Optimum Passive Bearing Estimation
V. H. McDonald, Peter M. Schultheiss · The Journal of the Acoustical Society of America · 1969
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 program.]