General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides
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 estimat...
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| Format: | Article |
| Language: | en_US |
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American Institute of Physics
2014
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| Online Access: | http://hdl.handle.net/1721.1/87701 https://orcid.org/0000-0003-4369-296X |
| _version_ | 1811081180514091008 |
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| author | Bertsatos, Ioannis Zanolin, Michele Ratilal, Purnima Chen, Tianrun Makris, Nicholas |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Bertsatos, Ioannis Zanolin, Michele Ratilal, Purnima Chen, Tianrun Makris, Nicholas |
| author_sort | Bertsatos, Ioannis |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:42:43Z |
| format | Article |
| id | mit-1721.1/87701 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:42:43Z |
| publishDate | 2014 |
| publisher | American Institute of Physics |
| record_format | dspace |
| spelling | mit-1721.1/877012022-10-01T05:25:32Z General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides Bertsatos, Ioannis Zanolin, Michele Ratilal, Purnima Chen, Tianrun Makris, Nicholas 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 Makris, Nicholas C. Makris, Nicholas Chen, Tianrun Bertsatos, Ioannis Ratilal, Purnima 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. 2014-06-09T15:56:50Z 2014-06-09T15:56:50Z 2010-11 2010-07 Article http://purl.org/eprint/type/JournalArticle 00014966 http://hdl.handle.net/1721.1/87701 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. https://orcid.org/0000-0003-4369-296X en_US http://dx.doi.org/10.1121/1.3488303 Journal of the Acoustical Society of America Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Institute of Physics Prof. Makris via Angie Locknar |
| spellingShingle | Bertsatos, Ioannis Zanolin, Michele Ratilal, Purnima Chen, Tianrun Makris, Nicholas General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides |
| title | General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides |
| title_full | General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides |
| title_fullStr | General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides |
| title_full_unstemmed | General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides |
| title_short | General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides |
| title_sort | general second order covariance of gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides |
| url | http://hdl.handle.net/1721.1/87701 https://orcid.org/0000-0003-4369-296X |
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