TxDOT GPS User’s Manual: Data Processing

Section 7: Data Processing

Overview

In the scope of these specifications, GPS data processing includes the review and cataloging of collected data files, processing phase measurements to determine baseline vectors and/or unknown positions, and performing adjustments and transformations to the processed vectors and positions.

Each step requires quality control analysis, using statistical measures and professional judgment, to achieve the desired level of confidence. Each of these steps is also very dependent upon the measurement technique, the GPS receiver, and antenna types; the observables recorded, and the processing software.

The point position (absolute) coordinates of the initial station, held fixed in each baseline solution, must be referenced to the datum for the satellite orbits and must be known, horizontally and vertically better than ten (10) meters.

Ideally, all baselines should be processed with the initial published position of the CORS station or the highest accuracy station in the network. From that initial coordinate (NAD83) HARN latitude, longitude, and ellipsoid height) all baselines should be processed, seeding each of the new stations based on the results of the baseline processing from the known stations. While technically WGS84 is the datum of GPS, the NAD83 datum may be accepted as an identical substitute for surveying in Texas.

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Orbit Ephemeris

Always use an ephemeris other than the broadcast or predicted ephemeris when processing. The type of orbit ephemeris used can have an effect on the quality of processed baselines. The longer the baseline, the greater the effect can be. For baselines exceeding twenty (20) kilometers, use either the rapid or the precise ephemerides.

All of the ephemerides are available in the SP3 format at the following Web site: http://igscb.jpl.nasa.gov/components/prods_cb.html

The naming convention of the orbit files are as follows:

Anchor: #i1008617Table 6.4 Orbit Files Naming Convention Example: lgxwwwd hh.sp3
where x =	type of orbit (p=precise, r=rapid, u=ultra rapid
where www =	GPS week
where d =	Day of week (0=Sunday)
where hh	UTC hour

The following table illustrates ephemeris types, their availability, and accuracy:

Anchor: #i1008633Table 6.5 Ephemerides Availability and Accuracy
Ephemeris Type	When Available	Product Accuracy
Precise	13 days	5 cm
Rapid	17 hours	5 cm
Ultra Rapid	3 hours	5 cm
Predicted	Real-time	10 cm
Broadcast	Real-time	200cm

In the event that the baseline processing software only accepts the binary orbit file type (EF18), the following web site will translate the ASCII SP3 format file: http://www.ngs.noaa.gov/GPS/GPS.html

The table below lists the requirements for the use of the various types of ephemerides.

Anchor: #i1008661Table 6.6 Baseline Processing Requirements
Level of Survey Accuracy*	Level 0	Level 1	Level 2	Level 3	Level 4
Minimum Elevation Mask in Degrees (Processing)**	18	15	15	15	13
Use Broadcast (B), UltraRapid (U), Rapid (R), Precise (P) Ephemerides	P	P or R	P, R or U	P, R, U or B	P, R, U or B
Accuracy of WGS84 Position Held Fixed in Each BL Solution (see Overview, Ch. 6 Sec. 7)	2.5m	10m	10m	10m	10m
Processing Must Account for Phase Center Offsets	Y	Y	Y	Y	Y
Maximum Number of Rejected Simultaneous Phase Observations	5%	10%	10%	10%	10%

* This table does not apply to levels 5-7 mapping grade surveys. ** Under certain conditions when an acceptable solution cannot be determined with the minimum elevation mask, the data may include space vehicles (satellites) less than the minimum elevation cutoff.

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Atmospheric Error Reduction

A standard model for ionospheric group delay and tropospheric zenith delay, using broadcast coefficients, may be used for all baseline processing. Ionospheric modeling for Ll carrier phase measurements has shown reduction in the group delay of 50 to 60 percent.

The remaining unmodeled error, due to group delay, is expected to be 1 to 2 ppm.

Ionospheric-free processing using a linear combination of Ll and L2 carrier should be considered for baselines over 5-25km depending on the manufacturer hardware and software. Follow manufacturer recommendations for ionospheric free processing. This is generally included in the processing software defaults and does not require user intervention.

