The filtering effect of orbit correction on geopotential errors

Abstract

The geophysical interpretation of satellite tracking residuals generally ignores the filtering effect of initial orbit correction on the true errors of the model. While the filtered information is usually regarded as lost, knowing the spectral characteristics of the filter is a great aid in the detailed interpretation of residuals, especially of global data sets. In this regard, we derive the filter characteristics (admittances) of orbit correction in the presence of geopotential-caused trajectory errors. We then apply the filter to determine the likely power of the lost radial information in crossover differences of sea heights determined from satellite altimetry or in the latitude lumped coefficients derived from them. For example, we find that resonant geopotential information with periods longer than the corrected orbit's arc length is largely lost in residual crossover data. Results are given for GEOSAT, ERS-1 and TOPEX/Poseidon in their Exact Repeat Missions, using calibrated variancecovariance matrices of the harmonic geopotential coefficients of several recent Earth gravity models. To prove that filtering is important, we first employed a simple cut of all perturbing terms with periods longer than the general tracking period (4 days for GEOSAT and ERS-1, and 10 days for TOPEX). But the cut is too crude a method from a theoretical viewpoint, and thus, we developed two new filters. A comparison of their admittances explains the differences (and sometimes anomalous behaviour) between them and the cut. Many numerical examples (single-satellite crossover errors and latitude lumped coefficient errors, as projected from the variance-covariance matrices) are presented. This paper has been presented during the Panel on Satellite Dynamics, at COSPAR 1994, in Hamburg, Germany.