A Uniform Approach to the Estimation Problems of Satellite Altimetry

Abstract

Satellite altimeter data analysis seeks to extract from measured altimeter ranges information of oceanographic or geophysical interest, such as the shape of the mean sea surface or the temporal variability of sea surface heights (SSHs). Removal of residual radial orbit error is often a first, separate step (though with orbits of the quality of those for the Topex/Poseidon mission, orbit error removal may no longer be the essential step it once was). In the analysis of collinear data orbit error removal has often been done by some process of along-track filtering (Chelton et al., 1990), with attendant difficulties in bridging gaps in the data. Crossover adjustments have usually been done through crossover differencing, often together with the (untenable) hypothesis that there is little change in SSHs over the interval in which differences are taken. In neither case does the estimation problem have full rank; the rank defect has been variously overcome by holding “master arcs” fixed, or by “ridging” the main diagonal of the normal equation matrix, or some other ad hoc method.