An analysis of subspace fitting algorithms in the presence of sensor errors

The recently introduced class of subspace fitting algorithms for sensor array signal processing (e.g. direction-of-arrival (DOA) estimation) includes deterministic maximum likelihood, ESPRIT, weighted subspace fitting, and both one- and multidimensional MUSIC as special cases. The performance of this class of algorithms is examined for situations where the sensor array response is perturbed from its nominal value. Theoretical expressions for the error in the DOA estimates are derived and compared with several simulation examples. It is shown that in difficult cases the algorithms are especially sensitive to the choice of subspace weighting. For a particular perturbation model, and optimal subspace weighting is proposed which minimizes the DOA estimate error variance over all possible weightings when finite sample effects are neglected