David B. Zilkoski
In the first article of this series, the basic concepts of GPS-derived heights were discussed. The article discussed the three types of heights involved in determining GPS-derived orthometric heights: ellipsoid, geoid and orthometric. It was also mentioned that each of these heights has its own error sources, which need to be detected, reduced and/or eliminated by following specific procedures or applying special models. GPS-derived ellipsoid heights are the basis for GPS-derived orthometric heights, so it makes sense to make these ellipsoid heights as close to error-free as possible. This article will discuss guidelines for detecting, reducing and/or eliminating error sources in ellipsoid heights.

Based on the new Federal Geographic Data Committee publication, “Geospatial Positioning Accuracy Standards” [http://www.fgdc.gov/ standards/document/standards/accuracy], guidelines were developed by the National Geodetic Survey (NGS) for performing GPS surveys intended to achieve ellipsoid height network accuracies of 5 cm at the 95 percent confidence level, as well as ellipsoid height local accuracies of 2 cm and 5 cm, also at the 95 percent confidence level. These guidelines were developed in partnership with federal, state and local government agencies, academia and private surveyors and are the result of processing various test datasets and having extensive discussions with various GPS user groups. NGS guidelines have been documented in a publication titled “Guidelines for Establishing GPS-derived Ellipsoid Heights (Standards: 2 cm and 5 cm), Version 4.3" and can be downloaded from NGS’ website at http://www.ngs. noaa.gov/pubs_lib/ngs-58.html.

NGS is confident that these guidelines, if followed, will result in achieving the intended accuracy. Additional tests may show that some of these guidelines can be relaxed. The NGS guidelines are intended for establishing geometric vertical control networks.

In addition, these guidelines have been expanded to include the establishment of GPS-derived orthometric heights that approach these same accuracies, 2 cm and 5 cm. The slight differences between the accuracies of GPS-derived ellipsoid heights and GPS-derived orthometric heights will be generally due to the accuracy of the geoid model and published orthometric heights used to evaluate the differences between the three height systems, i.e., ellipsoid, geoid and orthometric heights. GPS-derived orthometric heights will be addressed in the fourth and last article of this series.

If GPS users follow the NGS guidelines, they will reduce and/or eliminate errors in ellipsoid height and, at a minimum, they will detect problems or errors in data. If these problems or errors are detected and corrected before the project is completed, then they will not be problems to the end users. This is the most important aspect of determining GPS-derived heights.

This is NOT the proper method for checking the level or measuring the height of the antenna.

Good GPS Ellipsoid Heights

The basic concepts are very simple, but they all need to be followed exactly as prescribed.

Repeat base lines on different days and at different times of the day. This helps to detect and reduce the effects of multipath, differences in height values due to different satellite geometry, and the amount of time a user must occupy a station for a short baseline, e.g., 30 minutes of good, valid data over base lines less than 10 km.

The observing scheme for all stations requires that all adjacent stations (base lines) be observed at least twice on two different days and at two different times of the day. The purpose is to ensure different atmospheric conditions (different days) and significantly different satellite geometry (different times) for the two baseline measurements.

Keep base line lengths under 10 km. The closer the two stations are, the better chance that common errors will cancel or nearly cancel, such as unmodeled atmospheric errors. It helps to reduce the amount of time the user must occupy a station in order to collect enough good, valid data to correctly fix all the integers.

Use fixed height poles. This helps eliminate errors due to incorrectly measuring the height of the antenna above the mark. Of course, when listening to GPS users, nobody has ever measured the height of the tripod wrong. But, it is strange how that turns out to be the most common error when fixed height poles are not used.

Assure proper plumbing on the antenna. Plumbing bubbles on the antenna pole of the fixed-height tripod must be shaded when plumbing is performed. Plumbing bubbles must be shaded for at least three minutes before checking and/or re-plumbing. The perpendicularity of the poles must be checked at the beginning of the project and any other time there is suspicion of a problem.

Use a geodetic antenna with ground plane and/or choke ring. This helps reduce effects of local multipath.

Final processing shall consist of fixing all integers for each vector for all sessions except to some control sites. Users should be able to fix the integers over base lines that are less than 10 km. If the integers cannot be fixed, there is probably something wrong with the data, e.g., bad multipath effects, missing data due to blockage or interference. Baseline solutions with fixed integers prove to be more reliable, consistent and accurate.

Observe base lines between neighboring stations. This helps to ensure that closely spaced stations will have the desired accuracy and that they are the stations most users will want to use to validate their classical leveling results.

Establish a high-accuracy 3-D fiducial network that encompasses the entire project. This network helps to detect and reduce the effects of systematic errors in the local network observations. This also ensures that when two local networks are eventually connected, they will be consistent with each other. The survey shall be referenced to at least three existing National Spatial Reference System three-dimensional Federal Base Network (FBN) stations near the project area. The survey will also consist of at least three Cooperative Base Network (CBN) stations that are referenced to the three control stations and interspersed throughout the project. For these stations, receivers shall collect data continuously and simultaneously for at least three, five-hour sessions on three different days at different times of the day during the project. Note: it is only necessary to establish a new set of fiducial stations if a high accuracy reference network (HARN) accurate in all three components doesn’t exist in the area of the survey.

There are other minor but very important procedures that the user must follow, for example, use precise ephemerides, take a rubbing of the mark. Refer to NOAA Technical Memorandum NOS NGS-58, “Guidelines for Establishing GPS-derived Ellipsoid Heights (Standards: 2 cm and 5 cm), Version 4.3" for more details.

This article discussed procedures that need to be followed to detect, reduce and/or eliminate error sources to compute accurate GPS-derived ellipsoid heights. Analysis of the quality of project data shall be based on repeatability of measurements, adjustment residuals and analysis of loop misclosures. Please be aware that repeatability and loop misclosures do not always disclose all problems. The next article (July 2001) will discuss basic procedures for analyzing GPS project results to ensure the desired accuracy standard has been met.