematic applications require two reference receivers (set at known points) and at least one rover receiver.

Personnel

8-117. Personnel requirements are also project dependent. Most GPS equipment is compact and lightweight and only requires one person per station setup. However, when a station is not easily accessible or requires additional power for a data link, two individuals may be required.

Transportation

8-118. Normally, one vehicle is required for each GPS receiver used. Vehicles should be equipped to handle the physical conditions that may be encountered during the field observations. In most cases, a two-wheel-drive vehicle is adequate. If adverse site conditions exist, a four-wheel-drive vehicle may be required. Adequate and reliable transportation is important when the observation schedule requires moving from one station to another between observation sessions.

Auxiliary Equipment

8-119. Adequate power should be available for all equipment (such as, receivers,PCs, and lights) that will be used during the observations. PCs, software, and data-storage devices (floppy disks and/or cassette tapes) should be available for on-site field-data reduction. Other equipment should include tripods, tribrachs, tape measures, flags, flashlights, tools, equipment cables, a compass, and an inclinometer. A data link is also needed if real-time positioning is required.

OBSERVATION SCHEDULES

8-120. Planning a GPS-S requires a determination of when satellites will be visible for the given survey area. The first step in determining observation schedules is to plot the satellite visibility for the project area. Even when the GPS becomes fully operational, a full two-hour coverage of at least four satellites may not be available in all areas.

8-121. Most GPS-equipment manufacturers have software packages that predict satellite rise and set times. A satellite plot should have the satellites' azimuths, elevations, rise and set times, and PDOPs for the desired survey area. Satellite-ephemeris data is generally required as input for prediction software.

8-122. To obtain broadcast-ephemeris information, a GPS receiver collects data during a satellite window. The receiver antenna does not have to be located over a known point when collecting a broadcast ephemeris. The data is then downloaded into a satellite-prediction software. Besides inputting ephemeris data, the approximate latitude and longitude (usually scaled from a topographic map) and the time offset from UTC for the survey area are generally required.

8-123. The best time to perform a successful GPS-S can be obtained by taking advantage of the best combination of the satellites' azimuths, elevations, and PDOPs as determined by the satellite-visibility plot for the desired survey area. The number of sessions and/or stations observed per day will depend on the satellite visibility, the travel time between stations, and the final accuracy required. A receiver is often required to occupy a station for more than one session per day.

8-124. A >satellite sky plot (Figure 8-4) and a PDOP versus time plot (Figure 8-5) should be run before a site recon. The output files created by the satellite-prediction software are used in determining if a site is suitable for GPS surveying.

Figure 8-4. Sample Satellite Sky Plot

Figure 8-5. PDOP Versus Time Plot

8-125. Station occupation during each session should be designed to minimize travel time and to maximize the overall efficiency of the survey. Determination of session times is based mainly on the satellite-visibility plan with the following factors taken into consideration:

> > > - The time required to permit safe travel between survey sites.
> > > - The time to set up and take down the equipment before and after the survey.
> > > - The time to perform the survey.
> > > - The possible loss of observation time due to unforeseeable problems or complications.

SESSION DESIGNATIONS AND PLANNING FUNCTIONS

8-126. A GPS-S session is a single period of observation. Station/session designations are usually denoted by alphanumeric characters (for example, 0, 1, 2, A, B, C) and are determined before survey commencement.

8-127. If the party chief states that only eight numeric characters are permitted for station/session designations, the convention would be 12345678. The eight numeric characters are identified as follows:

> > > - First character. This character denotes the type of monument. The following convention is recommended:

> > > > - 1 = known horizontal-control monument.
> > > > - 2 = known BM.
> > > > - 3 = known 3D monument.
> > > > - 4 = new horizontal-control monument.
> > > > - 5 = new BM.
> > > > - 6 = new 3D monument.
> > > > - 7 = unplanned occupation.
> > > > - 8 = temporary 2D point.
> > > > - 9 = temporary 3D point.

> > > - >Second, third, and fourth characters. These characters denote the actual station number given to the station.
> > > - Fifth, sixth, and seventh characters. These characters denote the Julian day of the year.
> > > - Eighth character. This character denotes the session number.

8-128. An example of a station designation is:
Character position= 12345678
Station identifier= 40011821

> > > - The numeral 4 in the first position indicates that the monument is new and only the horizontal position is being established.
> > > - The numerals 001 are the station number for the monument.
> > > - The numerals 182 are the Julian date.
> > > - The numeral 1 in the eighth position identifies the session number during which observations are being made. If the receiver performed observations during the second session on the same day on the same monument, the session number should be changed to 2 for the period of the second session.

8-129. When alpha characters are permitted for a station/session designation, a more meaningful designation can be assigned. The date of each survey session should be recorded during the survey as calendar dates and Julian days and used in the station/session designation. Some GPS software programs will require Julian dates.

8-130. In addition to determining station/session designations, the following processes should be done before the survey begins:

> > > - Determine the occupant of each station.
> > > - Determine the satellite visibility for each station.
> > > - Request site-recon data for each station to be occupied (prior data may require clarification before survey commencement).
> > > - Develop a project sketch.
> > > - Issue explicit instructions on when each session is to begin and end.
> > > - Complete a station data-logging sheet for each station.

SECTION V - PRECISE-POSITIONING SURVEY CONDUCT

8-131. This section presents guidance on field >GPS-Ss for all types of projects. The primary emphasis in this section is on static and kinematic carrier-phase DGPS measurements.

### BASIC GPS-S PROCEDURES

8-132. The following are some general DGPS field-survey procedures. They should be performed at each station or during each session on a GPS-S.

RECEIVER SETUP

8-133. GPS receivers shall be set up according to manufacturers' specifications before beginning any observations. To eliminate any possibility of missing the beginning of the observation session, all equipment should be set up and power should be supplied to the receivers at least 10 minutes before the beginning of the observation session. Most receivers will lock on to satellites within 1 to 2 minutes of power-up.

ANTENNA SETUP

8-134. All tribrachs should be calibrated and adjusted before beginning each project. Since centering errors represent a major error source in all survey work, use both optical plummets and standard plumb bobs.

HI MEASUREMENTS

8-135. HI refers to the correct measurement of the distance of the GPS antenna above the reference monument over which it has been placed. Make HI measurements before and after each observation session, from the monument to a standard reference point on the antenna. Establish standard reference points for each antenna before the beginning of the observations. Make observations in both meters and feet for redundancy and blunder detection. Determine HI measurements to the nearest millimeter and to the nearest 0.01 foot. Note whether the HI is vertical or diagonal.

FIELD OBSERVATION PROCEDURES

8-136. Field-recording books, log sheets, log forms, or any acceptable recording media will be completed for each station and/or session. These records will be used for archival purposes. The amount of recording detail will depend on the project. Low-order geographic-mapping points do not need as much descriptive information as permanently marked primary-control points. Unit commands may require that additional data be recorded. These requirements are contained in the project instructions. The following data should be included in the field records:

> > > - Project name, project-directive number, observer name(s), and unit name.
> > > - Station-designation number.
> > > - Station file number.
> > > - Date and weather conditions.
> > > - Session start and stop time (local and UTC).
> > > - Receiver, antenna, DRU, and tribrach make, model, and serial number.
> > > - Antenna height (vertical or diagonal measures in inches [or feet] and centimeters [or meters]).
> > > - Satellite-vehicle (SV) designation and number.
> > > - Station-location sketch.
> > > - Geodetic location and elevation (approximate).
> > > - Problems encountered.

FIELD PROCESSING AND VERIFICATION

8-137. It is strongly recommended that GPS-data processing and verification be performed in the field (if applicable). This identifies any problems that may exist and can be corrected before returning from the field.

### ABSOLUTE POSITIONING

8-138. The accuracy obtained by GPS point positioning is dependent on the user's authorization. The SPS user can obtain an accuracy of 80 to 100 meters. SPS data are most often expressed in real time; however, the data can be postprocessed if the station occupation was over a period of time. The postprocessing produces a best-fit point position. Although this will provide a better internal approximation, the effects of S/A still degrade a positional accuracy of 80 to 100 meters. PPS users require a decryption device within the receiver to decode the effects of S/A. PPS provides an accuracy between 10 and 16 meters when a single-frequency receiver is used for observation. Dual-frequency receivers using the precise ephemeris may produce an absolute-positional accuracy of 1 meter or better. These positions are based on the absolute WGS-84 ellipsoid. PPS uses precise ephemeris, which requires the data to be postprocessed. The military uses a GPS-S receiver that is capable of meter-level GPS point positioning without postprocessing.8-138. The accuracy obtained by GPS point positioning is dependent on the user's authorization. The SPS user can obtain an accuracy of 80 to 100 meters. SPS data are most often expressed in real time; however, the data can be postprocessed if the station occupation was over a period of time. The postprocessing produces a best-fit point position. Although this will provide a better internal approximation, the effects of /font>

8-139. There are two techniques used for point positioning in the absolute mode long-term averaging of positions and differencing between signals. In long-term averaging, a receiver is set up to observe and store positions over a period of time. The length of the observation time depends on the accuracy required. The longer the period of data collection, the more accurate the position. The observation times can range between 1 and 2 hours. This technique can also be used in real time (the receiver averages the positions as they are calculated). The process of differencing between signals can only be performed in a postprocessed mode. NIMA has produced software that can perform this operation.