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Baseline Processing

All baseline processing should be accomplished using NGS-developed PAGES software or other interactive, graphics producing software by other vendors that produces results equivalent to PAGES. TxDOT surveyors can get help from the Information Systems Division (ISD) on Trimble TGO processing software. Trimble’s TGO software includes an adjustment program also supported by ISD. See Table 6.6 for baseline processing requirements.

For sessions of an hour or more, process data using 15 or 30-second epochs (5 second may be used, but probably does not add anything to the accuracy) and a 13-18 degree elevation mask outlined in Table 6.8. In no case will an elevation mask be applied that is greater than twenty (20) degrees above the horizon. For sessions less than an hour, static and faststatic observations may be processed using 5 or 15 second epochs. However, when operating FastStatic at the minimum observation time (8 to 20 minutes) use 5 second data. The use of shorter epochs may improve the ease of baseline processing.

Final processing should consist of fixing all integers for each baseline less than 40 kilometers. For baselines less than 5-10 kilometers, the L1 fixed solution may be the best choice. For baselines greater than 40 kilometers, but less than 200 kilometers, a session may consist of a set of partially fixed integers and may also include float solutions where no integers could be fixed. For baselines greater than 200 kilometers, the final solution should be an ionospheric free ambiguity float L1/L2 solution. In all cases, the user should refer to their manufacturer specifications if conflicts exist within the section of the specifications.

The quality of acquired data should be determined from the double difference residual plots and the RMSE values. Final coordinates and their quality assessment should be determined by loop closure analysis, least squares adjustment, analysis of repeated baselines, and free adjustment residuals.

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Troubleshooting Problematic Baselines

A problematic baseline can be defined as a line observed with two carrier-phase GPS receivers, L1 or L1/L2, and the baseline solution does not meet the manufacturer’s specification for quality. For short lines determined to need a double different fixed solution, or for longer lines, other solutions are acceptable as specified in Table 6.8. In most cases, the problematic baseline was observed with enough satellites for a long enough time period, but the quality indicators show the line to be unacceptable.

The first thoughts may be to re-observe the line. However, this should be the user’s last resort. There are enough tools available in the baseline processing software to allow one to examine the observational information to detect obvious problems.

The following are suggestions on what to look for when troubleshooting problematic baselines:

Look at the plot of all satellites during the observing session; there is a plot for each receiver. Software packages differ, but common to most is a plot showing each satellite observed, one below the other.
What to look for:
- When a cycle slip occurs, or there is a loss of lock due to obstructions, there will be a break in the line on the graph for that particular satellite.
- A short break indicates a cycle slip, a longer break; an obstruction.
- If too many breaks have occurred, eliminate that satellite and try the baseline solution again. In many cases, this solves the problem.
Look at the plot of satellites for both receivers.
- Was the start and stop time approximately the same, or did one receiver start or stop too early or too late?
- Start and stop times can be changed to encompass only common observing times and then re-observe the baseline.
Satellites with a high signal-to-noise ratio (SNR) can cause problems. In many cases, a high SNR occurs when the satellite is close to the horizon. It is possible to have a satellite low on the horizon for the entire session. In that case, the satellite should be eliminated from the solution, then resolve the baseline.
Another way to eliminate high SNR on satellites low to the horizon is to raise the elevation mask for the baseline solution.
If the length of the session is short, perhaps too short, try a baseline solution with a shorter epoch than normal.
- If the default on the baseline solution is thirty (30) seconds, try fifteen (15) seconds. This will increase the number of single, double, and triple differences needed to resolve the baseline.
If all the above suggestions fail, resolve the baseline using a more precise ephemeris than was started with.
As a last resort, the baseline must be re-observed. Be sure to select a time period different from the original observed time. Look at sky plots and select a time with many satellites and an area free of obstructions.

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Baseline Analysis

Prior to performing a least squares adjustment on the network or traverse, the GPS processed baselines should be analyzed for possible errors using three (3) tools:

evaluation of the results of each individual baseline
comparison of all redundant baselines
generation and analysis of loop closure reports.

