Optimum Passive Bearing Estimation in a Spatially Incoherent Noise Environment

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Abstract
This paper studies the minimum bearing error attainable with a linear passive array. Signal and noise are stationary Gaussian processes with arbitrary power spectra, and the noise is assumed to be statistically independent from hydrophone to hydrophone. The Cramér-Rao technique is used to set a lower bound on the rms bearing error and the results are compared with the bearing error of a slightly modified split-beam tracker. The latter reaches the lower bound for a two-element array and comes very close to reaching it for a linear array with an arbitrary number of equally spaced hydrophones. Thus, the modified split-beam tracker is very nearly optimal for the uniformly spaced array. Comparisons of split-beam tracker error with the Cramér-Rao lower bound are also obtained for nonuniform hydrophone spacings.

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