### DIFFERENTIAL POSITIONING

8-140. DGPS surveying is used to determine one location with respect to another location. When using this technique with the C/A- or P-code, it is called differential code-phase positioning or surveying. Differential code-phase positioning has limited application to detailed engineering surveying and topographic site-plan mapping applications. Exceptions include general recon surveys and military operational or geodetic-survey support functions. Additional applications for differential code-phase positioning have been on the increase as positional accuracy has increased. The code-phase-tracking differential system is a functional GPS-S system for positioning hydrographic-survey vessels and dredges. It also has application for small-scale, topographic mapping surveys or as input to a geographic-information-system (GIS) database. The collected data is used as input for a GIS database. A real-time dynamic DGPS positioning system includes a reference station, a communication link, and remote user equipment. If real-time results are not required, the communication link can be eliminated and the positional information postprocessed. Differential code-phase surveys can obtain accuracies of 0.5 to 0.05 meter.

REFERENCE STATION

8-141. A reference station is placed on a known survey monument in an area having an unobstructed view of at least four satellites that are 10� above the horizon. The reference station consists of a GPS receiver and antenna, a processor, and a communication link (if real-time results are desired). The reference station measures the timing and ranging information that is broadcast by the satellites and computes and formats range corrections for broadcast to the user's equipment. Using differential pseudoranging, the position of a survey vessel is found relative to the reference station. The pseudoranges are collected by the GPS receiver and transferred to the processor where PRCs are computed and formatted for data transmission. Many manufacturers have incorporated the processor within the GPS receiver, eliminating the need for an external processing device. The recommended data format is established by the Radio Technical Commission for Maritime (RTCM) Services Special Committee (SC). The processor should be capable of computing and formatting PRCs every 1 to 3 seconds.

COMMUNICATION LINK

8-142. A communication link is used as a transfer media for differential corrections. The main requirement of the communication link is that transmission be at a minimum rate of 300 bits per second. The type of communication system is dependent on the user's requirements.

Frequency Authorization

8-143. All communication links necessitate a reserved frequency for operation to avoid interference with other activities in the area. No transmission can occur over a frequency until the frequency has been officially authorized for transmitting digital data. This applies to all government agencies. Allocating a frequency is handled by the responsible frequency manager.

Ultrahigh-Frequency and Very-High-Frequency Broadcast Distance

8-144. Communication links operating at ultrahigh frequency (UHF) and very-high frequency (VHF) are viable systems for the broadcast of DGPS corrections. UHF and VHF can extend out 20 to 50 kilometers, depending on local conditions. The disadvantages of UHF and VHF links are their limited range to line of sight and the effects of signal shadowing (for example, islands, structures, and buildings), multipath, and licensing issues.

8-145. Several companies have developed low-wattage (1 watt or less) radio modems to transmit digital data. These radio modems require no license and can be used to transmit DGPS corrections in a localized area. The disadvantages of these radio modems is their limited range and line of sight.

USER'S (REMOTE-STATION) EQUIPMENT

8-146. The remote receiver should be a multichannel dual-frequency Y-code GPS receiver. The receiver must be able to store raw data for postprocessing. During postprocessing, the PRCs are generated with the GPS data from the reference station and then applied to the remote-station data to obtain a correct position. If the results are desired in real time, the receiver must be able to accept the PRCs from the reference station (via a data link) in the RTCM Services SC format and apply those corrections to the measured pseudorange. The corrected position data can then be input and stored in a database.

USCG DGPS NAVIGATION SERVICE

8-147. The USCG DGPS Navigation Service was developed to provide a nationwide (coastal regions, Great Lakes regions, and some inland waterways), all-weather, real-time, radio-navigation service in support of commercial and recreational maritime interests. Its accuracy was originally designed to fulfill an 8- to 20-meter maritime-navigation accuracy. However, a reconfigured version of the USCG system now yields a 1.5-meter 2-deviation RMS at distances upward of 150 kilometers from the reference beacon. The system operates on the USCG marine radio-beacon frequencies (285 to 325 kilohertz). Each radio beacon has an effective range of 150 to 250 kilometers at a 99.9 percent signal-availability level. It is fully expected that the USCG system, once completed, will be the primary marine-navigation device used by commercial and recreational vessels requiring meter-level accuracy.

### DGPS CARRIER-PHASE HORIZONTAL-POSITIONING SURVEYS

8-148. DGPS carrier-phase surveying is used to obtain the highest precision from the

> > > - Static.
> > > - Stop-and-go kinematic.
> > > - Kinematic.
> > > - Pseudokinematic.
> > > - Rapid-static.
> > > - OTF/RTK.

DGPS SURVEY TECHNIQUES

8-149. Procedures for performing each of these techniques are described below and should be used as guidelines for conducting a field survey. Specific manufacturers' procedures should also be followed. Project horizontal-control densification can be performed using any one of these techniques. Procedurally, all six techniques are similar in that each measures a 3D baseline vector between a receiver at one point (usually of known local-project coordinates) and a second receiver at another point, resulting in a vector difference between the two occupied points. The major distinction between static and kinematic baseline measurements is the way the carrier-wave integer-cycle ambiguities are resolved; otherwise, they are functionally the same process.

AMBIGUITY RESOLUTION

8-150. Cycle ambiguity (or integer ambiguity) is the unknown number of whole carrier wavelengths between the satellite and the receiver. Successful ambiguity resolution is required for successful baseline formulations. Generally, static surveying can provide instrumental error and ambiguity resolution through long-term averaging and simple geometrical principles, resulting in solutions to a linear equation that produces a resultant position. Ambiguity resolution can also be achieved through a combination of pseudorange and carrier-beat measurements, which are made possible by the PRN modulation code.

POSTOBSERVATION DATA REDUCTION

8-151. All carrier-phase relative-surveying techniques (except OTF/RTK), require postprocessing of the observed data to determine the relative baseline-vector differences. OTF/RTK can be performed in a real-time or postprocessed mode. Postprocessing of observed satellite data involves the differencing of signal-phase measurements recorded by the receiver. The differencing process reduces biases in the receiver and satellite oscillators and is performed with a PC. All baseline reductions should be performed in the field (if possible) to allow an on-site assessment of the survey adequacy.

### STATIC SURVEYING

8-152. Static surveying is perhaps the most common technique of densifying project network control. Two GPS receivers are used to measure a GPS-baseline distance. The line between a pair of GPS receivers from which simultaneous GPS data have been collected and processed is a vector referred to as a baseline. The station coordinate differences are calculated in terms of a 3D ECEF coordinate system that uses X, Y, and Z values based on the WGS-84 ellipsoid. These coordinate differences are then subsequently shifted to the project's coordinate system. GPS receiver pairs are set up over stations of either known or unknown locations. Typically, one of the receivers is positioned over a point whose coordinates are known (or have been carried forward as on a traverse) and the second is positioned over another point whose coordinates are unknown, but desired. Both GPS receivers must receive signals from the same four (or more) satellites for a period of time that can range from a few minutes to several hours, depending on the conditions of observation and the precision required.

STATIC BASELINE-OCCUPATION TIME

8-153. Station-occupation time is dependent on the baseline length, the number of satellites observed, and the GPS equipment. In general, 30 minutes to 2 hours is a good occupation time for baselines of 1 to 30 kilometers. A rough guideline for estimating station-occupation time is shown in Figure 8-6.

Figure 8-6. Station-Occupation Time

<

8-154. There is no definitive guidance for determining the baseline-occupation time; the results from the baseline reduction (and subsequent adjustments) will govern the adequacy of the observation irrespective of the actual observation time. The most prudent policy is to exceed the minimum estimated times, especially for lines where reoccupation would be difficult or field-data assessment capabilities are limited.

8-155. For baselines longer than 50 kilometers, the ionosphere may have an adverse effect on the solution. When using a dual-frequency GPS receiver, adverse ionosphere effects can shorten the baseline length.

SATELLITE-VISIBILITY REQUIREMENTS

8-156. The selected stations must have an unobstructed view of the sky for at least 15� or greater above the horizon during the observation window. An observation window is the period of time when observable satellites are in the sky and the survey can be successfully conducted.

COMMON SATELLITE OBSERVATIONS

>8-157. It is critical for a static-survey baseline reduction/solution that the receivers simultaneously observe the same satellites during the same time interval. For instance, if receiver number 1 observes a satellite constellation during the time interval 1000 to 1200 and receiver number 2 observes that same satellite constellation during the time interval 1100 to 1300, only the period of common observation (1100 to 1200) can be processed to formulate a correct vector difference between these receivers.

DATA POSTPROCESSING

8-158. After completing the observation session, the received GPS signals from both receivers are processed in a PC to calculate the 3D baseline-vector components between the two observed points. From these vector distances, local or geodetic coordinates may be computed and/or adjusted.

SURVEY CONFIGURATION

8-159. Static baselines may be extended from existing control using a control-densification method. These methods include networking,traverse, spur techniques, or combinations thereof. Specific requirements are normally contained in the project's instructions.

RECEIVER OPERATION AND DATA REDUCTION

8-160. Receiver operation and baseline-data postprocessing requirements are manufacturer-specific. The user should consult and study the manufacturer's operations manual (including the baseline data-reduction examples).

ACCURACY

8-161. Accuracy of static surveys will usually exceed 1 ppm. Static is the most accurate of all GPS techniques and can be used for any order survey.

