An efficient multiple source localization approach: dynamic programming

A dynamic programming (DP) algorithm based on Bellman´s principle of optimality (1962) for computing the MLE (maximum likelihood estimation) is proposed. By this algorithm, the multidimensional ML maximization problem is transformed into a recursively one-dimensional maximization problem. The global optimum of the MLE is guaranteed and obtained by simply maximizing the recursive likelihood function. The performance of the DP-MLE is compared to that of MUSIC via simulation. Three sources in the far field emitting plane waves into a linear sensor array of five elements uniformly half a wavelength apart are considered. It is shown that the noise performance of the DP-MLE is superior to that of MUSIC. This superiority is pronounced at low signal-to-noise ratios. It is concluded that the DP approach is an efficient algorithm for computing the MLEs of a number of sources and their directions of arrival.<>