Specification and Performance of Passive Sonar Spectral Estimators

The application of existing estimation theory to the problem of specification and performance of passive sonar spectral estimators is considered. The classification function is addressed, so that the signal is assumed to be present, and so that the energy arrival angle is known. The spatial filter considered is a line array of M equally spaced omnidirectional hydrophones. Signal and ambient noise are both zero-mean, wide-sense, stationary Gaussian random processes that differ in their spatial correlation across the face of the array. The signal is a plane wave that can be made totally spacially corrected between array elements by inserting delays between sensors to invert the signal propagation delay. The noise correlation is a function of frequency, bandwidth, element separation, and the relative time delay between sensors. Under these assumptions, the Cramer-Rao lower bound is derived for the class of unbiased estimates of signal power in a narrow frequency band at the hydrophone in the presence of correlated ambient noise of known power. The bound is examined numerically, resulting in a threshold phenomenon with M that constitutes a new design consideration. In addition, there is a striking insensitivity to realistic values of ambient noise correlation, and there are ranges in signal-to-noise ratio for which one gains more by increasing M than by increasing the bandwidth-time product. Specific processors, including a new unbiased estimator when noise power is unknown, are developed.