### STOP-AND-GO KINEMATIC SURVEYING

8-162. Stop-and-go kinematic surveying is similar to static surveying in that it requires at least two receivers simultaneously recording observations. A major difference between static and stop-and-go surveying is the amount of time required for a receiver to stay fixed over an unknown point. In stop-and-go surveying, the first receiver (the home or reference receiver) remains fixed on a known control point. The second receiver (the rover receiver) collects observations statically on a point of unknown position for a period of time (usually a few minutes) and then moves to subsequent unknown points to collect signals for a short period of time. During the survey, at least four (preferably five) common satellites need to be continuously tracked by both receivers. Once all required points have been occupied by the rover receiver, the observations are postprocessed by a PC to calculate the baseline-vector and coordinate differences between the known control point and points occupied by the rover receiver during the survey session. The main advantage of this technique over static surveying is the reduced occupation time required over the unknown points. Because less occupation time is required, the time spent and the cost of conducting the survey are significantly reduced. Achievable accuracies typically equal or exceed third order.

PROCEDURES

8-163. Stop-and-go surveying is performed similarly to a conventional EDM traverse or electronic total-station radial survey. The GPS is initially calibrated by performing either an antenna swap (described below) with one known point and one unknown point or by performing a static measurement over a known baseline. This calibration process is performed to resolve initial cycle ambiguities. The known baseline may be part of the existing network or can be established using static-survey techniques. The roving receiver traverses between unknown points as if performing a radial-topographic survey. Typically, the points are double-connected, or double-run, as in a level line. Optionally, two fixed receivers may be used to provide redundancy on the remote points. With only 1 1/2 minutes at a point, production of coordinate differences is high and limited only by satellite observation windows, travel time between points, and overhead obstructions.

SATELLITE LOCK

8-164. During a stop-and-go survey, the rover station must maintain satellite lock on at least four satellites during the period of observation (the reference station must be observing at least the same four satellites). Loss of lock occurs when the receiver is unable to continuously record satellite signals or a transmitted satellite signal is disrupted and the receiver is not able to record it. If satellite lock is lost, the roving receiver must reobserve the last control station that was surveyed before loss of lock. The receiver operator must monitor the GPS receiver when performing a stop-and-go survey to ensure that loss of lock does not occur. Some manufacturers have incorporated an alarm into their receiver that warns the user when loss of lock occurs.

SITE CONSTRAINTS

8-165. Survey-site selection and the route between rover stations to be observed are critical. All sites must have a clear view (a vertical angle of 15� or greater) of the satellites. The route between rover stations must be clear of obstructions so that the satellite signal is not interrupted. Each unknown station to be occupied should be occupied for a minimum of 1 1/2 minutes. Stations should be occupied two or three times to provide redundancy between observations.

ANTENNA-SWAP CALIBRATION

8-166. Although antenna-swap calibration can be used to initialize a stop-and-go survey it also determine precise baseline and azimuth between two points. Both stations occupiedthe path must maintain an unobstructed view of horizon. minimum four satellites maintainable satellite lock are requiredhowevermore than preferred. One receiver/antenna is placed over known control point second distance 10 100 meters away from first receiver. receivers at each station collect data for about 2 4 minutes. Then locations swapped. moved unknown site while other site. again collected swapped back their original locations. This completes antenna-swap calibration. If lost procedure repeated.

ACCURACY

8-167. Accuracy of stop-and-go baseline measurements will usually exceed 1 part in 5,000; thus, third-order classification for horizontal control can be effectively, efficiently, and accurately established using this technique. For many projects, this order of horizontal accuracy will be more than adequate; however, field procedures should be designed to provide adequate redundancy for open-ended or spur points. Good satellite geometry and minimum multipath are also essential for performing acceptable stop-and-go surveys.

### KINEMATIC SURVEYING

8-168. Kinematic surveying using differential carrier-phase tracking is similar to stop-and-go and static surveying because it also requires two receivers to record observations simultaneously. Kinematic surveying is often referred to as dynamic surveying. As in stop-and-go surveying, the reference receiver remains fixed on a known control point while the roving receiver collects data on a constantly moving platform (for example, a vehicle, a vessel, an aircraft, or a backpack). Kinematic surveying techniques do not require the rover receiver to remain motionless over the unknown point. The observed data is postprocessed with a PC, and the relative vector/coordinate differences to the roving receiver are calculated.

PROCEDURES

8-169. A kinematic survey requires two single-frequency (L1) receivers. One receiver is set over a known point (reference station) and the other is used as a rover. Before the rover receiver can move, a period of static initialization or an antenna swap must be performed. This period of static initialization is dependent on the number of satellites visible. Once this is done, the rover receiver can move from point to point as long as satellite lock is maintained on at least four common satellites (common with the known reference station). If loss of lock occurs, a new period of static initialization must take place. It is important to follow the manufacturers' specifications when performing a kinematic survey.

DATA PROCESSING

data, the user must ensure that satellite lock was maintained on four or more satellites and that cycle slips were adequately resolved within the data recorded.8-170. Kinematic data-processing techniques are similar to those used in static surveying. When processing kinematic GPS /font>

ACCURACY

8-171. Kinematic-survey errors are correlated between observations received at the reference and rover receivers. Test results indicate kinematic surveys can produce results in centimeters. Test results from a full-kinematic GPS-S conducted by TEC personnel at White Sands Missile Range verified (under ideal test conditions) that kinematic GPS surveying could achieve centimeter-level accuracy for distances of up to 30 kilometers.

### PSEUDOKINEMATIC SURVEYING

8-172. Pseudokinematic surveying is similar to >kinematic surveying except that loss of lock is tolerated when the receiver is transported between occupation sites (the roving receiver can be turned off during movement, but this is not recommended). This feature provides the surveyor with a more favorable positioning technique since obstructions such as a bridge overpass, tall buildings, and overhanging vegetation are common. Loss of lock that may result due to these obstructions is more tolerable when pseudokinematic techniques are employed. Mission planning is essential for conducting a successful pseudokinematic survey. Especially critical is the determination of whether or not common satellite coverage will be present for the desired period of the survey.

PROCEDURES

8-173. Pseudokinematic surveying requires that one receiver must continuously occupy a known control station. A rover receiver occupies each unknown station for 5 minutes. About 1 hour after the initial station occupation, the same rover receiver must reoccupy each unknown station.

COMMON SATELLITE REQUIREMENTS

8-174. Pseudokinematic surveying requires that at least four of the same satellites be observed between the initial station occupations and the requisite reoccupation. For example, the rover receiver occupies Station A for the first 5 minutes and tracks satellites 6, 9, 11, 12, and 13; then 1 hour later, during the second occupation of Station A, the rover receiver tracks satellites 2, 6, 8, 9, and 19. Only satellites 6 and 9 are common to the two sets, so the data cannot be processed because four common satellites were not observed between the initial station occupation and the requisite reoccupation.

DATA PROCESSING AND ACCURACY

8-175. Pseudokinematic-survey satellite-data records and resultant baseline processing are similar to those performed for static GPS-Ss. Since pseudokinematic surveying requires each station to be occupied for 5 minutes and then reoccupied for 5 minutes about one hour later, it is not suitable when control stations are widely spaced and transportation between stations within the allotted time is impractical. Pseudokinematic-surveying achieves accuracies of a few centimeters.

### RAPID-STATIC SURVEYING

8-176. Rapid-static surveying is a combination of stop-and-go kinematic, pseudokinematic, and static surveying. The rover receiver spends only a short time on each station (loss of lock is allowed between stations) and accuracies are similar to static surveying. However, rapid-static surveying does not require reobservation of remote stations like pseudokinematic surveying. Rapid-static surveying requires the use of dual-frequency GPS receivers with either cross correlation or squaring or any other technique used to compensate for AS.

PROCEDURES

8-177. Rapid-static surveying requires that one receiver be placed over a known control point. A rover receiver occupies each unknown station for 5 to 20 minutes, depending on the number of satellites and their geometry. Because most receiver operations are manufacturer-specific, following the manufacturers' guidelines are important.

DATA PROCESSING AND ACCURACY

8-178. Data should be processed according to the manufacturers' specifications. Accuracies are similar to static surveys of 1 centimeter or less. Rapid-static surveying can be used for medium- to high-accuracy surveys up to 1:1,000,000.

### OTF/RTK SURVEYING

8-179. OTF/RTK surveying is similar to kinematic surveying because it requires two receivers that record observations simultaneously and allows the rover receiver to be moving. Unlike kinematic surveying, OTF/RTK surveying uses dual-frequency GPS observations and can handle loss of lock. OTF/RTK surveying uses the L2 frequency, and the GPS receiver must be capable of tracking the L2 frequency during AS. Two techniques that are used to obtain L2 during AS include squaring and cross correlation.

AMBIGUITY RESOLUTION

8-180. Successful ambiguity resolution is required for successful baseline formulations. The OTF/RTK technology allows the rover receiver to initialize and resolve baseline integers without a period of static initialization. If loss of lock occurs, reinitialization can be achieved while the remote is in motion. The integers can be resolved at the rover receiver within 10 to 30 seconds, depending on the distance from the reference station. OTF/RTK surveying requires that the L2 frequency be used in the ambiguity resolution. After the integers are resolved, only the L1 C/A-code is used to compute the positions.

PROCEDURES

8-181. OTF/RTK surveying requires dual-frequency GPS receivers. One of the GPS receivers is set over a known point and the other is placed on a moving or mobile platform. If the survey is performed in real time, a data link and a processor (external or internal) are needed. The data link is used to transfer the raw data from the reference station to the remote. If the OTF/RTK surveying is performed with an internal processor, follow the manufacturers' guidelines. If OTF/RTK surveying is performed with external processors, the PC at the reference station collects and formats the raw GPS data and sends it via a data link to the rover receiver. A notebook computer at the rover receiver is used to process the raw data from the reference and remote receivers to resolve the integers and obtain a position.

