Maximum likelihood estimation of the position of a radiating source in a waveguide

An array of sensors is receiving radiation from a source of interest. The source and the array are in a one-or two-dimensional waveguide. The maximum-likelihood estimators of the coordinates of the source are analysed under the assumptions that the noise field is Gaussian. The Cramer–Rao lower bound is of the order of the number of modes which define the source excitation function. The results show that the accuracy of the maximum likelihood estimator of source depth using a vertical array in a infinite horizontal waveguide (such as the ocean) is limited by the number of modes detected by the array, regardless of the array size.