To facilitate the error detection process, vector data should be displayed with the horizontal and vertical components separated. Table 6.8 summarizes all of the requirements for baseline (vector) analysis.

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Baseline Processing Reports

The user should pay close attention to the evaluation of the baseline processing reports. Additionally, the user should be ready to explain to TxDOT the various aspects of the report and summarize what to look for, as far as how to evaluate the quality of the processed vectors.

These reports should display such items as:

the elevation cut off angle
the type of tropospheric and ionospheric models used
a priori and a posteriori baseline errors
the common satellites used
GDOP and/or PDOP values
RMS error of the baseline
the presence or absence of cycle slips in the data; etc.

Depending on the baseline length, use the following specifications for the final acceptable baseline type:

Anchor: #i1008707Table 6.7 Final Acceptable Specifications
Baseline Length	Desired Final Solution
Less than 5 km	L1 Only Fixed Solution
5-20 km	L1 Only Fixed or L1/L2 IonoFree Fixed Solution
20-50 km	L1/L2 IonoFree Fixed Solution
50-90 km	L1/L2 IonoFree Fixed or Float Solution
Greater than 90 km	L1/L2 IonoFree Float Solution

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Comparison of Redundant Baselines

Comparison of redundant baselines is an excellent way of detecting blunders in a network.

There are two (2) types of redundant baselines to consider.

The first is the comparison between two (2) or more measured baselines between the same two (2) stations.
The second is the comparison between the published baseline and the measured values. Table 6.8 describes the way redundant baselines to test for validity.

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Loop Closure Reports

Running loop closures on a network of baselines is another validation check for blunders and ill-fitting baselines. Again, Table 6.8 (Pre-adjustment Baseline Analysis Requirement) describes several tests to run when creating and evaluating loop closures.

When running loop closures for any level of survey, each closure must contain at least one baseline each from two (2) separate observing sessions. Loop closures run around baselines from the same session containing at least one (1) dependent baseline that is an unacceptable closure for any survey performed.

The table below provides tests for loop closures:

Table 6.8 Pre-adjustment Baseline Analysis Requirements
Level of Survey Accuracy*	Level 1	Level 2	Level 3	Level 4
Baseline Processing
Processing Requirements	M	M	M	M
Maximum Standard Deviation of the Range Residuals in the BL Solution (RMSE)	2cm	2cm	4cm	6cm
Redundant BL’s
Differences Between Repeat Unadjusted Baselines Computed and Compared	Y ^a	Y ^a	Y ^a	Y ^a
Differences Between Known and Observed Baselines Computed and Compared	Y ^b	Y ^b	Y ^b	Y ^b
Loop Closures
Baselines from Independent Observing Sessions, Not Less than	2 ^c	2 ^c	2 ^c	2 ^c
Loop Length, Not to Exceed (km)	600	500	200	n/a
Number of Loop Closures Required Per Project	2	2	2 ^d	2 ^d
Maximum Number of Legs in any Loop	10	10	10^d	10^d
Maximum Misclosure for Any Single Loop (ppm)	5 e	12.5 e	25^{d e}	75^{d e}
Maximum Average Project Loop Misclosure (ppm)	4 f	8 f	16^{d f}	50^{d f}
Maximum Misclosure in Any Component; Not to Exceed (cm)	10	10	10^d	n/a

* This table does not apply to mapping grade Levels 5, 6 and 7.

Notes for Table 6.8 Data (Baseline) Analysis Requirements:

M - The processing software user should follow the specifications published from the manufacturer in processing the observational data. The percentage of unacceptable baselines, processed within each session of data, should not exceed 33% of the total number of independent baselines possible for each session. If this percentage is exceeded, the session should be repeated or ignored providing there is a sufficient amount of redundancy remaining in the network.

a - Repeat baseline closures should be computed for each repeat baseline combination. The absolute value of the difference in each baseline component and the distance dependent error (parts per million) are analyzed to determine if blunders exist. The difference in each vector component is compared to the rejection threshold (RT). The RT includes a base error and length dependent error that corresponds to the survey level. In addition, the results of the repeat baseline measurements should be compared to the instrument specifications stated by the manufacturer.