ACCURACY

8-182. OTF/RTK surveys are accurate to within 10 centimeters when the distance from the reference receiver to the rover receiver does not exceed 20 kilometers. The results of testing by the TEC produced accuracies of less than 10 centimeters.

SECTION VI - PRECISE-POSITIONING SURVEY-DATA PROCESSING

8-183. GPS-baseline solutions are usually generated through an iterative process. Using approximate values of the positions occupied and observation data, theoretical values for the observation period are developed. Observed values are compared to computed values and an improved set of positions occupied is obtained using least-squares-minimization procedures and equations that model potential error sources. This section discusses general postprocessing issues. Due to the increasing number and variety of software packages available, consult the manufacturer's guidelines when appropriate. Processing time is dependent on the accuracy required, the software, the PC, the data quality, and the amount of data. In general, high-accuracy solutions, crude computer software and hardware, low-quality data, and high volumes of data require longer processing times. Special care must be taken when attempting a baseline formulation with observations from different brands of GPS receivers. It is important to ensure that observables being used for the formulation of the baseline are of common format.

### PROCESSING TECHNIQUES

8-184. The capability to determine positions using the GPS is dependent on the ability to determine the range or distance of the satellite from the receiver located on the earth. There are two general techniques used to determine this range pseudoranging and carrier-beat-phase measurement.

PSEUDORANGING

8-185. The observable pseudorange is calculated from observations recorded during a GPS-S. The observable pseudorange is the difference between the time of signal transmission from the satellite (measured in the satellite time scale) and the time of signal arrival at the receiver antenna (measured in the receiver time scale). When the differences between the satellite and the receiver clocks are reconciled and applied to the pseudorange observations, the resulting values are corrected pseudorange values. The value found by multiplying this time difference by the speed of light is an approximation of the true range between the satellite and the receiver. The value can be determined if ionosphere and troposphere delays, ephemeris errors, measurement noise, and unmodeled influences are taken into account when pseudoranging calculations are performed. A pseudorange can be obtained from either the C/A-code or the more precise P-code.

CARRIER-BEAT-PHASE OBSERVATIONS

8-186. The observable carrier-beat phase is the phase of the signal remaining after the internal oscillated frequency that is generated in the receiver is differenced from an incoming carrier signal of the satellite. The observable carrier-beat phase can be calculated from the incoming signal or from observations recorded during a GPS-S. By differencing the signal over a period or epoch of time, the number of wavelengths that cycle through the receiver during any given specific duration of time, can be counted. The unknown cycle count passing through the receiver over a specific duration of time is known as the cycle ambiguity. There is one cycle-ambiguity value per satellite/receiver pair as long as the receiver maintains continuous phase lock during the observation period. The value found by measuring the number of cycles going through a receiver during a specific time, when given the definition of the transmitted signal in terms of cycles per second, can be used to develop a time measurement for transmission of the signal. The time of transmission of the signal can be multiplied by the speed of light to yield an approximation of the range between the satellite and the receiver. The biases for carrier-beat-phase measurements are the same as for pseudoranges, although a higher accuracy can be obtained using the carrier. A more exact range between the satellite and the receiver can be formulated when the biases are taken into account during derivation of the approximate range between the satellite and the receiver.

### BASELINE SOLUTION BY LINEAR COMBINATION

8-187. The accuracy achievable by pseudoranging and carrier-beat-phase measurement in both absolute- and relative-positioning surveys can be improved through processing that incorporates differencing of the mathematical models of the observables. Processing by differencing takes advantage of the correlation of error (for example, GPS-signal, satellite- ephemeris, receiver-clock, and atmospheric-propagation errors) between receivers, satellites, and epochs, or combinations thereof, to improve GPS processing. Through differencing, the effects of the errors that are common to the observations being processed are greatly reduced or eliminated. There are three broad processing techniques that incorporate differencing single, double, and triple. Differenced solutions generally proceed in the following order: differencing between receivers takes place first, between satellites second, and between epochs third.

SINGLE DIFFERENCING

8-188. There are three general single-differencing techniques between receivers, between satellites, and between epochs.

> > > - Between receivers. Single differencing the mathematical models for pseudorange (C/A- or P-code) carrier-phase observable measurements between receivers will eliminate or greatly reduce satellite-clock errors and a large amount of satellite-orbit and atmospheric delays.
> > > - Between satellites. Single differencing the mathematical models for pseudorange or carrier-phase observable measurements between satellites will eliminate receiver-clock errors. Single differencing between satellites can be done at each individual receiver during observations as a precursor to double differencing and to eliminate receiver-clock errors.
> > > - Between epochs. Single differencing the mathematical models between epochs takes advantage of the Doppler shift (apparent change in the frequency of the satellite signal by the relative motion of the transmitter and the receiver). Single differencing between epochs is generally done in an effort to eliminate cycle ambiguities. Three forms of single-differencing techniques between epochs are intermittently integrated Doppler (IID), consecutive Doppler counts (CDC), and continuously integrated Doppler (CID).

> > > > - IID. IID is a technique whereby the Doppler count is recorded for a small portion of the observation period. The Doppler count is reset to zero and, then at a later time, the Doppler count is restarted during the observation period.
> > > > - CDC. CDC is a technique whereby the Doppler count is recorded for a small portion of the observation period. The Doppler count is reset to zero and then restarted immediately.
> > > > - CID. CID is a technique whereby the Doppler count is recorded continuously throughout the observation period.

DOUBLE DIFFERENCING

8-189. Double differencing is a differencing of two single differences. Double differencing eliminates clock errors. There are two general double-differencing techniques receiver-time and receiver-satellite.

> > > - Receiver time. This technique requires the use of a change from one epoch to the next in the between-receiver single differences for the same satellite. This technique eliminates satellite-dependent integer-cycle ambiguities and simplifies the editing of cycle slips.
> > > - Receiver satellite. There are two techniques that can be used to compute a receiver-satellite double difference. One technique involves using two between-receiver single differences and a pair of receivers that record different satellite observations between two satellites. The second technique involves using two between-satellite single differences and a pair of satellites, but different receivers, and then differences the satellite observations between the two receivers.

TRIPLE DIFFERENCING

8-190. The triple-differencing technique is called receiver-satellite time. All errors eliminated during single and double differencing are also eliminated during triple differencing. When used in conjunction with carrier-beat-phase measurements, triple differencing eliminates initial cycle ambiguity. During triple differencing, the data is automatically edited by the software to delete any data that is ignored during the triple-difference solution. This is advantageous because of the reduction in the editing of data required; however, degradation of the solution may occur if too much of the data are eliminated.

### BASELINE SOLUTION BY CYCLE-AMBIGUITY RECOVERY

8-191. The resultant solution (baseline vector) that is produced from carrier-beat-phase observations when differencing resolves cycle ambiguity is called a "fixed" solution. The exact cycle ambiguity does not need to be known to produce a solution; if a range of cycle ambiguities is known, then a "float" solution can be formulated from the range of cycle ambiguities. It is desirable to formulate a fixed solution. However, when the cycle ambiguities cannot be resolved, which occurs when a baseline is between 20 to 65 kilometers, a float solution may actually be the best solution. The fixed solution may be unable to determine the correct set of integers (fix the integers) required for a solution. Double-difference fixed techniques can be effective for positional solutions over short baselines (less than 20 kilometers).Double-difference float techniques normally can be effective for positional solutions of medium-length lines (20 to 65 kilometers).

### DATA PROCESSING AND VERIFICATION

8-192. Baselines should be processed daily in the field to identify any problems that may exist. Once baselines are processed, each baseline output file should be reviewed. The procedures used in baseline processing are manufacturer-specific. Certain computational items within the baseline output are common among manufacturers and may be used to evaluate the adequacy of the baseline observation in the field. The triple-difference float solution is normally listed. The geodetic azimuth and the distance between the two stations are also listed. The RMS is a quality factor that helps identify which vector solution (triple, float, or fixed) to use in the adjustment. The RMS is dependent on the baseline length and the length of baseline observation. Table 8-6 provides guidelines for determining the baseline quality. If the fixed solution meets the criteria in this table, the fixed vector should be used in the test. If the vector does not fit into the network after adjustment, try using the float vector in the adjustments or check to make sure that the stations were occupied correctly.

Table 8-6. Postprocessing Criteria

Distance Between Receivers (km) | RMS Criteria Formulation (d = Distance Between Receivers) | Formulated RMS Range (Cycles) | Formulated RMS Range (m)
--- | --- | --- | ---
0 -10 | <[0.02 + (0.0040 � d)] | 0.020 - 0.060 | 0.004 - 0.012
10 - 20 | <[0.03 + (0.0030 � d)] | 0.060 - 0.090 | 0.012 - 0.018
<20 - 30 | < [0.04 + (0.0025 � d)] | 0.090 - 0.115 | 0.018 - 0.023
30 - 40 | < [0.04 + (0.0025 � d)] | 0.115 - 0.140 | 0.023 - 0.027
40 - 60 | < [0.08 + (0.0015 � d)] | 0.140 - 0.170 | 0.027 - 0.032
60 - 100 | < 0.17 | 0.170 | 0.032
>100 | >< 0.20 | 0.200 | 0.040
NOTES: 1. These are general postprocessing criteria that may be superseded by GPS receiver/software manufacturers' guidelines; consult those guidelines when appropriate. 2. For lines longer than 50 kilometers, dual-frequency GPS receivers are recommended to meet these criteria.

