SIMPLE COMPUTATIONAL METHODS OF THE AP ALGORITHM FOR MAXIMUM-LIKELIHOOD LOCALIZATION OF MULTIPLE RADIATING SOURCES

In this correspondence, we present two simple computational algorithms of the alternating projection (AP) algorithm, which is an iterative algorithm for computing efficiently the deterministic maximum likelihood (ML) estimator of the locations of multiple sources in passive sensor arrays. One is a recursive projection (RP) algorithm that utilizes the projection matrix updating formula, and the other is a maximum eigenvector approximation (MEA) algorithm that approximates the Hermitian maximization problem in every iteration to a problem for maximizing the modulus of the projection onto the maximum eigenvector subspace. By transforming the computation of Hermitian forms into that of only inner products of vectors, these algorithms reduce significantly the computational complexity per iteration without any recognizable loss in the estimation performance and convergence behaviors. Computer simulation results that validate this approximation are also included.