Orbit performance measured by orbit overlaps

One gauge of the fidelity of the resultant geopotential models is to calculate the RMS difference in position between successive overlapping arcs. Three sets of overlaps were used:

1. Twelve overlaps of thirteen 30-hour arcs in February 1999. These arcs overlapped by six hours, and adjusted a drag coefficient (C_d) every eight hours, a solar radiation reflectivity coefficient (C_r), the spacecraft state, and the empirical accelerations for the AMD events (see Table 4).

2. Six overlaps of five to six day arcs in March 1999. These arcs adjusted a C_d per day, a C_r per arc, the spacecraft state, the empirical accelerations for the AMD events, and an empirical along-track acceleration per day (see Table 5). The overlaps average 2022 minutes in length, and on average 20 to 25 percent of each arc are in each pair of overlaps.

3. Eight overlaps of five to six day arcs in April through June 1999 (see Table 6). These arcs adjusted the same set of parameters as the arcs in the March 1999 overlap tests. These data are always independent (not included in the solution), whereas the data in February and March 1999 may or may not be independent, depending on the solution tested (see Table 3). These arcs are not as high quality as the arcs in February and March 1999 since (a) only a mean measurement offset was applied for the High Gain Antenna after deployment, and (b) the tracking data show evidence of greater noise following HGA deployment.

   
   

   Table 4: MGS Orbit Overlaps in February 1999
   Model	Orbit Overlap Differences (m)1
   	Radial	Cross-track	Along-track	Total
   MGM0890	41.72	10034.	432.98	10049.
   MGM0890I	1.98	200.92	10.46	201.32
   MGM0964C5A	0.80	220.86	7.65	221.10
   MGM0964C18	0.35	77.88	3.40	78.04
   MGM0964C20	0.18	42.64	2.02	42.72

   ¹ Average RMS of 12 overlaps.
   
   
   

   
   

   Table 5: MGS Orbit Overlaps in March 1999
   Model	Orbit Overlap Differences (m)1
   	Radial	Cross-track	Along-track	Total
   MGM0890	38.53	196.56	156.53	266.23
   MGM0890I	7.82	33.37	24.09	45.54
   MGM0964C5A	2.28	20.30	6.74	22.68
   MGM0964C18	1.34	19.84	5.51	21.06
   MGM0964C20	0.60	5.28	2.01	6.26

   ¹ Average RMS of six overlaps.
   

   
   

   
   

   Table 6: MGS Orbit Overlaps after HGA deployment
   Model	Orbit Overlap Differences (m)1
   	Radial	Cross-track	Along-track	Total
   MGM0890I	11.89	113.48	234.80	263.01
   MGM0964C5A	6.07	24.55	52.01	58.35
   MGM0964C18	5.52	21.32	39.33	45.54
   MGM0964C20	5.23	8.59	24.76	27.12

   ¹ Average RMS of eight overlaps in April, May and June 1999
   

   
   
   
   For consistency in these tests, all the results reported in Tables 4, 5 and 6 used the improved and refiltered solar array and spacecraft quaternions, even though the normals of the February and March 1999 data that contributed to the MGM0890I, MGM0964C5A, and the MGM0964C18 solutions used the first cut, unfiltered quaternions. The overlaps show that the weight selected for the tracking data plays an important role. Earlier solutions weighted the data too pessimistically at 7.14 mm/s (0.1 Hz). The X Band Doppler data have a precision of 0.1 mm/s, or better. Upweighting the data to 0.36 mm/s (0.01 Hz), as in the MGM0964C18 and in MGM0964C20 (see Table 3) allows these data to contribute more fully to the geopotential solution. The improvement observed with the MGM0964C20 field (in comparison to the antecedent solution, MGM0964C18) is due both to the reiteration, and also to the careful refiltering and reconstruction of the quaternions. Using the first set of quaternions (unfiltered) resulted in average overlaps using MGM0964C18 for the February data of 0.46 m in the radial direction, 108.84 m cross-track, 3.72 m along-track, and 109.05 m in total position. So simply switching quaternion sets improved the orbits (as reported in Table 4, the average radial overlap for the February data with the refiltered quaternions and MGM0964C18 is 0.35 m in the radial direction, and 78.04 m in total position). However, the second order improvement occurred with the development of the MGM0964C20 model. Nonconservative force mismodelling that had compromised the earlier solutions was removed in MGM0964C20.

   The radial orbit overlaps with the latest MGM0964C20 solution in February and March 1999 are on average only a tens of cm. The dramatic radial consistency of the orbits is due not just to the fidelity of the gravity solution, but also the observing geometry. In February and March 1999 the tracking body (the Earth) was located from -4 to +14 above the MGS orbit plane. Thus, the MGS orbit was nearly edge-on as seen from the Earth. This edge-on geometry was propitious for maximizing the sensitivity to the Doppler data and to the determination of the MGS orbit in the radial direction. The overlaps are overall better in March (see Table 5) rather than in February 1999 (see Table 4). The adjustment of extra empirical accelerations in March 1999 compensates for the sparser tracking.

   The overlaps are not shown following HGA deployment for the MGM0890 field (see Table 6). It is encouraging, that even with independent data (none of the post-HGA deployment data were used in the geopotential solutions), the total consistency of the orbits in all directions shows the same trends as the overlaps in February and March 1999.