8-193. The first step in processing the data is to transfer the observation data to a storage device for archiving and/or further processing. The types of storage devices include a hard disc, a 3.5-inch diskette, or a magnetic tape.

8-194. Once observation data have been downloaded, preprocessing of the data can be completed. Preprocessing consists of smoothing and editing the data and ephemeris. Smoothing and editing ensures data quantity and quality. Smoothing and editing includes determining and eliminating cycle slips; editing gaps in information; and differencing between receivers, satellites, and epochs.

8-195. Retrieval of postprocessed ephemerides may be required depending on the type of receiver used for the survey. Codeless receivers require a postprocessed ephemerides file. This file can be recorded by another GPS receiver concurrent with the survey or by postprocessed ephemerides provided by an ephemeris service. Code receivers do not require postprocessed ephemerides since they automatically record the broadcast ephemerides during the survey.

8-196. Generally, postprocessing software will provide three solutions a triple difference, a double-difference fixed solution, and a double-difference float solution. In addition to RDOP as a measurement of the quality of data reduction, two methods that can be used to gauge the success of an observation session (based on data processing done by a differencing process) are RMS and repeatability.

> > > - RMS. RMS is a measurement (in units of cycles or meters) of the quality of the observation data collected during a point in time. RMS is dependent on the line length, the signal strength, the ionosphere, the troposphere, and multipath effects. In general, the longer the line and the more signal interference by other electronic gear, the ionosphere, the troposphere, and multipath effects, the higher the RMS will be. A good RMS factor (between 0.01 and 0.2 cycles) may not always indicate good results but should be considered. RMS can generally be used to judge the quality of the data used in postprocessing and the quality of the postprocessed baseline vector.
> > > - Repeatability. Redundant lines should agree to the level of accuracy that the GPS is capable of measuring. For example, if the GPS can measure a 10-kilometer baseline to 1 centimeter �1 ppm, the expected ratio of misclosure would be as follows:

> > > > = =
> > > > Repeated baselines should be near the corresponding ratio.

8-197. A baseline solution typically includes the following information:

> > > - The file name.
> > > - The type of solution (single-, double-, or triple-difference).
> > > - The satellites' availability during the survey for each station occupied.
> > > - The ephemeris file used for the solution.
> > > - The type of satellite selection (manual or automatic).
> > > - The elevation mask.
> > > - The minimum number of satellites used.
> > > - Meteorological data (for example, pressure, temperature, or humidity).
> > > - The session date and time.
> > > - The data-logging start and stop time.
> > > - >Station information (for example, location [latitude, longitude, and height], the receiver's serial number, and the antenna's serial number and height).
> > > - >The RMS.
> > > - The solution files (X, Y, and Z between stations, the slope distance between stations, latitude and longitude between stations, the horizontal distance between stations, and the height differences).
> > > - The epoch intervals.
> > > - The number of epochs.

8-198. Sample static-baseline formulations are shown in Figure 8-7. The baseline formulations compensate for the height differences between antennas.

Figure 8-7. Sample Static-Baseline Formulations

### LOOP-CLOSURE CHECKS

8-199. Postprocessing criteria are aimed at an evaluation of a single baseline. To verify the adequacy of a group of connected baselines, a loop closure must be performed on the established baselines. When GPS-baseline traverses or loops are formed, their linear (internal) closure should be determined in the field. If the job requires less than third-order accuracy (1:10,000 or 1:5,000) and the internal loop/traverse closures are very small, a formal (external) adjustment may not be warranted.

LOOP-CLOSURE SOFTWARE

8-200. The internal closure determines the consistency of the GPS measurements. Internal closures are applicable for loop traverses and GPS networks. It is required that one baseline in the loop be independent. An independent baseline is observed during a different session or different day. Many of the better postprocessing software packages come with a loop-closure program. Refer to the user's manual for the particulars of the loop-closure program.

GENERAL LOOP-CLOSURE COMPUTATION

8-201. If the postprocessing software does not contain a loop-closure program, the user can perform a loop-closure computation as described in the following steps.

> > > Step 1. List the X, Y, Z, and the distance components for all baselines used in the loop closure.

> > > Step 2. Sum the X, Y, Z, and the distance components for all baselines used in the loop closure.

> > > Step 3. Add the square of each of the summations together and then take the square root of this sum. This resultant value is the misclosure vector for the loop.

> > > Step 4. Calculate the loop-misclosure ratio as follows:

> > > where
> > > m = misclosure vector for the loop
> > > L = total-loop distance (perimeter distance)

8-202. The resultant value can be expressed as 1:loop-misclosure ratio. All units for the expressions are stated in terms of the units used in the baseline formulations (for example, meters, feet, or millimeters).

EXTERNAL CLOSURES

8-203. External closures are computed in a manner similar to internal loops. External closures provide information on how well the GPS measurements conform to the local coordinate system. Before the closure of each traverse is computed, the latitude, the longitude, and the ellipsoid height must be converted to geocentric coordinates (X, Y, and Z). If the ellipsoid height is not known, geoid-modeling software can be used with the orthometric height to get an approximate ellipsoid height. The external closure aids in determining the quality of the known control and how well the GPS measurements conform to the local network. If the control stations are not of equal precision, the external closures will usually reflect the lower-order station. If the internal closure meets the requirements of the job but the external closure is poor, the known control is probably deficient and an additional known control point should be included in the system.

### DATA ARCHIVAL

8-204. The raw data is the data recorded during the observation period. Raw data should be stored on an appropriate medium (such as a floppy disk, a portable hard drive, or a magnetic tape). The raw data and the hard copy of the baseline reduction (resultant baseline formulations) should be stored at the discretion of each unit's command.

SECTION VII - PRECISE-POSITIONING SURVEY ADJUSTMENTS

8-205. Differential carrier-phase GPS-S observations are adjusted the same as conventional-survey observations. Each 3D GPS-baseline vector is treated as a separate distance observation and adjusted as part of a network. A variety of methods may be used to adjust the observed GPS baselines to fit existing control. Since GPS-S networks often contain redundant observations, they are usually adjusted by some type of a rigorous least-squares-minimization method. This section describes some of the methods used to perform horizontal GPS-S adjustments and provides guidance on evaluating the adequacy and accuracy of the adjustment results.

### GPS ERROR-MEASUREMENT STATISTICAL TERMS

8-206. To understand the adjustment results of a GPS-S, some simple statistical terms are defined

> > > - Accuracy. Accuracy is how close a measurement or a group of measurements are in relation to a true or known value.
> > > - Precision. Precision is how close a group or sample of measurements are to each other. For example, a low standard deviation indicates high precision. A survey or group of measurements can have a high precision but a low accuracy (for example, measurements are close together but not close to the known or true value).
> > > - Standard deviation. The standard deviation is a range of how close the measured values are from the arithmetic average. A low standard deviation indicates that the observations or measurements are close together.

### ADJUSTMENT CONSIDERATIONS

8-207. Although vertical elevations are necessarily carried through the baseline reduction and adjustment process, the relative accuracy of these elevations is normally inadequate for engineering and construction purposes. Special procedures and constraints are necessary to determine approximate orthometric elevations from relative GPS observations.

8-208. The baseline-reduction process provides the raw relative-position coordinates that are used in a 3D GPS-network adjustment. In addition, and depending on the software, each reduced baseline will contain various orientation parameters, covariance matrices, and cofactor and/or correlation statistics that may be used in weighting the final network adjustment. Most least-squares adjustments use the accuracy or correlation statistics from the baseline reduction; however, other weighting methods may be used in a least-squares or approximate adjustment.

8-209. The adjustment procedure employed (and the time devoted to it) must be commensurate with the project's accuracy requirements. Care must be taken to prevent the adjustment process from becoming a project in itself. There is no specific requirement for performing a rigorous least-squares adjustment on topographic surveys, whether conventional, GPS, or mixed observations. Traditional approximate-adjustment methods may be used in lieu of the least-squares method and will provide comparable, practical accuracy results.

8-210. Commercial software packages designed for high-order geodetic-densification surveys often contain a degree of statistical sophistication that is unnecessary for engineering survey-control densification (for example, second-order or less). The distinction between geodetic surveying and engineering surveying must be fully considered when performing GPS-S adjustments and analyzing the results.

8-211. Connections and adjustments to existing control networks, such as the NGRS, must not become independent projects. It is far more important to establish dense and accurate local-project control than to consume resources tying into first-order NGRS points that are miles from the project. Engineering, artillery, construction, and property/boundary referencing requires consistent local control with high relative accuracy. Accurate connections/references to distant geodetic datums are of secondary importance (exceptions are projects in support of military aviation operations). GPS-surveying technology has provided a cost-effective means of tying previously established, poorly connected projects to the NGRS and simultaneously transforming the project to the newly defined NAD 83. In adjusting these connections, do not distort or warp long-established project reference points.

### SURVEY ACCURACY

8-212. The accuracy of a survey (whether performed using conventional or GPS methods) is a measure of the difference between observed and true values (such as, coordinates, distance, or angle). Since the true values are rarely known, only estimates of survey accuracy can be made. These estimates may be based on the internal observation closures (such as on a loop traverse) or connections with previously surveyed points assumed to have some degree of reliability.

