ROBUST ESTIMATION WITH APPLICATION TO HIPPARCOS MINOR PLANET DATA M.L. Bougeard

Abstract

Forty eight minor planets have been observed by the Hipparcos satellite. Pooling their precise position may allow to investigate a possible rotation between the dynamical reference frame and the ICRSHipparcos Reference system. Due to the repartition of the observations, ill-conditioning of the global system and outliers simultaneously occur. So, a direct least-squares fit is potentially misleading and we resort to the use of robust statistical alternatives. While it is now clear that no single robust regression is best, the L1 and Huber-M estimators are currently attracting attention under the occurence of contaminated Gaussian errors. Here, we present new algorithms based on the Spingarn Partial Inverse proximal decomposition method for L1 and HuberM estimation that take into account both primal and dual aspects of the optimization problem. The result is a family of highly parallel algorithms attractive for large scale problems. Implemented on the Connection Machine CM5, their comput..