Three-dimensional source localization in a waveguide

This paper deals with three-dimensional (3-D) passive localization of a narrowband point source in a 21/2-dimensional waveguide using an array of sensors. Two different maximum likelihood (ML) procedures for estimating the source range, depth, and direction-of-arrival (DOA) based on the normal mode representation of the received data are studied. In the first procedure, ML estimation of range and depth is applied on the data collected by a vertical array, and DOA is estimated using the ML algorithm on the data received by a separate, horizontal array. In the second procedure, the ML algorithm is applied on the data received by a two-dimensional (2-D), hybrid array for simultaneously estimating of all three source location parameters. Our study shows that although a horizontal array is sufficient for 3-D localization, to reduce sensitivity of the localization algorithm, a 2-D array should be used. The presented performance analysis of the two algorithms enables one to determine the performance losses in using the stage-wise, suboptimal algorithm relative to the optimal one in any given scenario. Numerical examples with channel parameters, which are typical to shallow water source localization, show performance losses of 0-3 dB. Simulation results of the two ML algorithms and their comparison with the Cramér-Rao bound (CRB) support the theory.