Modified Ziv-Zakai lower bound on the errors of the estimation of DOA

Abstract

This thesis has been directed toward the problem of deriving a computable tight lower bound on the error of DOA estimation with the array processing. This work is developed based on the logic implied in Ziv-Zakai's idea and the work for Cramer-Rao lower bound (CRLB). A profound understanding of Ziv-Zakai's idea is presented. The lowest bound on the variance of DOA estimate with one incoming signal is derived applying the logic of Ziv and Zakai. Then the modified Ziv-Zakai lower bound (MZLB) on the covariance matrix of the multiple DOA estimates is developed. The theoretic analysis and the simulation results show that MZLB is a tight lower bound over a wide range of signal-noise ratio. It follows the SNR-threshold phenomenon occurring in the performance of the DOA estimation well, and it is easily computable. It is proved that, the maximum-likelihood estimation of DOA parameters based on Data Model(2) discussed in this thesis is asymptotically efficient.