Efficient subspace-based estimator for localization of multiple incoherently distributed sources

In this paper, a new subspace-based algorithm for parametric estimation of angular parameters of multiple incoherently distributed sources is proposed. This approach consists of using the subspace principle without any eigendecomposition of the covariance matrix, so that it does not require the knowledge of the effective dimension of the pseudosignal subspace, and therefore the main difficulty of the existing subspace estimators can be avoided. The proposed idea relies on the use of the property of the inverse of the covariance matrix to exploit approximately the orthogonality property between column vectors of the noise-free covariance matrix and the sample pseudonoise subspace. The resulting estimator can be considered as a generalization of the Pisarenko's extended version of Capon's estimator from the case of point sources to the case of incoherently distributed sources. Theoretical expressions are derived for the variance and the bias of the proposed estimator due to finite sample effect. Compared with other known methods with comparable complexity, the proposed algorithm exhibits a better estimation performance, especially for close source separation, for large angular spread and for low signal-to-noise ratio.