Error Analysis

It is useful to project the predicted error from the gravity field covariances to 70x70, and ascertain the formal commission error due to uncertainties in the gravity field on the MGS orbit. These results are summarized in Table 11. The total radial error has decreased from 44 meters with MGM0890 to 8 to 10 cm with the MGM0964C18 and MGM0964C20 models. Similarly, the total error is reduced from 205 meters with MGM0890, to 1.6 to 2.0 meters with the latest MGS derived gravity models. These order of magnitude improvements in the predicted orbit error for MGS beg the question as to how realistic they really are. They certainly are a lower bound, since they omit the contribution of terms higher than degree 70. Unfortunately, other than the orbit overlap tests, we have no means to really test these orbit error predictions.

Table 11: Mars Global Surveyor Predicted Orbit Error
Model	Orbit Error Projections (meters)
	Radial	Cross-track	Along-track	Total
MGM0890	43.95	184.33	79.68	205.57
MGM0964C18	0.10	1.53	1.29	2.01
MGM0964C20	0.08	1.17	1.09	1.60

Some insight into the validity of the covariance may be gauged by examining the calibrations of the mapping orbit data in the geopotential solutions. As described by Lerch[31], the calibration factor measures the aggregate change in the geopotential coefficients divided by the aggregate change in the sigmas of these geopotential coefficients, when a set of data is removed from a geopotential solution. If the weighting of the data is appropriate, then the calibration factors should be close to unity. If the calibration factors are greater than unity, this is an indication that the set of data is contributing information inconsistent with the information supplied by the other sets of data in the solution. All things being equal, higher calibration factors suggest either overweighting of data or mismodelling problems with the data.

As discussed in Lemoine et al.[32], the calibration factors are averaged by degree or by order. The calibration factors were computed for the MGM0964C18 and the MGM0964C20 solutions, and are shown in Figure 5 and Figure 6. The average calibration factors for the mapping orbit data used in MGM0964c18 were: 1.082 (by degree), and 1.036 (by order). For the data used in the MGM0964C20 field, the calibration factors were 0.901 (by degree) and 0.818 (by order). Indeed, with MGM0964C20, the calibration factors suggest that the MGS data in February and March 1999 could even be slightly upweighted from 0.01 Hz (0.36 mm/s). The lower calibrations MGM0964C20 compared to MGM0964C18 are due to the improved nonconservative force modelling. Mismodelling of the nonconservative forces deleteriously affects the solution at the higher degrees and orders. Relatively high calibration factors at the lower degrees even with the MGM0964C20 model remain to be elucidated. By this internal consistency test, then the covariance of the MGM0964C20 solution is at least not overly optimistic.

 

Figure 5: Calibration factors for the MGS mapping orbit data used in the MGM0964C18 solution.

Figure 6: Calibration factors for the MGS mapping orbit data used in the MGM0964C20 solution.