Equation for determining base errors:

Where:

e = Base error is 0.008m for survey level 0 & 1. Base error is 0.01m for survey levels 2- 4.

SLppm = Survey Level (i.e. Level 0- 4)

d = Distance in meters (m)

b - Similar to the repeat baseline closures, known minus observed baseline closures provide insight on the location and possible cause of outliers. The differences between the known vector and the observed vector components are compared to the same rejection threshold presented for repeat baseline closures.

c - Computational loops should be composed of those baselines that close upon themselves in the shortest distance possible.

d - Not required if survey method is PPK or RTK.

e - In any component (X,Y,Z), the maximum misclosure, in terms of loop length, should not exceed this value in terms of parts per million (ppm). Take the misclosure divided the loop length times 1,000,000 to calculate each loop’s ppm.

f - In any component (X,Y,Z), the average misclosure, in terms of loop length, should not exceed this value in terms of parts per million (ppm). To calculate this, take the sum of all of the loop closure ppm’s and divide by the number of loops to yield the average loop closure in ppm’s.

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Data Adjustment Analysis

The purpose of a least-squares adjustment is to estimate and remove random errors; provide a single solution even when there is redundant data; minimize corrections made to the observations; detect blunders and large errors; and generate information for analysis, including estimates of precision.

The network adjustment occurs in two major steps:

The first step is the minimally constrained or free adjustment, which acts as a quality control check of the user’s observations. The purpose of the minimally constrained adjustment is to check the internal consistency of the network; detect blunders or ill-fitting observations; and obtain accurate observation error estimates.

The second step is the fully constrained adjustment. The purpose of the fully constrained adjustment is to reference the network to existing control (datum); verify existing control; produce network transformation parameters (optional); and obtain accurate coordinate error estimates.

Both steps are required to obtain a complete adjustment and to provide confidence in the results.

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Minimally Constrained Adjustment

A minimally constrained adjustment (MCA) is an adjustment with only one control point held fixed in the survey network. Holding one control point fixed, shifts observations to the correct location within the chosen datum. Not fixing a control point forces the software to perform a free adjustment. A free adjustment is accomplished by minimizing the size of the coordinate shift throughout the network. This equates to a mean coordinate shift of 0 (zero) in all dimensions.

A minimally constrained or free adjustment acts as one quality control check on the network. This adjustment helps to identify bad observations in the network. If an observation does not fit with the rest of the observations, it is highlighted as an outlier. The minimally constrained or free adjustment also checks on how well the observations hold together as a cohesive unit.

All minimally constrained adjustments must be performed in the WGS-84 datum. Since all GPS observations are made on the WGS-84 datum, the adjustment of the observations should be tied closely to the WGS-84 datum. Realistic error estimates for tribrach centering and H.I. measurement should also be factored into the minimally constrained adjustment.

The following minimally constrained adjustments should be done for Level 1 and Level 2 surveys. The required reports and/or spreadsheets are listed.

An MCA to determine network reference accuracy:

Submit a minimally constrained adjustment holding the closest CORS fixed – use the NAD83 CORS coordinate in latitude, longitude, and ellipsoid height.
Create a spreadsheet (or select a report) to compare the published CORS coordinates to the coordinates determined in the MCA.

An MCA to determine local HARN relationship if applicable:

Submit a minimally constrained adjustment holding the highest order (1^st priority) and most central to the project (2^nd priority) HARN station.
Create a spreadsheet (or select a report) that shows the comparison between the measured values and the published values of other HARN stations included in the survey.

An MCA to show the relationship of benchmarks used in the survey:

Submit a minimally constrained adjustment holding the highest order (1^st priority), highest stability monument (2^nd priority), and most central (3^rd priority) to the project vertical control stations.
Create a spreadsheet (or select a report) showing differences between published orthometric heights (elevations) and measured values.

