Establishing orthometric heights using GNSS — Part 4

Part 1 of this series appeared in the June Survey Scene newsletter, Part 2 appeared in the August newsletter, and Part 3 appeared in the October newsletter. Upcoming Survey Scene newsletters will carry additional columns in this series.

Basic Procedures and Tools for Ensuring GNNS-Derived Ellipsoid Heights Meet the Project’s Desired Accuracy

David B. Zilkoski

In Part 1 of this series, I discussed the basic concepts of GNSS-derived heights; the article discussed the three types of heights involved in determining GNSS-derived orthometric heights: ellipsoid, geoid, and orthometric.

Part 2 discussed guidelines for detecting, reducing, and/or eliminating error sources in ellipsoid heights. It focused on guidelines for establishing accurate ellipsoid heights in a local geodetic network. It discussed procedures that need to be followed to detect, reduce, and/or eliminate error sources to estimate accurate GNSS-derived ellipsoid heights, and procedures for evaluating published NAD 83 (2011) ellipsoid heights.

Part 3 in this series described the differences between a scientific gravimetric geoid model and a hybrid geoid model, and why it is important to use both geoid models in your analysis. It highlighted that the latest published United States National Geodetic Survey (NGS) hybrid geoid model, Geoid12B, is made consistent with the United States national vertical height reference frame, that is the North American Vertical Datum of 1988 (NAVD 88). It emphasized that this means a user will be consistent with NAVD 88 when using GEOID12B to estimate GNSS-derived orthometric heights, but it doesn’t guarantee that your GNSS-derived orthometric heights are accurate. It demonstrated how to use these geoid models and ellipsoid heights to identify potential issues with published NAVD 88 heights.

This column (the fourth in this series) will focus on basic procedures and tools that should be used to establish accurate GNSS-derived ellipsoid heights for a project. It will provide basic procedures for ensuring a project’s GNSS-derived ellipsoid heights are meeting the desired accuracy. The accuracy of the adjusted ellipsoid heights must be evaluated first, so if there is an issue with the difference between the GNSS-derived orthometric height and published NAVD 88 height, the user will know if the ellipsoid height or the orthometric height is the problem.

NGS has developed guidelines that address the establishment and densification of vertical control networks through the use of GNSS surveys and valid NAVD 88 orthometric control. NGS has documented these procedures in NOAA Technical Memorandum NOS NGS-59, titled “Guidelines for Establishing GNSS-derived Orthometric Heights (Standards: 2 cm and 5 cm). The document provides basic rules and procedures that need to be adhered to for computing accurate NAVD 88 GNSS-derived orthometric heights. However, before we can validate NAVD 88 height constraints used to estimate GNSS-derived orthometric heights, we first need to ensure that the GNSS-derived ellipsoid heights are accurate to the desired requirements. It is impossible to describe all situations in a short newsletter, so this column will address the basic procedures with a few caveats.

Validating Your GNSS Survey Project’s Ellipsoid Heights

Part 2 discussed guidelines for detecting, reducing and eliminating error sources in ellipsoid heights (NGS 58). It focused on evaluating published NAD 83 (2011) ellipsoid heights. This column will discuss a few basic procedures for analyzing a GNSS project’s data to ensure the desired ellipsoid height accuracy standard has been met.

GNSS data can be evaluated by analyzing repeat baseline differences, network loop closures and residuals from a minimum-constraint least-squares adjustment. It was noted in the second article that if GNSS users follow the NGS guidelines, they will reduce and/or eliminate errors in ellipsoid heights and, at a minimum, they will detect problems or errors in data. It was also mentioned that the basic concepts are very simple, but they all need to be followed exactly as prescribed. For example, “the observing scheme for all stations requires that all adjacent stations (baselines) be observed at least twice on two different days and at two different times of the day.”

GNSS can provide “absolute” and relative positioning information much easier, faster and more precisely than some classical techniques. However, the wrong station can still be occupied, the height of the antenna can be measured wrong or incorrectly entered during the baseline reduction processing phase, the receiver can malfunction, an abnormal atmospheric condition can cause large errors in the height component, or some “unknown Gremlin” can be causing an error source.

Classical techniques of establishing horizontal and vertical control used networks that consisted of many loops, triangles and braced quadrilaterals. This design provided enough redundant observations to detect data outliers. NGS guidelines for establishing GNSS-derived heights were designed with this same concept in mind. Since all baselines must be repeated and adjacent station observed, analyzing repeat baseline differences, loop closures and residuals from minimum-constraint least-squares adjustments are very effective analysis tools for detecting data outliers.

