Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Passive Source Localization Using Time Differences of Arrival and Gain Ratios of Arrival
IEEE Transactions on Signal Processing
Explicit Ziv-Zakai lower bound for bearing estimation
IEEE Transactions on Signal Processing
Extended Ziv-Zakai lower bound for vector parameter estimation
IEEE Transactions on Information Theory
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The Ziv-Zakai bound (ZZB) is developed for the estimation error of a radiating source located in a plane, and observed by sensors widely distributed over the same plane. The source is non-cooperative in the sense that the transmitted waveform and its timing are unknown to the sensors. The sensors do have however, information on the power spectral density of the source. Moreover, sensors have ideal mutual time and phase synchronization. The source location is estimated by coherent processing exploiting the amplitude and phase information between pairs of sensors. An analytical expression is developed for the ZZB relating the estimation error to the carrier frequency, signal bandwidth, the number of sensors, and their location. Numerical examples demonstrate that the ZZB closely predicts the performance of the maximum likelihood estimate across the full range of signal to noise ratio (SNR) values. At low SNR, the ZZB bound demonstrates performance dominated by noise, at medium SNR, the performance is dictated by the presence of sidelobes in the localization metric, and at high SNR, it is shown that the ZZB converges to the Cramer-Rao bound.