Cramer-Rao bound for location systems in multipath environments

The Cramer-Rao lower bound for source localization is studied in the context of multipath stochastic sources, multipath propagation, and observations, in an array of sensors. A general expression is derived and then specialized to simpler configurations and related to results previously reported in the literature. The special case of a single stochastic source in a multipath environment is treated. The relative importance for source localization of the temporal (multipath) and spatial (array baseline) structures of the incoming wavefield is assessed. It is shown that for an array of K sensors the multipath contribution to the Fisher information matrix can be interpreted as the contribution of K independent arrays whose size depends on the number of spatially resolved replicas. The degradation due to unknown source spectra is analyzed. When the source spectrum is completely arbitrary, source location is not possible with a single sensor. If a parametric form of the source spectrum is available, the multipath structure can be used to locate the acoustic source