Ziv-Zakai lower bounds in bearing estimation

Bounds on the MSE in estimating the bearing of a planewave signal is of considerable interest in many fields. Of particular importance is the ability of a bound to closely characterize performance in the small error or asymptotic region, and the large error or ambiguity region, and to accurately predict the location of the threshold between the regions. The vector Ziv-Zakai bound is applied to the problem of estimating two-dimensional bearing with planar arrays of arbitrary geometry. The bound is calculated for square and circular arrays, and compared with the Weiss-Weinstein (1983, 1984) bound. The Ziv-Zakai bound is shown to be tighter than the Weiss-Weinstein bound in the threshold and asymptotic regions.