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GOCE orbit determination
To derive a highly precise gravity field from the GOCE gradiometer data, accurate information about the satellite's orbit is mandatory. On the one hand this information is necessary to assign the actual position to the gradiometer data and on the other hand the differences between the real orbit and an ideal one (not affected by the gravity field) are used to determine the long-wave part of the GOCE gravity field.
For the GOCE orbit determination observations of one of the two GPS antennas onboard GOCE will be used.
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| Fig. 1: One of the two GPS antennas onboard GOCE (© ESA). |
Two different methods are used for the GOCE orbit determination:
- Kinematic orbit determination: for every epoch (every single second) the three components of the satellite position and the receiver clock error are estimated from the GPS observations.
- Reduced-dynamic orbit determination: To estimate the orbit for a period of 30 hours the initial Keplerian elements and additional disturbing accelerations are estimated in a least-squares-adjustment. In addition, for every epoch (every 10 seconds) a receiver clock error has to be determined.
The GOCE orbit determination is computationally intense due to the amount of estimated parameters and the number of observations. For the determination of a 30-hour arc from a test dataset the following number of parameters has to be estimated:
|
|
kinematic |
reduced-dynamic |
|
Ambiguities |
530 |
530 |
|
Receiver clock errors |
107879 |
10779 |
|
Coordinates |
323637 |
--- |
|
Orbit parameters |
--- |
909 |
|
Number of parameters |
432046 |
12218 |
|
Number of observations |
971019 |
97022 |
The processing of a 30-hour arc (kinematic and reduced-dynamic) is performed within about 90 minutes on one node of the LRZ Linux Cluster.
Three different methods can be used to get an estimate for the accuracy of the estimated satellite orbits:
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Differences between kinematic and reduced-dynamic
satellite orbits:
As can be seen from Fig. 2, the 3D-RMS is about 10 mm for a 30-hour arc.
 |
| Fig. 2: Orbit differences (kinematic minus reduced-dynamic) |
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Comparison of the overlaps of two subsequent arcs:
Due to the computation of 30-hour arcs for each day a 6-hour overlap can be used to compare orbits of two subsequent days. As can be seen from Fig. 3, the 3D-RMS for 6 hours of overlap is clearly below 10 mm.
 |
| Fig. 3: Orbit differences (overlaps) |
- Validation with satellite laser ranging: With a cornercube onboard GOCE it is possible to determine the ranges between terrestrial ground stations and GOCE by laser ranging. These ranges can be used to compute residuals which can show possible systematic errors within the orbit determination process.
Further reading: Bock H, Jäggi A, Svehla D, Beutler G, Hugentobler U, Visser P - Precise orbit determination for the GOCE satellite using GPS - Advances in Space Research 39(10): 1638-1647, 2007, DOI: 10.1016/j.asr.2007.02.053
Contact: Markus Heinze
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