California Surveyors Forums

ATC Cal Surveyor Tech Tip: GPS Network Analysis and Adjustments

We present here an outline for GPS adjustment procedures to test whether we as a profession are following similar thought processes and a guide for those that haven’t made up there minds yet.

Network analysis and adjustments can be defined generally as the process of validating the integrity of the measurements and constraining the measurements to known horizontal and vertical coordinates. This process is applicable to radial networks as well as complex interconnected arrays. The adjustments, horizontal and vertical, technically should be handled as separate processes when determining horizontal positions or orthometric heights (elevations). If both are required for a project then the process occurs in the following steps.

Step 1: Validate the internal consistency of the measurements and remove bad data.
Step 2: Fix a single position (Latitude, Longitude, Ellipsoid Height on a known valid control point) and analyze closures on other known points
Step 3: Fix all acceptable control points to develop horizontal coordinates on all points in the survey
Step 4: Fix a single height to develop heights and analyze closures on other known heights
Step 5: Fix all acceptable heights to develop vertical coordinates on all points in the survey

Step One is a minimally constrained adjustment used to validate the integrity and accuracy of the measured stand alone vectors (baselines). Step Two follows after removing unacceptable measurements. Step Two is a minimally constrained adjustment fixing a known latitude, longitude and ellipsoid height (GPS coordinates) for the purpose of comparing the computed verses record positions (closures) at other known points. Step Three is the constrained adjustment which fixes all the points determined to be acceptable in Step Two and is used to develop adjusted three dimensional GPS coordinates. These adjusted coordinates (latitude, longitude and ellipsoid height) are the basis for applying a projection (i.e. State Plane or local) and computing grid coordinates.

If orthometric heights (elevations) are necessary then technically the adjustments should be processed separately and be free in the horizontal dimension. Step Four fixes a single point for horizontal and a single point at a known orthometric height for the purpose of comparing the computed verses record heights (closures) at other known points. Step Five fixes acceptable points in a vertically constrained adjustment to develop orthometric heights on all points in the network. The best results will be obtained if an NAVD88 height is used and includes a geoid model (i.e. Geoid03). Fixing an NAVD88 height and applying the geoid model results in pseudo-ellipsoid heights (pseudo meaning “as ifâ€￾) that may vary about 10 centimeters from the actual ellipsoid heights determined in Steps Two and Three. The resulting orthometric heights will only be as good as the geoid model and the measured ellipsoid height differences. The absolute accuracy can be better than 3 centimeters and the relative accuracy could approach 1 centimeter over a local area if diligent procedures are followed. There are some variations of these adjustments where tilts or rotations in the surfaces are solved to improve the overall fit with existing local control point positions and heights and will be discussed in a separate article.

This thread is posted for comments and questions by the Advanced Technologies Committee for the purpose of encouraging the opportunity for exchange and development.

Submitted on behalf of the CLSA ATC Committee

Michael,

Thanks for the great information. I have a question about this sentence regarding the vertical component:

"The absolute accuracy can be better than 3 centimeters and the relative accuracy could approach 1 centimeter over a local area if diligent procedures are followed."

What type of occupations are required in order to achieve these accuracies? Have we moved beyond the 2-5 hours on separate days/times? Or are those specs I'm thinking of now outdated?

Thanks for the tips.

Dave Ryan

The key word is diligent procedures. Over a small area of a few square miles, given good GPS site conditions, using procedures that identify and mitigate error sources, designing a network that focuses or isolates measurement errors, double (sometimes triple) independent 20 minute occupations (different times and different days preferred) can result in one centimeter relative accuracy. It is important to note that obtaining one centimeter residuals in the adjustments is an indication of the relative accuracy of the measurements but is not a validation that the survey has obtained orthometric heights at one centimeter. Professionalism would dictate that some independent method be incorporated to validate the results. Testing the relative height differences of a representative sample of points with differential leveling is certainly one way to responsibly validate the reported accuracy.