Establishing Orthometric Heights Using GNSS — Part 2

August 5, 2015  - By
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Part 1 of this column appeared in the June Survey Scene newsletter.


Basic Procedures for Establishing Accurate GNSS-Derived Ellipsoid Heights

David B. Zilkoski

David B. Zilkoski

In my first newsletter column of this series, Part 1, I discussed the basic concepts of GNSS-derived heights. My article discussed the three types of heights involved in determining GNSS-derived orthometric heights: ellipsoid, geoid, and orthometric. I also mentioned that each of these heights has its own error sources that need to be detected, reduced or eliminated by following specific procedures or applying special models.

GNSS-derived ellipsoid heights are the basis for GNSS-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 eliminating error sources in ellipsoid heights. It will focus on guidelines for establishing accurate ellipsoid heights in a local geodetic network.

Based on the Federal Geographic Data Committee publication “Geospatial Positioning Accuracy Standards, Part 2: Standards for Geodetic Networks,” guidelines were developed by the National Geodetic Survey (NGS) for performing GNSS surveys that are 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 data sets and having extensive discussions with various GNSS users groups. These guidelines, known as NGS 58, have been documented in a publication titled “Guidelines for Establishing GPS-derived Ellipsoid Heights (Standards: 2 cm 9and 5 cm), Version 4.3″ and can be downloaded from the NGS website. NGS is reevaluating the guidelines and, based on its research results, will update the document appropriately (NGS, Personnel Communication).

Guidelines have also been written to establish GNSS-derived orthometric heights that approach these same accuracies, 2 cm and 5 cm. The slight differences between the accuracies of GNSS-derived ellipsoid heights and GNSS-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: ellipsoid, geoid and orthometric heights. The topic “procedures for estimating accurate GNSS-derived orthometric heights” will be addressed in a future newsletter in this series.

If users follow the NGS guidelines, they will reduce or eliminate errors in ellipsoid height or, 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.

Basic Procedures for Detecting, Reducing, and Eliminating Errors in GNSS Ellipsoid Heights

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

First and probably one of the most important procedure is to repeat baselines 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, for instance, 30 minutes of good, valid data over baselines less than 10 km. (Although, it should be noted that to obtain 30 minutes of good, valid data, the user may have to obtain 45 to 60 minutes of data.)

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 baseline 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 GNSS users, nobody has ever measured the height of the tripod wrong. But, it’s strange how that turns out to be the most common error when fixed-height poles are not used.

Antenna set-up is critical. 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 3 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. The user should also ensure the antenna is properly seated in the mount.

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 baselines that are less than 10 kilometers. If the integers cannot be fixed, there is probably something wrong with the data, such as bad multipath effects, missing data due to blockage, or interference. Baseline solutions with fixed integers prove to be more reliable, consistent and accurate.

Simultaneously observe baselines between neighboring stations. This helps to ensure that closely spaced stations (neighboring stations) will have the desired local accuracy and are the stations that 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 remaining 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. This is a very important aspect of establishing accurate GNSS-derived ellipsoid heights using the guidelines documented in NGS 58. The survey should be referenced to at least three existing Continuous Operating Reference Stations (CORS) [NOAA CORS or equivalent] near the project area. The survey should also consist of at least three control stations that are referenced to the three CORS and interspersed throughout the project. For these control stations, receivers should collect data continuously and simultaneously for at least three, 5-hour sessions on three different days at different times of the day during the project. As previously stated, NGS is reevaluating the guidelines and will update them based on the results of their research. Until NGS updates the guidelines, the user should continue to collect long data sets at these control stations, because they are extremely important to detecting potential errors in the stations established using short data observing sessions.

Evaluating the Quality of Published NAD 83 (2011) Ellipsoid Heights

A description of the National Adjustment of 2011 Project (Alignment of passive control with the latest realization of the North American Datum of 1983: NAD 83(2011/PA11/MA11) epoch 2010.00) is available online.

I’ve listed a few paragraphs (and highlighted a few statements) from the write-up that I believe are important to anyone using published NAD 83 (2011) ellipsoid heights as control stations.

