From the Ground Up: Accurate Elevations from GPS.
It is true that GPS elevations are less accurate than the horizontal positions gained from GPS. In fact, GPS elevations generally have two to three times the error of horizontal positions gained from GPS. Even so, there is a tremendous value to the elevations provided by precise, carrier-phase GPS observations. These elevations have many uses in the surveying, mapping and engineering arenas.
Technological ImprovementsIf GPS can serve as a useful tool in establishing control elevations, why is there so much debate about the issue? The accuracy of GPS elevations is dependent on a number of factors, including the:
- accuracy of the baselines gained from the GPS observations;
- accuracy of the geoid model used in the conversion to orthometric heights;
- accuracy of the antenna height measurement above observation points; and the
- number, accuracy and geometric location of vertical control points within the network.
Much of the debate arises from factors that influenced the accuracy of GPS elevations during the early years of the system. During these years, carrier-phase receivers were single frequency, the number of operational satellites was significantly less than the full complement of 27 that we have today, and the geoid models available were less accurate than today's models. Each of these factors has a significant impact on the accuracy of GPS elevations.
Dual-frequency GPS receivers are common today. They have significant advantages over their single frequency counterparts. By tracking both GPS frequencies (L1 and L2), a receiver is able to accurately determine the atmospheric effects and remove their impact from the GPS signal.
Additionally, many of today's receivers are equipped with improved technology including effective multipath rejection and the ability to track weak satellite signals. We benefit through increased accuracy.
The number of satellites tracked by the receiver is also an important factor impacting accuracy. GPS achieved a full constellation of 24 satellites in June 1993 and Initial Operation Capability was declared by the Department of Defense later that year. (Today we actually have 27 operational GPS satellites.) Why is this important? Baseline accuracy improves as a receiver tracks more satellites. GPS observations result in elevations referenced to a mathematically perfect ellipsoid surface. An elevation referenced to this ellipsoid is known as a height above ellipsoid, or HAE. Mapping and surveying professionals, however, require elevations referenced to the geoid surface. These elevations are technically known as orthometric elevations. You may refer to them as "mean sea leve" elevations.
Geoid modeling provides us with the ability to accurately convert from ellipsoid to orthometric heights. A geoid model describes the vertical difference between the ellipsoid and geoid surfaces. The National Geodetic Survey (NGS) recently released its latest model, GEOID99. Earlier models included GEOID96, GEOID93, etc. Each new model has provided improvements over earlier versions and, therefore, better accuracy for the orthometric elevations gained from GPS.
Accuracy EvaluationOne of the best ways to evaluate the accuracy of elevations derived from survey grade GPS observations is to examine the results from actual projects. In a recent control survey completed for the Kentucky Transportation Cabinet (KTC) in Meade County, Ky., the control was performed for the mapping of a section of new roadway. The GPS network encompassed an area extending approximately 15 miles along the new roadway corridor. In addition to providing photo control positions for the mapping of the project area, the control points will be used for the design and construction surveys that follow.
The GPS network was established as a strong geometric figure with considerable redundancy (Figure 1). Only independent baselines were processed with the GPS software. Dual-frequency Trimble 4000 SSI receivers (Trimble Navigation Ltd., Sunnyvale, Calif.) were used. One-hour static observations were employed for the longer baselines. Rapid static sessions lasting 25 minutes were used for all remaining baselines.
At the same time, differential levels were used to establish precise elevations on 60 of the 126 network points. A Leica NA2002 (Leica Geosystems Inc., Norcross, Ga.) digital level was used for all level runs. Third order procedures were used. Two NGS first order, Class II benchmarks provided the control for the level runs.
The project environment was ideal for the comparison of differential versus GPS elevations since so many network points had elevations established by differential levels. In the initial analysis, only one of the 60 known vertical points was held in the network adjustment. For the final evaluation of the vertical accuracy, six of the 60 network points were held fixed within the GPS network. In both cases the remaining known vertical points were allowed to "float" within the final solution. The orthometric elevations derived from the GPS network for these points were then compared to the elevations gained from the differential level runs. The differences between the two sources of elevation data are detailed in the analysis.
Minimally Constrained AdjustmentThe integrity and reliability of a GPS network can be evaluated by performing a minimally constrained adjustment and comparing the values of all known control points used in the network with their positions obtained from the GPS network. In a minimally constrained adjustment, only one horizontal and one vertical control point are held fixed. The position of all other network points is determined from the GPS observations.
In the case of the Meade County project, the horizontal position of a Kentucky High Accuracy Reference Network (HARN) point and the vertical position of one of the known vertical points lying near the center of the project were held fixed in the minimally constrained adjustment.
The minimally constrained adjustment proved the network would provide reliable position data. The vertical differences between the GPS elevations and the elevations derived from the differential level runs ranged from -0.13 to +0.21'. These results were very strong considering one point was used to control a network extending some 15 miles in length. The distribution of the vertical differences is shown in Figure 2.
While these results are impressive, any control network must make use of more than one fixed horizontal and vertical control point. In fact, the Federal Geodetic Control Committee (FGCC) requires a minimum of two horizontal and four vertical control points in a final network adjustment for C-order (the lowest order) GPS control.
Final Adjustment and EvaluationFor the final evaluation, both known horizontal and six vertical control points were held fixed in the final network adjustment (Figure 3). Since differential elevations were established at 60 network points, 54 points were used in the evaluation of the vertical accuracy.
Again the differences between the differential and GPS elevations were determined. As expected, these differences improved substantially from those found in the minimally constrained adjustment. The differences ranged from -0.08 to +0.09' as shown in Figure 4.
The standard deviation of the vertical differences was 0.04'. Theoretically, 68 percent of the differences will fall within plus or minus one standard deviation (this is known as the one sigma error). In other words, we should expect 68 percent of our GPS elevations to fall within 0.04' of their true elevation. The probability increases to 95 percent at the two sigma level (two standard deviations). In other words 95 percent of the GPS elevations should fall within 0.08' of their true elevation. In this example, only one of the GPS elevations differed by more than 0.08'.
ConclusionThe results from this project were especially enlightening. Admittedly, these results are from a single project. They are, however, typical of many other precise GPS control networks that I have worked with using the same GPS planning and observation methodology. What conclusions can be drawn? Elevations derived from GPS observations are sufficiently accurate for even the most demanding photogrammetric mapping projects. Moreover, GPS elevations are appropriate for many other control applications in the surveying and engineering arenas.
Perry Semones, survey coordinator for the KTC, knows the value of GPS elevations. "We have a lot more confidence in vertical components obtained from GPS today," he said. "The results can be truly amazing when the technology is applied correctly."