8-213. GPS internal accuracies are typically far superior to most previous control networks (including the NAD-83 NGRS). Therefore, determining the accuracy of a GPS-S based on misclosures with external points is not always valid unless statistical-accuracy estimates (for example, station variance-covariance matrices or distance/azimuth relative accuracy estimates) from the external network's original adjustments are incorporated into the closure analysis for a new GPS-S.

8-214. Most survey specifications and standards classify accuracy as a function of the resultant relative accuracy between two usually adjacent points in a network. This resultant relative accuracy is estimated from the statistics in an adjustment and is defined by the size of a 2D or 3D relative error ellipse formed between the two points. Relative distance-, azimuth-, or elevation-accuracy specifications and classifications are derived from this model and are expressed either in absolute values (for example, �1.2 centimeters or �3.5 inches) or as ratios of the propagated standard errors to the overall length (for example, 1:20,000).

INTERNAL ACCURACY

8-215. A loop traverse that originates and ends from a single point will have a misclosure when observations (for example, EDM traverse angles/distances or GPS-baseline vectors) are computed forward around the loop and back to the starting point. The forward-computed misclosure provides an estimate of the relative or internal accuracy of the observations in the traverse loop, or more directly, the internal precision of the survey. This is perhaps the simplest method of evaluating the adequacy of a survey. These point misclosures (usually expressed as ratios) are not the same as relative distance accuracies).

8-216. Internal-accuracy estimates made relative to a single fixed point are obtained when free, unconstrained, or minimally constrained adjustments are performed. In the case of a single loop, no redundant observations (or alternate loops) back to the fixed point are available. When a series of GPS-baseline loops (or networks) are observed, then the various paths back to the single fixed point provide multiple position computations. This allows for a statistical analysis of the internal accuracy of not only the position closure but also the relative accuracies of the individual points in the network (including relative distance- and azimuth-accuracy estimates between these points). The magnitude of these relative internal-accuracy estimates (on a free adjustment) determines the adequacy of the control for subsequent design, construction, and mapping work.

8-217. Loop traverses are not recommended for most conventional surveys due to potential systematic distance or orientation errors, which can be carried through the network undetected. FGCS classification standards for geodetic surveys do not allow traverses to start and terminate at a single point. Such techniques are unacceptable for incorporation into the NGRS network. However, due to many factors (primarily economic), loop traverses or open-ended spur lines are commonly employed in densifying project control for engineering and construction projects. Since such control is not intended for inclusion in the NGRS and usually covers limited project ranges, these practices have been acceptable for GPS-Ss that are performed in support of similar engineering and construction activities.

EXTERNAL ACCURACY

8-218. The coordinates (and reference orientation) of a single, fixed starting point will also have some degree of accuracy relative to the network in which it is located (such as the NGRS if it was established relative to the system/datum). This external accuracy (or inaccuracy) is carried forward in the traverse loop or network; however, any such external variance (if small) is generally not critical to engineering and construction projects. When a survey is conducted relative to two or more points on an existing reference network (such as project control or the NGRS), misclosures with these fixed control points provide an estimate of the absolute accuracy of the survey. This analysis is usually obtained from a final adjustment (usually a fully constrained least-squares-minimization method) or by another recognized traverse-adjustment method (for example, a transit or a compass).

8-219. This absolute accuracy estimate assumes that the fixed (existing) control is superior to the survey being performed and that any position misclosures at connecting points are due to internal observational errors and not the existing control. This has always been a long-established and practical assumption and has considerable legal basis in property/boundary surveying. New work is rigidly adjusted to existing control regardless of known or unknown deficiencies in the fixed network.

8-220. Since the relative positional accuracies of points on the NGRS are known from the NAD-83 readjustment and GPS-baseline-vector accuracy estimates are obtained from individual reductions, variations in misclosures in GPS-Ss are not always due totally to errors in the GPS work. Forcing a GPS traverse/network to rigidly fit the existing (fixed) network usually results in a degradation of the internal accuracy of the GPS-S, as compared with a free or unconstrained adjustment.

### INTERNAL VERSUS EXTERNAL ACCURACY

8-221. Conventional geodetic surveying is largely concerned with absolute accuracy or the best fit of intermediate surveys between points on a national control network, such as the NGRS. Alternatively, in engineering and construction surveying and to a major extent in relative- or local-boundary surveying, accuracies are more critical to the project at hand. Thus, the absolute NAD-27 or NAD-83 coordinates (in latitude and longitude) relative to the NGRS datum reference are of less importance; however, accurate relative coordinates for a given project are critical to design and construction.

8-222. For example, when establishing basic mapping and construction-layout control for a military installation, developing a dense and accurate internal relative-control network is far more important than considering the values of the coordinates relative to the NGRS. Surveys performed with GPS-S, and the final adjustment thereof, should be configured/designed to establish accurate relative (local) project control. This is of secondary importance in connection with NGRS networks.

8-223. Although reference connections with the NGRS are desirable and recommended and should be made where feasible and practicable, it is critical that such connections (and subsequent adjustments thereto) do not distort the internal accuracy of intermediate points from which design, construction, or project boundaries are referenced. Connections and adjustments to distant networks (for example, NGRS) can result in mixed datums within a project area, especially if not all existing project control has been tied in. This can lead to errors and contract disputes during both design and construction. On existing projects with long-established reference control, connections and adjustments to outside reference datums/networks should be performed with caution. The impacts on legal-property and project-alignment definitions must also be considered before such connections.

8-224. On newly authorized projects or on projects where existing project control has been largely destroyed, reconnection with the NGRS is highly recommended. This will ensure that future work is supported by a reliable and consistent basic network, while minimizing errors associated with mixed datums.

### ADJUSTMENTS

8-225. GPS-Ss are usually adjusted and analyzed relative to their internal consistency and external fit with existing control. The internal-consistency adjustment (for example, free or minimally constrained) is important from a mission compliance standpoint. The final (or constrained) adjustment fits the GPS-S to the existing network. This is not always easily accomplished since existing networks often have lower relative accuracies than the GPS observations being fit. The evaluation of a survey's adequacy should not be based solely on the results of a constrained adjustment.

INTERNAL ADJUSTMENT

8-226. An internal (or geometric) adjustment (also referred to as a free adjustment) is made to determine how well the baseline observations close internally or fit within themselves. Other EDM distances or angles may also be included in the adjustment. This adjustment provides a measure of the internal precision of the survey.

8-227. In a simplified example, a conventional EDM traverse that is looped back to the starting point will misclose in both azimuth and position. Conventional approximate-adjustment methods will typically assess and proportionately adjust the azimuth misclosure (usually evenly per station), recompute the traverse with the adjusted azimuths, and obtain a position misclosure. This position misclosure (in X and Y) is then distributed among all the points on the traverse using various weighting methods (for example, distance, latitudes, or departures). Final-adjusted azimuths and distances are then computed from grid inverses between the adjusted points. The adequacy/accuracy of such a traverse is evaluated based on the azimuth misclosure and the position misclosure after the azimuth adjustment (usually expressed as a ratio to the overall length of the traverse).

8-228. A least-squares adjustment of the same conventional loop traverse will end up adjusting the points similarly to the approximate methods traditionally employed. The only difference is that a least-squares adjustment simultaneously adjusts both the observed angles (or directions) and the distance measurements. A least-squares adjustment also allows variable weighting to be set for individual angle/distance observations, which is a somewhat more complex process when approximate adjustments are performed. In addition, a least-squares adjustment will yield more definitive statistical results of the internal accuracies of each observation and/or point, rather than just the final closure. This includes estimates of the accuracies of individual station coordinates, relative azimuths, and relative distances.

8-229. A series of GPS baselines forming a loop off a single point can be adjusted and assessed similarly to a conventional-EDM traverse loop described above. The baseline-vector components may be computed (accumulated) around the loop with a resultant 3D misclosure back at the starting point. These misclosures (in X, Y, and Z) may be adjusted using either approximate or least-squares methods. The method by which the misclosure is distributed among the intermediate points in the traverse is a function of the weighting adjustment.

8-230. In the case of a simple EDM traverse adjustment, the observed distances (or position corrections) are weighted as a function of the segment length and the overall traverse length or the overall sum of the latitudes/departures (transit rule). Two-dimensional EDM distance observations are not dependent on their direction (a distance's X and Y components are uncorrelated).

8-231. GPS-baseline-vector components (in X, Y, and Z) are correlated due to the geometry of the satellite solution (the direction of the baseline vector is significant). Since satellite geometry is continuously changing, remeasured baselines will have different correlations between the vector components. Such data are passed down from the baseline-reduction software for use in the adjustment.

8-232. The magnitude of the misclosure of the GPS-baseline vectors at the initial point provides an estimate of the internal precision or geometric consistency of the loop (survey). When this misclosure is divided by the overall length of the baselines, a relative internal-accuracy estimate results. This misclosure ratio should not be less than the relative distance accuracy intended for the survey. For example, if the position misclosure of a GPS loop is 0.08 meter and the length of the loop is 8,000 meters, then the loop closure is 0.08 divided by 8,000, which equals 1:100,000.

8-233. When an adjustment is performed, the individual corrections/adjustments made to each baseline (so-called residual errors) provide an accuracy assessment for each baseline segment. A least-squares adjustment can also provide relative distance-accuracy estimates for each line, based on the standard-error propagation between the adjusted points. This relative distance-accuracy estimate is most critical in engineering and construction work and represents the primary basis for assessing the acceptability of a survey.

