Ambiguity Function and Cramer-Rao Lower Bounds for Passive Synthetic Aperture Sonar (SAS)

The resolving power of passive SAS is addressed by computing and plotting its ambiguity function in the frequency/bearing plane. It is proven that, even in ideal conditions, the apparently better spatial resolution of passive SAS is due only to the better frequency resolution which results from the longer processing time. In other respects the computation of Cramer-Rao Lower Bounds (CRLB) for joint source bearing and frequency estimation is detailed. It is shown that, in realistic situations, i.e. when the source frequency is not known, the bearing accuracy (standard deviation) does not depend upon the own speed (and hence on the length of the synthetic aperture). In fact the true, and maybe the sole, practical interest of the many proposed passive SAS algorithms [2, 4] is that they may appear as manners to perform a coherent very long time integration, thus possibly allowing detection of weak coherent narrow band sources.