General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides
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general_second-order JASA_2010.pdf
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Author(s)
Bertsatos, Ioannis
Zanolin, Michele
Ratilal, Purnima
Chen, Tianrun
Makris, Nicholas
Date Issued
November 2010
Journal
Journal of the Acoustical Society of America
Publisher
American Institute of Physics
Citation
Bertsatos, Ioannis, Michele Zanolin, Purnima Ratilal, Tianrun Chen, and Nicholas C. Makris. “General Second-Order Covariance of Gaussian Maximum Likelihood Estimates Applied to Passive Source Localization in Fluctuating Waveguides.” The Journal of the Acoustical Society of America 128, no. 5 (2010): 2635. © 2010 Acoustical Society of America.
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Final published version
Abstract
A method is provided for determining necessary conditions on sample size or signal to noise ratio (SNR) to obtain accurate parameter estimates from remote sensing measurements in fluctuating environments. These conditions are derived by expanding the bias and covariance of maximum likelihood estimates (MLEs) in inverse orders of sample size or SNR, where the first-order covariance term is the Cramer-Rao lower bound (CRLB). Necessary sample sizes or SNRs are determined by requiring that (i) the first-order bias and the second-order covariance are much smaller than the true parameter value and the CRLB, respectively, and (ii) the CRLB falls within desired error thresholds. An analytical expression is provided for the second-order covariance of MLEs obtained from general complex Gaussian data vectors, which can be used in many practical problems since (i) data distributions can often be assumed to be Gaussian by virtue of the central limit theorem, and (ii) it allows for both the mean and variance of the measurement to be functions of the estimation parameters. Here, conditions are derived to obtain accurate source localization estimates in a fluctuating oceanwaveguide containing random internal waves, and the consequences of the loss of coherence on their accuracy are quantified.
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1121/1.3488303