EXTERNAL ADJUSTMENT

8-234. An external (or fully-constrained) adjustment is the process used to best fit the survey observations to the established reference system. The internal, free adjustment provides adjusted positions relative to a single, often arbitrary, fixed point. Most conventional or GPS-Ss are connected between existing stations on some predefined reference network or datum. These fixed stations may be existing project-control points (on NAD 27) or stations on the NGRS (NAD 83). In OCONUS locales, other local or regional reference systems may be used.

8-235. A simple, conventional-EDM traverse between two fixed stations best illustrates the process by which comparable GPS-baseline vectors are adjusted. As with the loop traverse, the misclosure in azimuth and position between the two fixed points may be adjusted by any type of approximate or least-squares-adjustment method. Unlike a loop traverse, however, the azimuth and position misclosures are not wholly dependent on the internal errors in the traverse the fixed points and their azimuth references are not absolute but contain relative inaccuracies with respect to one another.

8-236. A GPS-S between the same two fixed points also contains a 3D position misclosure. Due to positional uncertainties in the two fixed points, this misclosure may (and usually does) far exceed the internal accuracy of the raw GPS observations. As with a conventional-EDM traverse, the 3D misclosures may be approximately adjusted by proportionately distributing them over the intermediate points. A least-squares adjustment will also accomplish the same thing.

8-237. For example, if a GPS-S is looped back to the initial point, the free-adjustment misclosure at the initial point may be compared with the apparent-position misclosure at the other fixed point. A free-adjustment loop misclosure is 1:100,000, whereas the misclosure relative to the two network-control points is only 1:5,000. Thus, the relative internal accuracy of a GPS-S is about 1:100,000 (based on the misclosure). If the GPS-baseline observations are constrained to fit the existing control, the 0.6-meter external misclosure must be distributed among the individual baselines to force a fit between the two end points.

8-238. After a constrained adjustment, the absolute-position misclosure of 0.6 meter causes the relative distance accuracies between individual points to degrade. They will be somewhat better than 1:5,000 but far less than 1:10,000. The statistical results from a constrained least-squares adjustment will provide estimates of the relative accuracies between individual points on the traverse.

8-239. This example illustrates the advantages of measuring the baseline between fixed network points when performing GPS-Ss, especially when weak control is suspected. Also illustrated is the need for making additional ties to the existing network. In this example, one of the two fixed points was poorly controlled when it was originally established or the two points may have been established from independent networks (for example, were never connected). A third or even fourth fixed point would be beneficial in resolving such a case.

8-240. If the intent of the survey in this example was to establish 1:20,000 relative-accuracy control, connecting between these two points would not provide that accuracy, given the amount of adjustment that must be applied to force a fit. For example, if one of the individual baseline vectors was measured at 600 meters and the constrained adjustment applied a 0.09-meter correction in this sector, the relative accuracy of this segment would be roughly 1:6,666. This distortion is not acceptable for subsequent design/construction work.

8-241. Most GPS-S networks are more complex than a simple traverse. They may consist of multiple loops and may connect with any number of control points on the existing network. In addition, conventional EDMs and differential-leveling and angle measurements may be included with the GPS baselines, resulting in a complex network with many adjustment conditions.

PARTIALLY CONSTRAINED ADJUSTMENTS

8-242. In the previous example of a simple GPS traverse, holding the two network points rigidly caused an adverse degradation in the GPS-S because of the differences between the free (loop) adjustment and the fully constrained adjustment. Another alternative is to perform a partially constrained adjustment of the network. In a partially constrained adjustment, the two network points are not rigidly fixed but are only partially fixed in position. Partially constrained adjustments are not practicable using approximate-adjustment methods.

>8-243. For example, if the relative distance accuracy between the two fixed points is about 1:10,000, it can be equated to a positional uncertainty between these points. Depending on the type and capabilities of the least-squares-adjustment software, the higher-accuracy GPS-baseline observations can be best fit between the two end points, such that the end points of the GPS network are not rigidly constrained to the original two control points but end up falling near them.

8-244. Adjustment software allows relative weighting of the fixed points to provide a partially constrained adjustment. Any number of fixed points can be connected, and these points may be given partial constraints in the adjustment. Performing partially constrained adjustments (as opposed to fully constrained adjustments) takes advantage of the inherent higher-accuracy GPS data relative to the existing network control. Less warping of the GPS data (due to poor existing networks) will occur.

8-245. A partial constraint also lessens the need for performing numerous trial-and-error constrained adjustments in attempts to locate poor external control points causing high residuals. Fewer ties to the existing network are needed if the purpose of such ties is to find a best fit on a fully constrained adjustment.

8-246. When connections are made to NAD 83, relative accuracy estimates of NGRS stations can be obtained from the NGS. Depending on the type of adjustment software, these partial constraints may be in the form of variance-covariance matrices, error ellipses, or circular accuracy estimates.

RIGOROUS LEAST-SQUARES ADJUSTMENT

8-247. Adjustment of GPS networks on PCs is typically a trail-and-error process for both the free and the constrained adjustments. When a least-squares adjustment is performed on a network of GPS observations, the adjustment software will provide 2D- or 3D-coordinate accuracy estimates, variance-covariance matrix data for the adjusted coordinates, and related error-ellipse data. Most software programs provide relative accuracy estimates (length and azimuth) between points. Analyzing these various statistics is not easy, and they are also easily misinterpreted. Arbitrary rejection and readjustment to obtain a best fit must be avoided. The original data-reject criteria must be established and justified in a final report.

8-248. When a series of loops are formed relative to a fixed point or off another loop, different redundant conditions are formed (this is comparable to loops formed in conventional-differential leveling networks). These different loops allow forward baseline-vector position computations to be made over different paths. From the different routes (loops) formed, different positional closures at a single fixed point results. These variances in position misclosures from the different routes provide additional data for assessing the internal consistency of the network, in addition to checking for blunders in the individual baselines. The number of different paths, or conditions, is partially related to the number of degrees of freedom in the network.

8-249. Multiple baseline observations provide additional redundancy or strength to a line or network since they are observed at two distinct times of varying satellite geometry and conditions. The amount of redundancy required is a function of the accuracy requirements of the survey. Performing a free adjustment on a complex network containing many redundancies is best performed using a least-squares method. Approximate-adjustment methods are difficult to evaluate when complex interweaving networks are involved.

8-250. Baseline-reduction vector-component error statistics are usually carried down into a least-squares adjustment; however, their use is not mandatory for lower-order engineering surveys. GPS-network least-squares adjustments can be performed without all the covariance and correlation statistics from the baseline reduction.

8-251. In practice, any station on the network can be held fixed for all three coordinates, along with the orientation of the three axes and a network-scale parameter. Usually one of the higher-order points on the existing network is used.

8-252. Least-squares-adjustment software will output various statistics from the free adjustment to assist in detecting blunders and residual outliers in the free adjustment. Most commercial packages will display the normalized residual for each observation (for example, GPS, EDM, angle, or elevation), which is useful in detecting and rejecting residual outliers. The variance of unit weight is also important in evaluating the overall adequacy of the observed network. Other statistics (such as chi-square, confidence levels, or histograms) are usually not significant for lower-order engineering projects and become totally insignificant if the user is not well versed in statistics and adjustment theory. The use of these statistics to reject data (or to report the results of an adjustment) without fully understanding their derivation and source within the network adjustment is not advised.

8-253. Relative positional- and distance-accuracy estimates resulting from a free adjustment of a GPS network are usually excellent in comparison to conventional surveying methods. Loop misclosures and relative distance accuracies between points commonly exceed 1:100,000. Relative distance-accuracy estimates between points in a network are determined by error propagation in the relative positional standard errors at each end of the tie. Relative accuracy estimates may be derived for resultant distances or azimuths between the points. The relative distance-accuracy estimates are those typically employed to assess the free and constrained accuracy classifications, expressed as a ratio (such as 1:80,000). Since each point in the network has its particular position variances, the relative distance accuracy propagated between any two points will also vary throughout the network.

8-254. The minimum value (or the largest ratio) will govern the relative accuracy of the overall project. This minimum value (from a free adjustment) is compared with the intended relative accuracy classification of the project to evaluate compliance. However, relative distance-accuracy estimates should not be rigidly evaluated over short lines (less than 500 meters).

8-255. Depending on the size and complexity of the project, large variances in the propagated relative distance accuracies can result. When a constrained adjustment is performed, the adequacy of the external fixed stations will have a major impact on the resultant and propagated distance accuracies, especially when connections are made to weak control systems. Properly weighted, partially constrained adjustments will usually improve the propagated distance accuracies.

8-256. The primary criteria for assessing the adequacy of a particular GPS-S is the relative distance-accuracy results from a minimally constrained free adjustment, not a fully constrained adjustment. This is due to the difficulty in assessing the adequacy of the surrounding network. If the propagated relative accuracies fall below the specified level, then reobservation is warranted.

8-257. If the relative distance accuracies significantly degrade the constrained adjustment (due to the inadequacy of the surrounding network), any additional connections to the network would represent a change in contract scope. A large variance of unit weight usually results in such cases.

8-258. If only approximate adjustments are performed, then the relative distance accuracies may be estimated as a function of the loop or position misclosure or the residual corrections to each observed length. For example, if a particular loop or line miscloses by 1:100,000, then individual-baseline relative accuracies can be assumed to be adequate if only a 1:20,000 survey is required.

