Cramér-Rao Bounds for
|Arthur B. Baggeroer
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139-4307
Abstract Matched field processing was developed in underwater acoustics for passive totalization of the range, depth, and azimuth of acoustics sources such as submarines. It exploits the coherence of the multipaths and/or modes for signals observed on vertical and horizontal arrays. One can also envision electromagnetic applications exploiting ground multipath and ionospheric multipaths. There are also companion tomographic methods where one uses the multipaths to infer properties of the propagation medium such as when propagation speeds are unknown. We have formulated very general results for the Cramér-Rao bounds estimating the source position using matched field methods in terms of the vector Green's function, which includes all dispersion effects, for the propagation of a signal from a source to a receiver array. This includes both the cases of an incoherent source, e.g., random vibrations or spread spectra, where only relative phase delays can be used and coherent sources, e.g., an active sonar signal, where group delays can be used. For the sonar case these bounds indicate the very close coupling between the propagation physics and the estimator performance.
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