Simple computational methods of the AP algorithm for maximum likelihood localization of multiple radiating sources

Two computational algorithms that reduce significantly the computational complexity per iteration of the alternating projection (AP) algorithm are presented. One is a recursive projection algorithm that utilizes the projection matrix updating formula, and the other is a maximum eigenvector approximation algorithm that approximates the Hermitian maximization problem in every iteration as the problem of 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 significantly reduce the computational complexity without noticeable loss in the estimation performance and convergence behavior. Computer simulation results that validate this approximation are included