General formulation of source localization for multiple receivers with fully saturated scattered signals

Abstract

A general formulation is provided for the problem of localizing a source from signals at multiple, arbitrarily separated receivers. The signals are assumed to be narrowband and fully saturated by scattering from homogeneous turbulence as they propagate along line-of-sight paths to the receivers. In this case, the complex Wishart distribution can be used to describe the joint distribution of the received signals. Previously derived results from the theory of wave propagation in random media can furthermore be used to model the covariance matrix between the received signals. Then, given a prior distribution on the source location, Bayes's theorem enables the maximum a posteriori (MAP) estimate for the source location to be formulated. This general approach incorporates source localization by beamforming and by signal amplitude as special cases. The behavior of the solution is illustrated with numerical examples.