Explicit Ziv-Zakai lower bound for bearing estimation

Abstract

The extended Ziv-Zakai bound for vector parameters is used to develop a lower bound on the mean square error (MSE) in estimating the two-dimensional bearing of a narrowband planewave signal using planar arrays of arbitrary geometry. The bound has a simple closed form expression which is a function of the signal wavelength, the signal-to-noise ratio (SNR), the number of data snapshots, the number of sensors in the array, and the array configuration. Analysis of the bound suggests that there are several regions of operation, and expressions for the thresholds separating the regions are provided. In the asymptotic region where the number of snapshots and/or SNR are large, the bound approaches the inverse Fisher information. In the a priori performance region where the number of snapshots or SNR is small, the bound approaches the a priori covariance. In the transition region, the bound varies smoothly between the two extremes. Results from simulation of the maximum likelihood estimator (MLE) demonstrate that the bound closely predicts the performance of the MLE in all regions.