Comparing Ellipsoid Height Differences from Repeat Baselines

This procedure is very simple: subtract one ellipsoid height difference from another, for instance, the ellipsoid height difference from baseline A to B on day 1 minus the ellipsoid height difference from baseline A to B on day 2. If this difference is greater than 2 cm, one of the baselines must be observed again. Comparing ellipsoid height differences from repeat baselines is a very simple procedure, but it’s also one of the most important. Many users complain about having to repeat baselines, but requiring an extra occupation session in the field can often save many days of analysis in the office. In addition, repeating the baseline provides the redundancy necessary to obtain the desired relative accuracy of the survey (that is, repeat measurements help to derive a more accurate result than a result derived from a single measurement).

Figure 1 depicts the network design of a 2015 North Carolina Geodetic Survey (NCGS) GNSS Height Modernization Project. The data from this GNSS project was provided to me by the North Carolina Geodetic Survey (James G. Gay, chief of Western Field Operations, North Carolina Geodetic Survey, Division of Emergency Management/Risk Management, North Carolina Department of Public Safety, 2090 US 70 Highway, Swannanoa, NC 28778). It should be noted that these results should be considered preliminary and have not been finalized by NCGS personnel. This is an excellent example of a GNSS project that followed the guidelines outlined in NGS 58. The network design includes short baselines with many loops. The average length of baselines is 2.9 km, the maximum baseline is 13.5 km, and there are 465 baselines connected to 182 stations. All baselines were repeated, making the analysis easy.

Figure 1. Plot depicting the Network Design of the NCGS Rowan County Height Modernization GNSS Project.

Figure 2 is a plot of the differences between repeat baselines. First, it should be noted that most baselines are less than 5 km and most repeat baselines differences are less than +/- 2 cm. There are some outliers, which is not unusual when performing GNSS surveys even when following all guidelines outlined in NGS 58. What is important is that these outliers are identified, and then additional observations are performed to meet the guidelines and obtain the desired accuracy of the survey.

The repeat baseline procedure helps to identify these outliers such as the baselines highlighted in figure 2. As noted in figure 2, the largest outliers are on two different baselines. These baselines should be re-observed to meet the NGS 58 guidelines. The requirement is to repeat the baseline on different days and at different time of the day. The reason for the requirement is to get two observations under different conditions and different satellite geometry. The user needs to determine which baseline is the outlier so he can ensure that he has two baselines with different satellite geometry. When a network is properly designed with short baselines and many loops, the results from a minimum-constraint least-squares adjustment can help identify the outlier.

Figure 2. Plot of repeat baselines for the NCGS Rowan County Height Modernization GNSS Project (does not include re-observations of repeat baselines that did not meet the 2 cm guideline).

Analyzing Loop Closures

Loop closures can be used to detect “bad” observations. If two loops with a common baseline have large closures, this may be an indication that the common baseline is an outlier. The following statement appeared in Part 2: “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.”  So why is it okay to use loop closures now?

Since users must repeat baselines on different days and at different times of the day, there are several different loops that can be generated from the individual baselines. If a repeat baseline difference is greater than 2 cm, then comparing the loop closures involved with the baseline may help determine which baseline is the outlier. As previously stated, according to NGS 58 guidelines, if a repeat baseline difference exceeds 2 cm, one of the baselines must be observed again, and baselines must be observed at least twice on two different days and at two different times of the day. If it can be determined which baseline is the potential outlier, the user will know which time of the day to re-observe the baseline. Therefore, loop closures can be very helpful in isolating errors when the user followed all of the guidelines outlined in the NGS 58 document.

Plotting Ellipsoid Height Residuals from Least Squares Adjustments

It is important that during the analysis of the GNSS-derived ellipsoid heights, the user performs a minimum-constraint least-squares adjustment and identifies potential outliers. This ensures that the GNSS-derived ellipsoid heights meet the user’s desired standards. This is not a complex procedure if the user knows how to perform a least-squares adjustment of GNSS data. Explaining least-squares adjustments is beyond the scope of this column. Today, most GNSS manufacturers provide support software that includes performing least-squares adjustments. NGS also provides software tools for validating data formats and performing adjustments. These tool can be found here. I used these tools to analyze and adjust the survey data of the Rowan County GNSS Height Modernization Project.

