By Theresa Diehl
The National Geodetic Survey (NGS) has issued a “Kinematic GPS Challenge” to the community in support of NGS’ airborne gravity data collection program, called Gravity for the Redefinition of the American Vertical Datum (GRAV-D). The “Challenge” is meant to provide a unique benchmarking opportunity for the kinematic GPS community by making available two flights of data from GRAV-D’s airborne program for their processing. By comparing the gravity products that are derived from a wide variety of kinematic GPS processing products, a unique quality assessment is possible.
GRAV-D has made available two flights over three data lines (one line was flown twice) from the Louisiana 2008 survey. For more information on the announcement of the Challenge and descriptions of the data provided, see Gerald Mader’s blog on November 29, 2011. The GRAV-D program routinely operates at long-baselines (up to 600 km), high altitudes (20,000 to 35,000 ft), and high speeds (up to 280 knots), a challenging data set from a GPS perspective. As of December 2011, ten groups of kinematic GPS processors have provided a total of sixteen position solutions for each flight. At two data lines per flight, this yielded 64 total position solutions. Only a portion of the December 2011 data is discussed here, but all test results will soon be available on when the Challenge website is completed.
Why use the application of airborne gravity to investigate the quality of kinematic GPS processing solutions? Because the gravity measurement itself is an acceleration, which is being recorded with a sensor on a moving platform, inside a moving aircraft, in a rotating reference frame (the Earth). The gravity results are completely reliant on our ability to calculate the motion of the aircraft— position, velocity, and acceleration. These values are used in several corrections that must be applied to the raw gravimeter measurement in order to recover a gravity value (Table 1). The corrections in Table 1 are simplified to assume that the GPS antenna and gravimeter sensor are co-located horizontally and offset vertically by a constant, known distance.
Table 1. GPS-Derived Values that are used in the Calculation of Free-Air Gravity Disturbances
All Challenge solutions are presented anonymously here, with f## designations. For each flight of data, the software that made the f01 solution is the same as for f16, f02 the same as f17, and so on.
Test #1: Are the solutions precise and accurate?
The first Challenge test compares each free-air gravity result versus the unweighted average of all the results, here called the ensemble average solution (Figure 1). This comparison highlights any GPS solutions whose gravity result is significantly different from the others, and will group together solutions that are similar to each other (precise). Precision is easy to test this way, but in order to tell which gravity results are accurate calculations of the gravity field, a “truth” solution is necessary. So, the Challenge data are also plotted alongside data from a global gravity model (EGM08) that is reliable, though not perfect, in this area.
Figure 1 shows two of the four data lines processed for the Challenge; these two data lines are actually the same planned data line, which was reflown (F15 L206, flight 15 Line 206) due to poor quality on the first pass (F06 L106, flight 6 Line 106). The 5-10 mGal amplitude spikes of medium frequency along L106 are due to turbulence experienced by the aircraft, turbulence that the GPS and gravity processing could not remove from the gravity signal.
Data from Flight 6, Line 106 (F06 L106, top) and Flight 15, Line 206 (F15, L206, bottom) for all Challenge solutions (anonymously labeled with f## designators). Figures 1 and 2. Comparison of Challenge free-air gravity disturbances (FAD) to the ensemble average gravity disturbance (dotted black line) and comparison to a reliable global gravity model, EGM08 (dotted red line).
Figures 3 and 4. Difference between the individual Challenge gravity disturbances and the ensemble average. The thin black lines mark the 2-standard deviation levels for the differences. For F15 L206, one solution (f23) was removed from the difference plot and statistics because it was an outlier. For both lines, the ensemble’s difference with EGM08 is not plotted because it is too large to fit easily on the plot.
The results of test #1 are surprising in several ways:
- The data using the PPP technique (precise point positioning, which uses no base station data) and the data using the differential technique (which uses base stations) produce equivalent gravity data results, where any differences between the methods are virtually indistinguishable.
- There was one outlier solution (f23) that was removed from the difference plots and is still under investigation. Also, on F15 L206, solution f28 had an unusually large difference from the average though it performed predictably on the other lines. Of the remaining solutions, four solutions stand out as the most different from all the others: f03/f18, f04/f19, f05/f20, and f07/f22.
- The solutions on the difference plots (right panels) cluster closely together, with 2-standard deviation values shown as thin horizontal lines on the plots. The Challenge solutions meet the precision requirements for the GRAV-D program: +/- 1 mGal for 2-standard deviations.
- However, the large differences between the Challenge gravity solutions and the EGM08 “truth” gravity (left panels) mean that none of the solutions come close to meeting the GRAV-D accuracy requirement, which is the more important criterion for this exercise.
Test #2: Does adding inertial measurements to the position solution improve results?
NGS operates an inertial measurement unit (IMU) on the aircraft for all survey flights. The IMU records the aircraft’s orientation (pitch, roll, yaw, and heading). Including the orientation information in the calculation of the position solution should yield a better position solution than GPS-only calculations, but it was not expected to be significantly better. Figure 2 shows the NGS best loosely-coupled GPS/IMU free-air gravity result versus the Challenge GPS-only results and Table 2 shows the related statistics.
Figures 5 and 6. F06 L105. (Figure 5) Comparison of Challenge FAD gravity solutions (ensemble=black dotted line) with EGM08 (red dotted line); (Figure 6) comparison of Challenge gravity solutions (all GPS-only; ensemble=black dotted line) with NGS’ coupled GPS/IMU gravity solution (red dotted line).
Table 2. Statistics for Comparison of GPS-only Challenge Ensemble Gravity and NGS GPS/IMU Gravity.
For all data lines, the GPS/IMU solution matches the EGM08 “truth” gravity solution more closely than any of the Challenge GPS-only solutions. In fact, the more motion that is experienced by the aircraft, the more that adding IMU information improves the solution. One conclusion from this test is that IMU data coupled with GPS data is a requirement, not optional, in order to obtain the best free-air gravity solutions.
Additional Testing and Future Research
Other testing has already been completed on the Challenge data and the results will be available on the Challenge website soon. Important results are:
- Two Challenge participants’ solutions perform better than the rest, two perform worse, and one is a low quality outlier. The reasons for these differences are still under investigation.
- A very small magnitude sawtooth pattern in the latitude-based gravity correction (normal gravity correction) is the result of a periodic clock reset for the Trimble GPS unit in the aircraft. This clock reset is uncorrected in the majority of Challenge solutions. The clock reset causes an instantaneous small change in apparent position, which results in a 1-2 mGal magnitude unreal spike in the gravity tilt correction at each epoch with a clock reset.
- There are significant differences, as noted by Gerry Mader, in the ellipsoidal heights of the Challenge solutions and the differences result in unusual patterns and magnitude differences in the free-air gravity correction.
In order to further explore these Challenge results, IMU data will be released to the GPS Challenge participants in the spring of 2012 and GPS/IMU coupled solutions solicited in return. Additionally, basic information about the Challenge participants’ software and calculation methodologies will be collected and will form the basis of the benchmarking study.
We will still accept new Challenge participants through the end of February, when we will close participation in order to complete final analyses. Please contact Theresa Diehl and visit the Challenge website for data if you’re interested in participating.