8-259. Most adjustment software will output the residual corrections to each observed baseline-vector component. These residuals indicate the amount that each segment was corrected in the adjustment. A least-squares adjustment minimizes the sum of the squares of these baseline residual corrections.

8-260. Commercial least-squares-adjustment software is available, which will adjust GPS networks using standard PCs. An example of an adjustment statistics summary from the software package used by Army topographic surveyors is shown in Figure 8-8.

Figure 8-8. Continuation of an Adjustment Statistics Summary Example

8-261. Relative GPS-baseline standard errors can be obtained from the baseline-reduction output and in some software programs can be directly input into the adjustment. These standard errors, along with their correlations, are given for each vector component (X, Y, and Z). They are converted to relative weights in the adjustment. The following typical input (a priori) weighting is commonly used:

> > > - Fixed. �3 millimeters (latitude) �5 millimeters (longitude) + 1 ppm �10 millimeters (height) + 1 ppm.
> > > - Float. �6 millimeters (latitude) �10 millimeters (longitude) + 2 ppm �10 millimeters (height) + 2 ppm.

These optimum standard errors have been found to be reasonable in standard work where extremely long baselines are not involved. The use of these optimum values is recommended for the first adjustment iteration.

8-262. The adequacy of the initial network weighting described above is indicated by the variance of unit weight, which equals the square of the standard error of unit weight. The variance of unit weight should range between 0.5 and 1.5 (or the standard error of unit weight should range between 0.7 and 1.2) with an optimum value of 1, signifying the realistic weighting of the GPS-input observations. A large unit variance (for example, 5) indicates that the initial GPS standard errors were too optimistic (low). A low unit variance (for example, 0.1) indicates that the results from the adjustment were better than the assumed GPS-baseline precisions. This unit-variance test, however, is generally valid only when a statistically significant number of observations are involved. This is a function of the number of degrees of freedom shown on the adjustment. To calculate the adequacy of a unit weight, a test (such as chi-square) is performed. Failure of such a test indicates that the variance factor may not be valid.

8-263. The input standard errors can easily be juggled to obtain a variance of unit weight near 1. This trial-and-error technique is generally not a good practice. If the input weights are changed, they should not be modified beyond reasonable levels (for example, do not input a GPS standard error of �50 + 50 ppm to get a good unit variance). If input standard errors are modified, these modifications should be the same for all lines, not just selected ones. Any such modifications of a priori standard errors must be justified in the adjustment report.

8-264. Changing the magnitude of the input standard errors or weights will not change the adjusted position or residual results in a free adjustment, provided all weight changes are made equally. Although the reference variance will change, the resultant precisions (relative line accuracies) will not change (this is not true in a constrained adjustment). Therefore, the internal accuracy of a survey can be assessed based on the free-adjustment line accuracies regardless of the initial weighting or variance of unit weight.

8-265. The magnitude of the residual corrections may be assessed by looking for blunders or outliers; however, this assessment should be performed in conjunction with the related, normalized- or standardized-residual statistic. This statistic is obtained by multiplying the residual by the square root of the input weight (the inverse of the square of the standard error). If the observations are properly weighted, the normalized residuals should be around 1. Most adjustment software will flag normalized residuals that exceed selected statistical outlier tests. Such residuals are candidates for rejection. As a rule of thumb, reject criterion should be set at three times the standard error of unit weight, provided that the standard error of unit weight is within the acceptable range given above. All rejected GPS observations must be justified in the adjustment report, and the test used to remove the observation from the file must be clearly described.

8-266. Error ellipses, or 3D error ellipsoids, generated from the adjustment variance-covariance matrices for each adjusted point are also useful in depicting the relative positional accuracy. The scale of the ellipse may be varied as a result of the 2-deviation function. A 2.45 sigma (or 95 percent) probability ellipse is usually selected for output. The size of the error-ellipse's relative distance or the azimuth-accuracy estimate between two adjacent points is a direct function of the size of these positional ellipses.

8-267. The relative distance accuracy is used to evaluate the acceptability of a survey. This is done using a free adjustment. The output is shown as a ratio or in ppm. The resultant ratios must be divided by 2 to equate them to FGCS 95 percent criteria. Further details on these statistical evaluations are beyond the scope of this manual.

8-268. The following is a summary of a network-adjustment sequence (recommended by the NGS) for surveys that are connected with the NGRS:

> > > - A minimally constrained 3D adjustment is performed initially as a tool to validate the data, to check for blunders and systematic errors, and to look at the internal consistency of the network.
> > > - A horizontally constrained 3D adjustment is performed by holding all previously published horizontal-control points fixed and using one height constraint. All previous observations are considered in the adjustment.
> > > - A fully constrained vertical adjustment is performed to determine the orthometric heights. All previously published BM elevations are held fixed along with one horizontal position in a 3D adjustment. Geoid heights are predicted using the latest model.
> > > - A final free adjustment is performed and the relative accuracy estimates are computed.

### EVALUATION OF ADJUSTMENT RESULTS

8-269. A survey shall be classified based on its horizontal-point closure ratio or its vertical-elevation-difference closure standard (Table 8-7).

Table 8-7. Point-Closure Standards for Horizontal- and
Vertical-Control Surveys

Horizontal
Classification | Point-Closure Standard (Ratio)
--- | ---
Second order, Class I | 1:50,000
Second order, Class II | 1:20,000
Third order, Class I | 1:10,000
Third order, Class II | 1:5,000
Fourth order (construction layout) | 1:2,500 - 1:20,000
Vertical
Classification | Point-Closure Standard (mm)
Second order, Class I |
Second order, Class II |
Third order |
Fourth order (construction layout) |

HORIZONTAL-CONTROL STANDARDS

8-270. The horizontal-point closure is determined by dividing the linear-distance misclosure of the survey into the overall circuit length of a traverse, loop, or network line/circuit. When independent directions or angles are observed (for example, a conventional survey [traverse or triangulation]), these angular misclosures may be distributed before assessing positional misclosure. In cases where GPS vectors are measured in geocentric coordinates, the 3D positional misclosure is assessed.

Approximate Surveying

8-271. Approximate surveying is classified based on the survey's estimated or observed positional errors. This includes absolute GPS and some DGPS techniques with positional accuracies ranging from 10 to 150 feet (2-deviation RMS). There is no order of classification for approximate work.

High-Order Surveys

8-272. Requirements for relative line accuracies exceeding 1:50,000 are rare for most applications. Surveys requiring accuracies of first-order (1:100,000) or better, should be performed using FGCS standards and specifications and must be adjusted by the NGS.

Construction Layout or Grade Control (Fourth-Order)

8-273. This classification is intended to cover temporary control used for alignment, grading, and measurement of various types of construction and some local site-plan topographic-mapping or photo-mapping control work. Accuracy standards will vary with the type of construction. Lower accuracies (1:2,500 to 1:5,000) are acceptable for earthwork, dredging, grading, and some site-plan stakeouts. Moderate accuracies (1:5,000) are used in most pipelines, sewers, culverts, catch basins, and manhole stakeouts; general residential-building foundation and footing construction; major highway pavement; and concrete-runway stakeouts. Somewhat higher accuracies (1:10,000 to 1:20,000) are used for aligning longer bridge spans, tunnels, and large commercial structures. For extensive bridge or tunnel projects, 1:50,000 (or even 1:100,000) relative-accuracy alignment work may be required. Vertical grade is usually observed to the nearest 0.005 meter for most construction work, although 0.04-meter accuracy is sufficient for riprap placement, grading, and small-diameter-pipe placement. Construction control points are typically marked by semipermanent or temporary monuments (for example, plastic hubs, nails, or wooden grade stakes). Control may be established by short, nonredundant spur shots, using total stations or the GPS, or by single traverse runs between two existing, permanent control points. Positional accuracy will be commensurate with, and relative to, that of the existing point(s) from which the new point is established.

VERTICAL-CONTROL STANDARDS

8-274. The vertical accuracy of a survey is determined by the elevation misclosure within a level section or level loop. For differential or trigonometric leveling, section or loop misclosures (in millimeters) shall not exceed the limits shown in Table 8-7, where the line or circuit length is measured in kilometers. Fourth-order accuracies are intended for construction-layout grading work. Procedural specifications or restrictions pertaining to vertical-control surveying or equipment should not be over restrictive.

### FINAL-ADJUSTMENT REPORTS

8-275. A variety of free- and/or constrained-adjustment combinations may be specified for a GPS-S. Specific stations to be held fixed may be indicated, and when they are partially constrained, appropriate statistical information must be provided. Either variance-covariance matrices or relative positional-accuracy estimates may be converted as approximate variance-covariance matrices in the constrained adjustment. All rejected observations will be clearly indicated, along with the criteria and the reason used for the rejection.

8-276. When different combinations of constrained adjustments are performed due to indications of one or more fixed stations causing undue biasing of the data, an analysis should be made as to a recommended solution that provides the best fit for the network. Any fixed control points that should be readjusted to anomalies from the adjustment(s) should be clearly indicated in a final recommendation.

8-277. The final-adjusted horizontal- and/or vertical-coordinate values are assigned an accuracy classification based on the adjustment statistical results. This classification should include the resultant geodetic or Cartesian coordinates and the baseline-differential results. The final-adjusted coordinates should state the 95 percent confidence region of each point and the accuracy in ppm between all points in the network. The datum will be clearly identified for all coordinate listings.

8-278. Final-report coordinate listings may be required on hard copy as well as specified computer media. A scaled plot should be submitted with the adjustment report showing the proper locations and designations of all stations established.