As part of continuing efforts to improve the NSRS, on June 30, 2012, NGS completed the National Adjustment of 2011 Project. This project was a nationwide adjustment of NGS “passive” control (physical marks that can be occupied with survey equipment, such as brass disk bench marks) positioned using GNSS technology. The adjustment was constrained to current North American Datum of 1983 (NAD 83) latitude, longitude and ellipsoid heights of NGS Continuously Operating Reference Stations (CORS). The CORS network is an “active” control system consisting of permanently mounted GNSS antennas, and it is the geometric foundation of the NSRS. Constraining the adjustment to the CORS optimally aligned the GNSS passive control with the active control, providing a unified reference frame to serve the nation’s geometric positioning needs.

For the final constrained adjustments, the median network accuracy for all stations was 0.9 cm horizontal and 1.5 cm vertical (i.e., ellipsoid height) at the 95% confidence level. The median change in coordinates from the previous published values was about 2 cm horizontally and vertically. However, some station coordinates changed by more than 1 meter horizontally and 60 cm vertically. Although some of the large coordinate changes resulted from new data and adjustment strategies, most horizontal changes greater than about 6 cm occurred in geologically active areas and were likely due to tectonic motion.

Results of the 2011 national adjustment for 79,677 passive control marks are available on NGS Datasheets, including their network and local accuracies.Of these passive marks, 79,161 are referenced to the North America tectonic plate as the 2011 realization (including CONUS, Alaska and the Caribbean); 345 are referenced to the Pacific plate as the PA11 realization (the central Pacific, including Hawaii, American Samoa and the Marshall Islands); and 171 are referenced to the Mariana plate as the MA11 realization (the western Pacific, including Guam, Palau and the Commonwealth of the Northern Mariana Islands). Although the passive marks are referenced to three different tectonic plates, all refer to a common 2010.0 epoch date. With the completion of the national adjustment, all passive marks on NGS Datasheets with NAD 83(2011/PA11/MA11) epoch 2010.00 coordinates will be consistent with results obtained using CORS and the NGS Online Positioning User Service (OPUS). Note that 183 stations were excluded from the final national adjustments due to lack of enabled vector connections; where possible, these stations will be reconnected to the network in subsequent individual adjustments.

Other technical issues addressed in the project include:

1. appropriate down-weighting of the up component of GNSS vectors to account for subsidence in the northern Gulf Coast region of CONUS;

2. use of variable weighted (stochastic) constraints for CORS based on formal accuracy estimates derived from the NGS MYCS1;

3. scaling of GNSS vector error estimates for all projects to ensure consistent weighting of observations;

4. use of down-weighting (rather than removal) for vector rejections;

5. splitting the conterminous U.S. into a Primary and Secondary network, as mentioned above, such that vectors observed prior to about 1994 were assigned to the Secondary network. This allowed the Primary network to be adjusted separately without the problems associated with older observations (e.g., single frequency receivers, no antenna phase center models, poor orbit accuracy, incomplete satellite constellation, lack of CORS, etc.).

Each of these technical challenges (and others) was satisfactorily resolved, and completion of the National Adjustment of 2011 Project represents a significant step toward a more integrated, consistent, and accurate NSRS.

First, I’d like to commend NGS for performing the NAD 83 (2011) national adjustment; it was a great accomplishment by NGS. It provides users with a consistent, accurate set of geodetic coordinates (latitude, longitude and ellipsoid height) that should serve the nation’s positioning requirements for many years. Saying that, there are some issues that the user needs to consider when using published NAD 83 (2011) ellipsoid heights as constraints in GNSS network adjustments:

  • Generally, the NAD 83 (2011) network design was sufficient for determining accurate horizontal coordinates (latitude and longitude) but may not have been sufficient for establishing the vertical component (ellipsoid height) accurate enough for use as control stations in NGS Height Modernization Projects (see this webpage for more information on NGS’ Height Modernization Program) . Many of the earlier GNSS projects, prior to the publication of NGS 58, did not repeat baselines; stations were, however, usually occupied at least twice and observing sessions lasted for two hours or more. They were generally evaluated using loop closures and adjustment statistics, but loop analysis and adjustments do not always detect, reduce and/or eliminate all problems.
  • In addition, prior to NGS 58, not all closely spaced stations (neighboring stations) were simultaneously observed during the same session. In my opinion, the published formal errors may be too optimistic for some of these stations. These stations may be very precise but based on the survey field procedures performed prior to the publication of NGS 58, it is my opinion that the relative ellipsoid height accuracy for closely-spaced stations that were not simultaneously observed during the same session may not be as accurate as their listed median accuracy value.
  • Stations that were observed following the NGS 58 document are labeled as Height Modernization stations on the NGS datasheet and their ellipsoid height values should be good to the 2-cm level if they were involved in the same project.

