Bayesian bounds for matchedfield parameter estimation

Wen Xu, Arthur B. Baggeroer, Christ D. Richmond

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations


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 Cramér-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.

Original languageEnglish (US)
Title of host publicationBayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
PublisherWiley-IEEE Press
Number of pages13
ISBN (Electronic)9780470544198
ISBN (Print)0470120959, 9780470120958
StatePublished - Jan 1 2007
Externally publishedYes


  • Arrays
  • Bayesian methods
  • Maximum likelihood estimation
  • Parameter estimation
  • Signal to noise ratio

ASJC Scopus subject areas

  • General Computer Science


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