Title :
Explicit Ziv-Zakai lower bound for bearing estimation
Author :
Bell, Kristine L. ; Ephraim, Yariv ; Van Trees, Harry L.
Author_Institution :
Dept. of Appl. & Eng. Stat., George Mason Univ., Fairfax, VA, USA
fDate :
11/1/1996 12:00:00 AM
Abstract :
The extended Ziv-Zakai bound for vector parameters is used to develop a lower bound on the mean square error in estimating the 2-D bearing of a narrowband planewave signal using planar arrays of arbitrary geometry. The bound has a simple closed-form expression that 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, estimation errors are small, and the bound approaches the inverse Fisher information. This is the same as the asymptotic performance predicted by the local Cramer-Rao bound for each value of bearing. In the a priori performance region where the number of snapshots or SNR is small, estimation errors are distributed throughout the a priori parameter space and the bound approaches the a priori covariance. In the transition region, both small and large errors occur, and the bound varies smoothly between the two extremes. Simulations of the maximum likelihood estimator (MLE) demonstrate that the bound closely predicts the performance of the MLE in all regions
Keywords :
covariance analysis; direction-of-arrival estimation; information theory; maximum likelihood estimation; 2D bearing estimation; SNR; Ziv-Zakai lower bound; array configuration; asymptotic performance; asymptotic region; closed-form expression; covariance; data snapshots; estimation errors; extended Ziv-Zakai bound; inverse Fisher information; local Cramer-Rao bound; maximum likelihood estimator; mean square error; narrowband planewave signal; parameter space; planar arrays; sensors; signal wavelength; signal-to-noise ratio; simulations; thresholds; Closed-form solution; Direction of arrival estimation; Estimation error; Geometry; Maximum likelihood estimation; Mean square error methods; Narrowband; Planar arrays; Sensor arrays; Signal to noise ratio;
Journal_Title :
Signal Processing, IEEE Transactions on