It is important to understand the quality of published NAD 83 (2011) ellipsoid heights because your project’s GNSS-derived ellipsoid height values will be evaluated by them. The project’s control stations help to detect and reduce the effects of remaining systematic errors in the local network so they need to be very accurately determined.

Identifying good, valid published NAD 83 (2011) ellipsoid heights accurate enough to evaluate the results of a GNSS project isn’t an exact science, but there are ways to identify good candidates. I’ve listed three ways of using NGS published datasheets to help the user evaluate the quality of NAD 83 (2011) ellipsoid heights.

  • Identify stations that were established in Height Modernization Projects (that is, the stations were established following NGS 58 guidelines).
  • Analyze the network and local accuracy values to identify stations with accuracy values less than 2 cm.
  • Use local accuracy tables of stations to determine if closely spaced monuments (neighboring stations) were occupied during the same session.

The user can retrieve NGS datasheets in text form or as a shape file using NGS’ Datasheet retrieval program. Identifying stations involved in a NGS Height Modernization Project is simple because the datasheet adds a note stating that a particular station is a Height Modernization Survey Station. The user can assume these stations were determined following NGS 58 guidelines. An example of a station involved in a height modernization project is station CARGO, DJ5933 (see the datasheet below). The NGS datasheet also lists the station’s network and local accuracies. On the datasheet, the network accuracy value is listed below the coordinates (for instance, 1.39 cm for station CARGO). Below the network accuracy value, the user can obtain the local accuracy values by clicking on the following link in the datasheet: “Click here for local accuracies and other accuracy information. You can obtain the full NGS datasheet for CARGO.

The NGS Data Sheet for Height Modernization Station CARGO (DJ5933)
PROGRAM = datasheet95, VERSION = 8.71 National Geodetic Survey, Retrieval Date = JULY 12, 2015
DJ5933***********************************************************************
DJ5933 HT_MOD – This is a Height Modernization Survey Station.
DJ5933 DESIGNATION – CARGO
DJ5933 PID – DJ5933DJ5933 STATE/COUNTY- NC/NEW HANOVERDJ5933 COUNTRY – US
DJ5933 USGS QUAD – WILMINGTON (1979)DJ5933DJ5933 *CURRENT SURVEY CONTROL
DJ5933 ______________________________________________________________________
DJ5933* NAD 83(2011) POSITION- 34 12 27.89075(N) 077 57 16.40009(W) ADJUSTED DJ5933* NAD 83(2011) ELLIP HT- -34.732 (meters) (06/27/12) ADJUSTED
DJ5933* NAD 83(2011) EPOCH – 2010.00
DJ5933* NAVD 88 ORTHO HEIGHT – 2.05 (meters) 6.7 (feet) GPS OBS
DJ5933 ______________________________________________________________________
DJ5933 NAVD 88 orthometric height was determined with geoid model GEOID03
DJ5933 GEOID HEIGHT – -36.78 (meters) GEOID03DJ5933 GEOID HEIGHT – -36.80 (meters) GEOID12BDJ5933 NAD 83(2011) X – 1,101,934.174 (meters) COMPDJ5933 NAD 83(2011) Y – -5,164,049.037 (meters) COMPDJ5933 NAD 83(2011) Z – 3,565,508.167 (meters) COMPDJ5933 LAPLACE CORR – -5.30 (seconds) DEFLEC12B

DJ5933

DJ5933 Network accuracy estimates per FGDC Geospatial Positioning Accuracy

DJ5933 Standards:

DJ5933 FGDC (95% conf, cm) Standard deviation (cm) CorrNE

DJ5933 Horiz Ellip SD_N SD_E SD_h (unitless)

DJ5933 ——————————————————————-

DJ5933 NETWORK 0.94 1.39 0.40 0.37 0.71 0.13140978

DJ5933 ——————————————————————-

DJ5933 Click here for local accuracies and other accuracy information.