The minimally constrained adjustment is an iterative process. Perform the minimally constrained adjustment to check the observations for internal consistency and estimates errors for all observations.

If bad observations are found, they should appear as outliers in a histogram of standardized residuals. If bad observations are discovered, they should be removed, one at a time, starting with the largest, so that the statistics of the network are not skewed.

An adjustment should then be performed again. Errors are estimated again. In the subsequent adjustments, the estimated error may be rescaled to produce more realistic error estimates.

These procedures should be repeated until the results meet the following conditions:

all outliers have been removed from the network
observations have the most accurate error estimates possible; and observations are adjusted such that they fit together well.

During the iteration process, two least squares statistics should be used to gauge progress:

Reference factor – The reference factor shows how well the observations, along with their respective error estimates, are working together. Once the reference factor approaches 1.00, the errors in the observations are properly estimated and all observations have received their appropriate adjustments.
Chi-square test – Typically when the reference factor approaches 1.00, the chi-square test of network error estimates, degrees of freedom, and level of confidence will pass. At this point, there is confidence that the network observations are working together and that there are no large errors remaining in the network.

Once the minimally constrained adjustment has been completed, move on to the fully constrained adjustment to fit the observations to the local control datum.

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Fully Constrained Adjustment

The fully constrained adjustment (FCA) transforms the network of observations to the control points in the network. Once the network is fixed to those control points, adjusted coordinates based on the project datum (using the appropriate datum adjustment as recommended by TxDOT) for all other points in the network can then be determined.

Use this step to check that the existing control fits together well. The minimally constrained adjustment (MCA) showed that the observations fit together and a fairly rigid network is defined. It is assumed that if any large errors are present in the fully constrained adjustment, the source is non-homogeneous control points (values). Any ill-fitting control points should not be fixed (constrained).

When designing the network, it is good practice to use a minimum of three (3) horizontal control points and four (4) vertical control points because two (2) horizontal and three (3) vertical control points are required to define transformation parameters. The additional horizontal and vertical control points can be used to check the consistency of the adjustment and defined transformation parameters. Adding additional control points builds more confidence in the calculated parameters. Levels 1 and 2 do require these three (3) horizontal coordinates and four (4) elevations at a minimum.

In the fully constrained adjustment, begin fixing the control values to determine how well the rigid network of observations fit the control. Essentially, the adjustment determines if the network of observations fit the network of fixed control points given some error estimate. These error estimates consist of the error estimates along with the applied scalar and set-up errors. The transformation parameters should then be calculated to allow the observations to fit to the control.

The following fully constrained adjustments (FCA) for Level 1 and Level 2 should be delivered along with the listed spreadsheets or reports.

An FCA to determine local accuracy for horizontal positions only:

Submit a fully constrained adjustment fixing a minimum of three (3) horizontal stations as noted above.
Submit a spreadsheet (or select a report) showing the comparison between the MCA above and the FCA for horizontal position.

An FCA to determine local accuracy for orthometric heights (elevations):

If there are unexpected differences in the MCA and published values for vertical, submit a fully constrained adjustment fixing a minimum of 4 benchmarks.
In many cases, a fully constrained adjustment will not be required for the final elevations of a control survey.
If the differences between the published and measured values of the MCA holding one benchmark fixed, fall within the acceptable error limits of a particular level of survey, the MCA elevations will be acceptable as the final results of the survey.

The following subsection explains the subject in further detail.

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Orthometric Height Determination

For all levels of survey in TxDOT projects, orthometric height determination must include the latest available geoid model (GEOID03 currently). Geoid models are used to compute the separations between the ellipsoid and geoid. Using the latest geoid model will insure the best possible orthometric height differences between stations established by GPS methods.

When performing the fully constrained adjustments, if multiple orthometric heights are going to be fixed, then the horizontal and vertical adjustments must be done separately. During the horizontal adjustment only three (3) verticals should be fixed. During the vertical adjustment, only two (2) horizontals should be fixed.

