Optimum Passive Bearing Estimation

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 Cramer‐Rao technique is used to set a lower bound on the rms hearing 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. The dependence of the rms error on signal‐to‐noise ratio is the same for the split beam tracker and for the Cramer‐Rao lower bound. Parts of the results are extended to arrays operating in a noise field containing a directional component. [Work supported by Office of Naval Research through prime contract with General Dynamics/Electric Boat under the SUBIC pr...