Orbit performance measured by altimeter crossovers

Altimeter crossovers from MOLA were used to evaluate the geopotential solutions MGM0890I, MGM0964C5A, MGM0964C18, and the MGM0964C20. The altimeter crossovers have the advantage of being completely independent data, and are globally distributed. Altimeter crossovers were formed for four five to six day arcs from starting on March 7, March 13, March 18, and March 23, 1999. Between 940 to 980 crossovers were computed internally to each arc. No crossovers were formed if telemetered spacecraft quaternions were missing for either the descending or ascending track of a potential crossover point. The modelling of the altimeter crossovers is described in Rowlands et al.[28]. Altimeter crossovers from the highly eccentric orbits in SPO were used to estimate corrections to the preflight measurements of the orientation of the MOLA instrument with respect to the spacecraft frame[6,28]. These new offset values of -0.0028 in roll,and -0.0086 in pitch were simply applied in the current tests with the mapping orbit altimetry. The crossovers are not used in these orbit determination solutions, which were determined solely from the range and the Doppler data for each gravity field model. The crossovers are editted for off nadir pointing angles, as well as the slope and the roughness of the terrain. Large crossover residuals (greater than 80 m) were eliminated. Because of the edit criterion of 80 m, the number of crossovers is not identical in all of the test arcs. The results are tabulated in Table 7 in aggregate for all four arcs. The crossovers show the same trend as the orbit overlaps, and the fits to the Doppler data. The crossover RMS is reduced as the fields are refined, and show the best performance with the MGM0964C20 field.

Table 7: MGS orbit performance measured by altimeter crossovers
Model	Doppler		Crossovers
	No. of obs.	RMS (mm/s)	No. of obs.	RMS (m)
MGM0890I	14,838	18.93	3400	21.04
MGM0964C5A	14,838	1.65	3455	5.61
MGM0964C18	14,838	0.84	3449	5.57
MGM0965C20	14,838	0.53	3455	5.01

It is of interest to see whether the crossovers can still contribute to orbit improvement in the near-circular orbit. Crossovers were processed simultaneously with the Doppler tracking in four arcs of March 1999. Empirical once per revolution along-track accelerations were adjusted daily for these arcs, in addition to a drag coefficient per day, a reflectivity coefficient per arc, and the empirical accelerations for the AMD events. March 1999 is a particularly tough test for the crossovers since the Doppler data - although sparse, are of high quality. In addition, the Doppler data in March 1999 were used in the MGM0964C20 solution. The average RMS overlap is shown in Table 8 for the three overlaps of these arcs.

Table 8: MGS Orbit Overlaps with Altimeter Crossovers
Model	Orbit Overlap Differences (m)1
	Radial	Cross-track	Along-track	Total
No Crossovers	0.59	0.81	1.83	2.17
With Crossovers	0.26	1.40	0.90	1.73

¹ Average RMS of three overlaps for four arcs from March 6, to March 23, 1999

The addition of the crossover data improves the orbits overall, and especially in the radial, and the along-track directions. Some degradation is observed in the cross-track direction. It is especially encouraging that the consistency in the radial direction has been further improved from 0.59 to 0.26 meters. The use of these additional data in the form of altimeter crossovers allows extra empirical parameters to be adjusted - for instance cross-track once per revolution empirical accelerations - that would further improve these orbit consistency results.