Maximum-Likelihood Direct Position Estimation in Dense Multipath

The problem of localizing a transmitting source by observing the signal at several base stations (BSs) is considered. In this paper, a direct position estimation (DPE) algorithm for a dense multipath channel is formulated and analyzed, based on a Gaussian approximation. The algorithm provides robust and accurate position estimation in a multipath environment, which is a challenging problem, particularly when the signal-to-noise ratio (SNR) is low and when the multipath is dense. It is shown that the DPE is superior to the common indirect approach. In the indirect approach, the time of arrival (TOA) is estimated independently at each BS, whereas in the DPE, all the received signals from all BSs are processed jointly. We show that the proposed algorithm approximates the maximum-likelihood (ML) solution. We treat TOA based on synchronized source and receivers and the differential TOA (DTOA) where only the receivers are synchronized. Analytic results for the performance of the algorithm are provided. Finally, simulations demonstrate the advantage of DPE over the indirect method at low SNR for various multipath channel models and that the analysis closely approximates the simulation results.