Local accuracies provided on the NGS datasheet can be used to determine if closely spaced stations were simultaneously observed during the same session. If two stations were simultaneously observed during the same session, they will have a local accuracy value listed in their table. Station TOWN CREEK (EA0883) is an example of a station that was simultaneously observed by BR 7 (EA0873) in one GNSS project and by LILIPUT (EA0875) in a different project. (Figure 1 depicts these stations and their NAD 83 (2011) network accuracy values.) Looking at the highlighted section of the tables below, station EA0883 is listed in the local accuracy tables for EA0873 and EA0875, so it was simultaneously observed during sessions with EA0873 and EA0875.

Saying that, we can also use the tables to show that EA0873 and EA0875 were not simultaneously observed during the same session. That is, EA0873 is not listed on EA0875 local accuracy table and EA0875 is not listed on EA0873 local accuracy table so they were not processed simultaneous in a session. Figure 2 depicts the two GNSS projects that include observations involving stations EA0873 and EA0875. The user can perform the same procedure to determine that stations EB0217 and EA0873, 8.3 km apart, were not simultaneously observed during the same session, and similarly EA0873 and EA0665, 7.5 km apart, were not simultaneously observed during the same project. Please note I am not suggesting that anything is wrong with these surveys; there may be good reasons why these stations were not simultaneously observed during the same project. I am only using it as an example in this column. Network and local accuracy values are good indicators of potentially “how good” a station is relative to its neighbor, but they should always be evaluated and investigated. My intent is to provide the user with tools for evaluating the quality of published NAD 83 (2011) ellipsoid heights. This is important because published coordinates are used to evaluate the adjustment results of new projects.

Local and Network Accuracy Data for NGS Datasheet – EA0873
Program lna_ret Version 2.7 Date April 6, 2015
National Geodetic Survey, Retrieval Date = JUNE 30, 2015
EA0873 ************************************************************
EA0873 ACCURACIES – Complete network and local accuracy information.
EA0873 DESIGNATION – BR 7
EA0873 PID – EA0873
EA0873
EA0873 Horiz and Ellip are the horizontal and ellipsoid height accuracies
EA0873 at the 95% confidence level per Federal Geographic Data Committee
EA0873 Geospatial Positioning Accuracy Standards. SD_N, SD_E and SD_h are
EA0873 the standard deviations (one sigma) of the coordinates (NETWORK) or
EA0873 of the difference in the coordinates (LOCAL) in latitude, longitude
EA0873 and ellipsoid height. CorrNE is the (unitless) correlation
EA0873 coefficient between the latitude and longitude components of either
EA0873 the coordinate (NETWORK) or coordinate difference (LOCAL). Dist is
EA0873 the three-dimensional straight-line slope distance, in km, between
EA0873 station EA0873 and the corresponding local station. Local stations
EA0873 are stations processed simultaneously in a session regardless of
EA0873 distance.
EA0873EA0873 Accuracy and standard deviation values are given in cm.EA0873EA0873 Type/PID Horiz Ellip Dist(km) SD_N SD_E SD_h CorrNEEA0873 ——————————————————————-

EA0873 NETWORK 0.71 2.37 0.32 0.25 1.21 +0.00543305

EA0873 ——————————————————————-

EA0873 LOCAL (009 points):