If users follow NGS guidelines and evaluate all repeat baselines, the adjustment results should confirm what has already been determined. For example, if a repeat baseline indicates a large difference between two vectors, then typically one of the residuals of one baseline should be larger than the other. Following NGS guidelines usually provides enough redundancy for the adjustment process to detect outliers and usually apply the residual to the appropriate observation, that is, the bad vector.

Like comparing repeat baselines, analyzing ellipsoid height residuals is also important. During this procedure, the user performs a 3D minimum-constraint least-squares adjustment of the GNSS survey project (constrain one latitude, one longitude and one ellipsoid height), plots the ellipsoid height residuals, and investigates all residuals greater than 2 cm.

Figures 3 and 4 depict the dU residuals from a least-squares adjustment of the Rowan County Height Modernization Project. NGS’ adjustment program provides the vector residuals in dX, dY and dZ; and dN, dE and dU (local geodetic horizon coordinate system). dU residuals are not the same as dh residuals, but for all practical purposes can be analyzed just like dh residuals. Looking at Figures 3 and 4, a few items should be noted. First, all dU residuals are less than 2 cm except for five baselines. Four of the five baselines had repeat baselines that exceeded the 2 cm repeat baseline requirement (see Figure 2). For example, the plot of repeat baseline differences indicated that baseline between station 296 and 442 disagreed by 5.25 cm (see Figure 2). The plot of dU residuals (Figure 4) from the least-squares adjustment shows that one of the baseline’s residual is -4.4 cm and the other is 0.9 cm. The adjustment results are indicating which baseline needs to be re-observed to meet the guideline’s requirement of repeat baselines on two different days at two different times of the day. That’s all there is to it, when the user follows NGS guidelines exactly as prescribed.

Figure 3. Plot depicting absolute dU residuals from the NCGS GNSS Height Modernization Project (does not include re-observations of repeat baselines that did not meet the 2 cm guideline).

Figure 4. Plot of all residuals from the NCGS Rowan County GNSS Height Modernization Project (does not include re-observations of repeat baselines that did not meet the 2 cm guideline).

The reader may have noticed that one large residual on the residual plot, baseline 442 to 253 (11.5 km), did not show up as a large different on the repeat baseline plot. There are several reasons why this could occur. For example, the stations involved in the baseline are not adjacent stations, so the baseline wasn’t repeated; the repeat baseline closure was large, but not greater than 2 cm; or the pair of stations are involved with many vectors and the one vector is inconsistent with the other vectors. Regardless of the reason, if there’s enough redundant observations to and from a station and the repeat baselines don’t indicate a problem, then the adjustment is doing what it’s designed to do; that is, detecting outliers and reducing their influence on the final adjusted height. In this particular case, the repeat baseline closure between stations 442 and 253 was 1.84 cm, which meets the NGS 58 guideline of 2 cm. The adjustment uses all of the data to determine the best set of coordinates. Based on the repeat baselines and loops surrounding the two stations, the adjustment indicated that one of the vectors fits better with the other vectors surrounding the two stations. Per the requirement of NGS 58 guidelines, the NCGS re-observed all five baselines with large residuals.

After all outliers are detected and removed from the adjustment, the user should compare the adjusted ellipsoid heights with the latest published ellipsoid heights, that is, NGS published NAD 83 (2011) ellipsoid heights. Figures 5 and 6 are plots of the adjusted ellipsoid heights from a minimum-constraint least-squares adjustment minus the NAD 83 (2011) ellipsoid heights. Since this was a minimum-constraint adjustment (that is, only one latitude, one longitude and one ellipsoid height value were constrained), a bias shift based on the average differences was removed from all differences. Most of the differences agree within +/- 2 cm. There are several that are greater than +/- 2 cm, but only one is greater than +/- 4 cm.

As mentioned in Part 2, many of the older GPS survey projects that were part of the NAD 83 (2011) network adjustment were not Height Modernization projects and were not performed following the NGS 58 guidelines. That is, most baselines are greater than 10 km and were not repeated. Therefore, in my opinion, many of the published ellipsoid heights local-height accuracies may be optimistic. The user should consider this when determining whether their results are more accurate than the published values. NGS’ Constrained Adjustment Guidelines for incorporating GNSS project data into NAD 83 (2011) state, “As a general rule, if the adjusted values of the constrained coordinates of a station shift by more than 2 cm horizontally and/or 4 cm in height, its horizontal coordinates and/or ellipsoid height, respectively, should be unconstrained.”

