Bayesian bounds for matched-field parameter estimation

• Published in: IEEE transactions on signal processing Vol. 52; no. 12; pp. 3293 - 3305
• Main Authors: Wen Xu, Baggeroer, A.B., Richmond, C.D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2004; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acoustic propagation; Acoustic waveguides; Acoustic waves; Ambiguity; Applied sciences; Asymptotic properties; Bayesian analysis; Bayesian estimation; Bayesian methods; Detection, estimation, filtering, equalization, prediction; Error analysis; Estimation error; Exact sciences and technology; Exact solutions; Frequency estimation; Information, signal and communications theory; matched-field processing; Mathematical models; maximum likelihood estimate; Maximum likelihood estimation; Oceans; Parameter estimation; performance bound; Position measurement; Sidelobes; Signal and communications theory; Signal, noise; Telecommunications and information theory; threshold phenomenon; Performance evaluation; Lateral lobe; Random signal; Averaging method; Parameter estimation; Error probability; Error estimation; Acoustic wave; Signal estimation; Acoustic method; Mean square error; matched-field processing; performance bound; Multiple frequency; Cramer Rao inequality; Estimation error; Bayesian estimation; Asymptotic behavior; Multitone system; Waveguide; Simulation; Source localization; Likelihood ratio test; threshold phenomenon; maximum likelihood estimate; Maximum likelihood; Signal to noise ratio
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2004.837437

Matched-field methods concern estimation of source locations and/or ocean environmental parameters by exploiting full wave modeling of acoustic waveguide propagation. Because of the nonlinear parameter-dependence of the signal field, the estimate is subject to ambiguities and the sidelobe contribution often dominates the estimation error below a threshold signal-to-noise ratio (SNR). To study the matched-field performance, three Bayesian lower bounds on mean-square error are developed: the Bayesian Crame/spl acute/r-Rao bound (BCRB), the Weiss-Weinstein bound (WWB), and the Ziv-Zakai bound (ZZB). Particularly, for a multiple-frequency, multiple-snapshot random signal model, a closed-form minimum probability of error associated with the likelihood ratio test is derived, which facilitates error analysis in a wide scope of applications. Analysis and example simulations demonstrate that 1) unlike the local CRB, the BCRB is not achieved by the maximum likelihood estimate (MLE) even at high SNR if the local performance is not uniform across the prior parameter space; 2) the ZZB gives the closest MLE performance prediction at most SNR levels of practical interest; 3) the ZZB can also be used to determine the necessary number of independent snapshots achieving the asymptotic performance of the MLE at a given SNR; 4) incoherent frequency averaging, which is a popular multitone processing approach, reduces the peak sidelobe error but may not improve the overall performance due to the increased ambiguity baseline; and finally, 5) effects of adding additional parameters (e.g., environmental uncertainty) can be well predicted from the parameter coupling.