A Monte-Carlo technique for weight estimation in satellite geodesy

Precise orbit determination, and satellite-geodetic applications such as gravity field modelling or satellite altimetry, rely on different observation types and groups that have to be processed in a common parameter estimation scheme. Naturally, the choice of the relative weights for these data sets as well as for added prior information is of importance for obtaining reliable estimates of the unknown parameters and their associated covariance matrices. If the observations are predominantly affected by random errors and systematic errors play a minor role, variance component models can be applied. However, most of the methods proposed so far for variance component estimation involve repeated inversion of large matrices, resulting in intensive computations and large storage requirements if more than a few hundred unknowns are to be determined. In addition, these matrices are not necessarily provided as standard output from common geodetic least-squares estimation software. Therefore, a method is proposed which is based on Monte-Carlo estimation of the redundancy contributions of disjunctive observation groups. The method can handle unknown variance components without the need for repeated inversion of matrices. It is computationally simple, numerically stable and easy to implement. Its application is demonstrated in an experiment concerning low-medium-degree gravity field recovery from simulated orbit perturbations of the GOCE mission, and compared in performance with Lerch’s method of subset solutions.