The stations that have height differences greater than 4 cm should be investigated. In addition, stations that have large relative height differences (greater than 4 cm) between closely spaced neighbors should also be investigated. For example, station Jockey’s difference is 3.6 cm, and two of its neighbors’ differences are only -0.5 cm. The relative difference exceeds 4 cm [3.6 cm – (-0.5 cm)] between two closely spaced stations.

Figure 5. Plot of adjusted ellipsoid height minus published NAD 83 (2011) Ellipsoid Heights (the number is the difference for that particular station; units = cm).

Figure 6. Plot of adjusted ellipsoid height minus published NAD 83 (2011) published heights.

It is important to understand the quality of the adjusted ellipsoid heights. When analyzing the project’s ellipsoid heights, the user should compute the local ellipsoid height accuracy values. Part 2 discussed NAD 83 (2011) network and local accuracies. NGS’ adjustment program has an option of computing network and local accuracy values.

Figures 7 and 8 are plots of NCGS Rowan County GNSS Height Modernization median local ellipsoid height accuracy values. Stations that have local ellipsoid height accuracy values greater than 2 cm should be investigated. Figure 7 highlights the two largest median local ellipsoid height values [Camping (3.19 cm) and Buffalo 2 (2.46 cm)]. The observations and residuals of the baselines in the area should be closely analyzed.

Figure 8 is a plot of the local ellipsoid height accuracy value with the absolute dU residual values. If the user follows all of the NGS 58 guidelines, then all baseline residuals should be small (less than 2 cm). In this project, the largest “dU” residual is 1.86 cm. Saying that, the network design could be modified to try to improve a station’s median local ellipsoid height accuracy value.

For example, station Buffalo 2 has a median local ellipsoid height accuracy value of 2.46 cm (see Figure 7). It’s only involved in one loop, and it’s relatively large. The loop has five baselines consisting of lengths of 13.5 km, 9.8 km, 7.9 km, 4.6 km and 0.7 km. Two of the baselines lengths are greater than the guideline’s average baseline recommendation of 7 km, but all repeat baselines meet the 2 cm guidelines, and all residuals are “reasonable.” Adding another baseline between two different stations to create two smaller loops from the one larger loop would decrease the size of the loop and increase the redundancy in the network.

In this particular case, station Buffalo 2 has a published NAD 83 (2011) ellipsoid height, and the difference between the adjusted height and the published height is only 1.1 cm (Figure 5), indicating the new survey is consistent with the old survey. Station Camping also has a published NAD 83 (2011) ellipsoid height, and the difference between the adjusted ellipsoid height and published height is -1.9 cm (Figure 5). Once again, this indicates that the Rowan County GNSS survey is consistent with the previous survey.

This column focused on describing procedures for analyzing a project’s GNSS-derived ellipsoid heights. As previously stated, it important to ensure that your GNSS-derived ellipsoid heights meet the desired accuracy of the project before using the survey data to estimate GNSS-derived orthometric heights.

Figure 7. Plot of NCGS Rowan County Height Modernization project’s median local ellipsoid height accuracy values.

Figure 8. Plot of NCGS Rowan County Height Modernization project’s median local ellipsoid height accuracy values and absolute dU residuals.

So far, this series has addressed the following topics:

• basic concepts of GNSS-derived heights
• NGS’ guidelines for establishing GNSS-derived ellipsoid heights (NGS 58)
• differences between hybrid and scientific geoid models, and
• procedures and tools for detecting GNSS-derived ellipsoid height data outliers.

These four columns were meant to provide the reader with basic concepts and procedures for estimating GNSS-derived ellipsoid heights.

My next column, which will appear in the February 2016 Survey Scene newsletter, will discuss procedures for estimating GNSS-derived orthometric heights. Determining valid NAVD 88 published heights is very important when using GNSS data and geoid models to estimate GNSS-derived orthometric heights. NGS has documented these procedures in NOAA Technical Memorandum NOS NGS-59. The NGS 59 guidelines are separated into three basic rules, four control requirements and five procedures that need to be adhered to for computing accurate NAVD 88 GNSS-derived orthometric heights. The next column will address the NGS 59 guidelines.