Robust parameter estimation in the presence of nuisance parameters

This paper presents a new, robust algorithm for parameter estimation in the presence of unknown nuisance parameters. The proposed algorithm is based on a decomposition of the data into subspaces characterized by their sensitivities to the errors in the nuisance parameters. The importance of this decomposition is that it isolates a subspace of the data which is not a function of the unknown nuisance parameters. The Maximum-Likelihood estimator is developed for the new decomposed model. It uses only the information carried by the insensitive subspace of the data while the deviations in the sensitive subspace are assumed to be unknown parameters. Identification of the insensitive subspace is made according to the second order joint statistics of the data. The algorithm is applied to a source localization problem in which the propagation conditions are not perfectly known.