On Correcting Radial Orbit Errors for Altimetric Satellites Using Crossover Analysis

Abstract

Radial orbit error, defined as the uncertainty in the geocentric altitude of a satellite, is the dominant error in the measurement of sea surface height by a satellite altimeter. Apart from a geographically dependent component (a function of latitude and longitude only), this error has been proven to be recoverable by analyzing the difference in altimetric measurement of sea surface height at ground track intersections (crossover differences). An effective approach to the problem is to model orbit error in terms of a Fourier series with the Fourier coefficients determined by minimizing the residual crossover difference in a least-square sense. The solution of the coefficients, however, is known to be singular due to the presence of geographically dependent orbit errors that cause no crossover differences. To obtain a unique solution, an a priori constraint is usually imposed (e.g., conforming the resulting ocean topography to a geoid model). In this paper we demonstrate that the problem can be solved by the use of singular value decomposition, without the need for any a priori constraint. The essence of the method is to leave the geographically dependent errors unchanged and make only those corrections that are warranted by the information contained in crossover differences, thus leaving the resultant ocean topography free from any undue distortion that may otherwise be incurred by an a priori constraint. The method will be particularly useful for application to high-accuracy altimetric missions such as Topex/Posceidon, because the orbit error can be reduced without compromising the accuracy of the measured mean ocean topography.