The network design process and preplanning phase is critical to avoiding the pitfalls in geoid modeling. Inconsistencies in the local vertical control network due to subsidence, disturbed monuments, or dissimilar control sources, must not be allowed to contaminate the computed trend parameters.

CAUTION: Failure to exercise extreme caution in this step can introduce significant errors into the computed heights.

For instance, a local area of subsidence, if not detected, could be entirely absorbed within the rotation parameters for the bias group. Errors in the geoid model or GPS ellipsoid heights could be similarly masked.

The analysis of the geoid modeling must identify the magnitude of vertical discrepancies and apply corrections to the geoid model and vertical constraints, which are appropriate to its source. This can only be accomplished with abundant levels of redundancy and careful analysis. The following table provides additional requirements specific to the geoid modeling process.

In addition to using the latest geoid model, the surveyor should use the latest National Vertical Datum, NAVD88 height values to control the project’s adjusted heights. Also recommended is that the surveyor be familiar with NGS’ guidelines for establishing GPS-derived ellipsoid heights when performing GPS surveys.

There are three (3) general requirements for establishing GPS-derived orthometric heights on TxDOT projects:

Anchor: #i1008855Table 6.9 GPS-Derived Orthometric Requirements
Project vertical control	will require the fixing of a geoid model for determining elevations with GPS surrounds the project with valid NAVD 88 bench marks, i.e., minimum number of stations is four (4) for Levels 3 and above, one in each corner of project users may have to extend well outside the project area to do this – maybe even run an additional level loop level 4 surveys are generally RTK and baseline distances kept under 10 kilometers are short enough that geoid undulation can be dealt with by using the most recent NGS Geoid model to determine elevations during data collection from a base station with valid orthometric height at the TxDOT surveyor’s discretion, very confined RTK work within less than a couple of kilometers may not require the use of a geoid model if the base station has a valid orthometric height.
For large project areas	there should be no points set farther than 20 kilometers of an occupied first or second order benchmark (or previously set GPS benchmark).
For projects located in mountainous regions	occupy valid bench marks at the base and the summit of mountains, even if distance is less than 20 km.

When processing the data, there are five (5) steps to follow for estimating GPS-derived orthometric heights:

Anchor: #i1008868Table 6.10 Steps in Processing the Data
Step	Action
1	Perform a 3-D minimally-constrained, least squares adjustment of the GPS survey project, i.e., constrain one latitude, one longitude, and one orthometric height value.
2	Using the results from the adjustment in procedure 1 above, detect and remove all data outliers. The user should repeat procedures 1 and 2 until all data outliers are removed.
3	Compute differences between the set of GPS-derived orthometric heights from the minimally constrained adjustment (using the latest National geoid model, e.g., GEOID03) from procedure 2 above and the published NAVD 88 benchmarks.
4	Using the results from step 3 of this table, determine which bench marks have valid NAVD 88 height values. This is the most important step of the procedure. Determining which bench marks have valid heights is critical to computing accurate GPS-derived orthometric heights. The user should include a few extra NAVD 88 bench marks in case some are inconsistent, i.e., are not valid NAVD 88 height values
5	Using the results from step 4 of this table, perform a fully constrained adjustment holding all valid known values fixed to arrive at the resulting elevations.

The following table provides adjustment analysis information:

Anchor: #i1008888Table 6.11 Office Procedures Guidelines
Adjustment Analysis Criteria	1 cm Horizontal 2 cm Vertical*	2 cm Horizontal 5 cm Vertical
Maximum variance of unit weight (1.0 ideal)	1.5	1.5
Minimum degrees of freedom per station	2 degrees of freedom	1 degree of freedom
Standard deviation of observation residuals, cm	.01 cm	0.1 cm
Standard error of baseline components, cm	.01 cm	0.1 cm
Standardized residuals - pass chi square test - pass tau criterion	yes yes	yes yes
Maximum % observations rejected	10%	10%

*Local Network Accuracy