A dynamic programming algorithm for the maximum likelihood localization of multiple sources

A dynamic programming algorithm is presented for simultaneously computing the maximum-likelihood (ML) estimator of the number of multiple sources and their directions of arrival (DOA) in sensor array processing. Based on the projection-matrix decomposition technique, the multivariate log-likelihood maximization problem is transformed into a multistage one-dimensional maximization problem. The estimation procedure is obtained with relatively light computational load. In addition, the estimator gives satisfactory performance in the case of both coherent and incoherent sources. The simulation results also show that, when the element SNR is low and/or the number of snapshots is small, the DP-ML algorithm is much superior to MUSIC