A performance analysis of subspace-based methods in the presence of model error. II. Multidimensional algorithms

This is the second of a two-part paper dealing with the performance of subspace-based algorithms for narrow-hand direction-of-arrival (DOA) estimation when the array manifold and noise covariance are not correctly modeled. In Part I, the performance of the MUSIC algorithm was investigated. In Part 11, we extend this analysis to multidimensional (MD) subspacebased algorithms including deterministic (or conditional) maximum likelihood, MD-MUSIC, weighted subspace fitting (WSF), MODE, and ESPRIT. A general expression for the variance of the DOA estimates is presented that can be applied to any of the above algorithms and to any of a wide variety of scenarios (e.g., gain/phase errors, mutual coupling, sensor position errors, noise covariance mismodeling, etc.). Optimally weighted subspace fitting algorithms are also presented for special cases involving random unstructured errors to the array manifold and noise covariance. In addition, it is shown that one-dimensional MUSIC outperforms all of the above MD algorithms for random angle-independent array perturbations.