Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem. The methods considered 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 the ML method. 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.
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