EA0873 EA0883 0.80 2.55 9.17 0.36 0.28 1.30 +0.04318242

EA0873 DD0987 0.95 2.41 9.27 0.43 0.34 1.23 +0.06526488

EA0873 DD0043 0.96 2.41 9.74 0.43 0.35 1.23 +0.06880830

EA0873 AB6778 0.69 2.25 13.02 0.31 0.25 1.15 +0.00318194

EA0873 EA0580 1.12 2.86 13.70 0.51 0.39 1.46 +0.03036288

EA0873 EB1389 0.71 2.37 15.11 0.32 0.25 1.21 -0.01876957

EA0873 AJ4968 0.78 2.65 17.14 0.35 0.28 1.35 -0.11220029

EA0873 AJ4967 0.76 2.67 17.63 0.34 0.27 1.36 -0.15139861

EA0873 EB0173 0.68 2.37 18.77 0.31 0.24 1.21 +0.01927597

EA0873

EA0873 MEDIAN 0.78 2.41 13.70

EA0873 ——————————————————————-

Local and Network Accuracy Data for NGS Datasheets – EA0875
Program lna_ret Version 2.7 Date April 6, 2015National Geodetic Survey, Retrieval Date = JUNE 30, 2015
EA0875 **********************************************************
EA0875 ACCURACIES – Complete network and local accuracy information.
EA0875 DESIGNATION – LILIPUT
EA0875 PID – EA0875
EA0875
EA0875 Horiz and Ellip are the horizontal and ellipsoid height accuracies
EA0875 at the 95% confidence level per Federal Geographic Data Committee
EA0875 Geospatial Positioning Accuracy Standards. SD_N, SD_E and SD_h are
EA0875 the standard deviations (one sigma) of the coordinates (NETWORK) or
EA0875 of the difference in the coordinates (LOCAL) in latitude, longitude
EA0875 and ellipsoid height. CorrNE is the (unitless) correlation
EA0875 coefficient between the latitude and longitude components of either
EA0875 the coordinate (NETWORK) or coordinate difference (LOCAL). Dist is
EA0875 the three-dimensional straight-line slope distance, in km, between
EA0875 station EA0875 and the corresponding local station. Local stations
EA0875 are stations processed simultaneously in a session regardless ofEA0875 distance.EA0875EA0875 Accuracy and standard deviation values are given in cm.EA0875EA0875 Type/PID Horiz Ellip Dist(km) SD_N SD_E SD_h CorrNE

EA0875 ——————————————————————-

EA0875 NETWORK 0.86 1.53 0.36 0.34 0.78 -0.07097297

EA0875 ——————————————————————-

EA0875 LOCAL (008 points):

EA0875 DG8640 0.80 1.33 5.44 0.33 0.32 0.68 -0.10635889

EA0875 EA0665 0.71 1.16 5.66 0.29 0.29 0.59 -0.11539688

EA0875 DG8641 0.75 1.22 6.58 0.31 0.30 0.62 -0.12427053

EA0875 EA0883 1.02 1.78 7.67 0.44 0.39 0.91 -0.02887498

EA0875 DG8644 0.73 1.23 11.49 0.31 0.29 0.63 -0.06563537

EA0875 EA0580 1.22 2.18 11.99 0.54 0.45 1.11 -0.01379332

EA0875 AB6778 0.83 1.39 16.10 0.35 0.33 0.71 -0.09147814

EA0875 EB0173 0.89 1.51 17.16 0.38 0.35 0.77 -0.06596524

EA0875

EA0875 MEDIAN 0.81 1.36 9.58

I haven’t discussed all procedures documented in NGS 58 here. There are other minor, but very important, procedures that the user must follow, such as use of precise ephemerides, taking a rubbing of the mark; the reader is referred 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 column discussed procedures that need to be followed to detect, reduce and eliminate error sources to estimate accurate GNSS-derived ellipsoid heights. Analysis of the quality of project data should be based on repeatability of measurements, adjustment residuals and analysis of loop closures. Please be aware that repeatability and loop closures do not always disclose all problems, and that is why it is important to adhere to the procedures outlined in NGS’ publications.

It is important to understand geoid models when estimating GNSS-derived orthometric heights. The user should understand the differences between NGS’ scientific gravimetric geoid model and hybrid geoid models, and why it is important to use both types of geoid models in an analysis. As I mentioned in Part 1, the latest NGS hybrid geoid model, Geoid12B, is made consistent with the published NAVD 88 heights. This means you will be consistent with NAVD 88 when using GEOID12B to estimate GNSS-derived orthometric heights. However, this doesn’t guarantee that your GNSS-derived orthometric heights are accurate. NGS’ new Beta experimental geoid height model xGEOID14B is not distorted to fit the published NAVD 88 heights so it is useful for identifying valid NAVD 88 benchmarks. In my next column, I’ll address how to use these geoid models and published NAD 83 (2011) ellipsoid heights to evaluate potential issues with published NAVD 88 heights.

Figure 1. NAD 83 (2011) Ellipsoid Network Accuracies – units cm (Network accuracies were obtained from NGS datasheets).

Figure 1. NAD 83 (2011) Ellipsoid Network Accuracies – units cm (Network accuracies were obtained from NGS datasheets).

Figure 2. NAD 83 (2011) Network Design for Stations EA0873 and EA0875. [Note: GNSS Vectors for GNSS projects GPS 1588 and GPS 2057 were provided by NGS].

Figure 2. NAD 83 (2011) Network Design for Stations EA0873 and EA0875. [Note: GNSS Vectors for GNSS projects GPS 1588 and GPS 2057 were provided by NGS].

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