SENSOR ARRAY-PROCESSING BASED ON SUBSPACE FITTING

A large number of signal processing problems are concerned with estimating unknown signal parameters from sensor array measurements. This area has drawn much interest and many methods for parameter estimation based on array data have appeared in the literature. This paper presents some of these algorithms as variations of the same subspace fitting problem. The methods considered herein are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace method. These methods are formulated in a subspace fitting based framework, which provides insight into their algebraic and asymptotic relations. It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as ML. The asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified. The resulting optimal technique is termed the weighted subspace fitting (WSF) method. Numerical examples indicate that the asymptotic variance of the WSF estimates coincides with the Cramer-Rao bound. The performance improvement compared to the other techniques is found to be most prominent for highly correlated signals. A simulation study is presented, indicating that the asymptotic variance expressions are valid for a wide range of scenarios.