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Doris group calculates orbits to better than 10 cm

F. Nouel, Doris Orbitography group (CNES, France)

Once upon a time a bunch of people thought that the Topex/Poseidon specification for orbital precision would be 13.6 cm!

This was the challenge for us to meet, but six months after the launch we are achieving not only 5 to 8 cm precision but accuracy better than 5 cm!

True, it took us a while to get it right. First, working on the instruments: Doris was designed for precisely that task, and was tested in flight on the Spot-2 satellite. Laser technology was already tried-and-tested and could also be used as a check via a physical measurement close to the specification on the radial component. The GPS demonstration receiver on board Topex/Poseidon is providing its first results, which seem to be compatible.
Then the Doris orbitography software needed to meet the new performance requirements, while the numerical models or orbit determination strategies had to approximate the real trajectory as closely as possible. Let's look at this.

Mathematically, the trajectory can be split into a deterministic part and a random part. Finely-tuned numerical models have been developed, in particular for the terrestrial potential field. When Topex/Poseidon was launched, Nasa's Goddard Space Flight Center (GSFC) and the University of Texas's Center for Space Research (CSR) produced the JGM1 model. Doris measurements on Spot-2 were used to generate it.
Other Doris measurements on Topex/Poseidon will be fed into the model to give JGM2. For forces of non-gravitational origin in the trajectory calculation, Doris, thanks to its extensive orbitography network (40 to 50 beacons) provides a rich data set which can be used to test different strategies on the random part of the calculation so as to follow, as closely as possible, what the measurements tell us. As to the reference systems and station coordinates, Doris on Spot-2 and the co-location of Doris beacons with laser and VLBI at a few special sites provided us with accuracy to within a few centimeters.

On the software side, our Software Intercomparison Plan (SIP) looked at GSFC's Geodyn, CSR's Utopia and the Doris Orbitography Group's Zoom program. The SIP quoted specs in millimeters. The job was long and hard, but gave our orbitography teams the precision they needed on the deterministic part.

All this was made possible by excellent cooperation between the Precise Orbit Determination (POD) teams in the US and France. It involved exchanges of Doris and laser data and comparisons of orbits between the two centers. But to be independent statistically, we still worked separately too.

About two weeks after the end of a Topex/Poseidon cycle, the Doris orbitography group produces a 10-cm orbit from DORIS measurements for production of the Interim Geophysical Data Records (IGDRs). Next comes a thorough examination of how best to calculate this preliminary orbit. Once the group receives certain observed physical parameters such as Earth's rotation parameters or solar activity to calculate the atmospheric density, it is ready to produce and validate the most precise orbit possible from all this data, plus the laser orbit, as input for the GDRs. Special attention must be paid to satellite attitude events, which play an important role in calculating surface forces and produce observable meter-level effects with Doris. Various criteria for validating the results are examined:

  • the orbit calculated over 10 days with Doris is compared with ten one-day orbits.
    The aim here is to detect and correct any long-term effects. But on any particular day the Doris measurements may not be spread equally over time, in which case the one-day ephemeris is less precise than over ten days,
  • with the Zoom software, we calculate a Doris orbit and a laser orbit over ten days. Here too, the spread of the data over time can influence the results. However, this reveals any difference between the two measurement systems,
  • comparing the Nasa/POD ephemeris with the Cnes/POD ephemeris is part of our external criteria. Here also, the computation conditions must be taken carefully into account when interpreting the figures. This avoids producing low-quality orbits, always a risk when a group works alone.

The table below shows the comparisons over the first 15 Topex/Poseidon cycles. They were done during the Verification phase and the figures are likely to change during the Observational phase. Strictly speaking the figures are not comparable as the conditions vary from one cycle to another. However, the table shows that the initial system specifications are met and that the 13.6 cm rms criterion is still satisfied.
We can thus compile statistics.

Following the JVT workshops, it seems that the rms criterion is inadequate, especially since the results are better. Different comparison procedures are being studied so that we can better characterize radial error. They will be applied for the Observational phase and will help us to enhance the statistical information for users.

This centimeter-level work called for close collaboration with our American colleagues, as well as teamwork at Cnes. The last survivors here at Cnes are-I hope I haven't left anyone out-Muriel Deleuze, Adèle Guitart, Philippe Laudet, Alfred Piuzzi and Christophe Valorge.

 

RMS differences in radial orbit error (cm)

Cycle number Doris zoom
10 days / 10 x 1 day.
Doris zoom
Laser zoom
Doris zoom
GSFC Doris + laser
Mean per cycle
1
2
3
4
5
6
7
8
9
10(1)
11
12
13
14
15
Mean
5.0
3.3
4.0
3.7
6.7(2)
7.4(2)
3.2
3.4
3.7

6.0(2)
3.7
3.7
3.3
4.2
4.4
4.5
3.0
2.6
2.2
3.4
5.5
3.5
3.8
4.3

7.6(3)
3.3
2.1
2.9
2.7
3.7
5.0
3.9
4.8
3.8
4.5
6.2
5.8
4.0
5.1

19.9(4)
6.4
5.2
5.9
4.9
4.8 / 8.5
|
|
|
|
| A
|
|
|
|

|
|
| B
|
|
4.8
3.4
3.8
3.2
4.9
6.4
4.2
3.7
4.4

11.2
4.5
3.7
4.0
3.9
4.3 / 5.5
|
|
|
|
| A
|
|
|
|

|
|
| B
|
|
      over cycles "A" / over cycles "B" over cycles "A" / over cycles "B"

Comments:
1 ­ Doris measurements on cycle 10 not processed yet.
2 ­ For cycles 5, 6 and 11 there are major gaps in
Doris coverage, and ephemeris is not as good.
3 ­ No laser measurements for last day of cycle 11.
4 ­ From cycle 11, GSFC ephemeris are those for laser measurements only.

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