Strong consistency of the over- and underdetermined LSE of 2-D exponentials in white noise
We consider the problem of least squares estimation of the parameters of two-dimensional (2-D) exponential signals observed in the presence of an additive noise field, when the assumed number of exponentials is incorrect. We consider both the case where the number of exponential signals is underesti...
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| Veröffentlicht in: | IEEE transactions on information theory 2005-09, Vol.51 (9), p.3314-3321 |
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| creator | Kliger, M. Francos, J.M. |
| description | We consider the problem of least squares estimation of the parameters of two-dimensional (2-D) exponential signals observed in the presence of an additive noise field, when the assumed number of exponentials is incorrect. We consider both the case where the number of exponential signals is underestimated, and the case where the number of exponential signals is overestimated. In the case where the number of exponential signals is underestimated, we prove the almost sure convergence of the least squares estimates (LSE) to the parameters of the dominant exponentials. In the case where the number of exponential signals is overestimated, the estimated parameter vector obtained by the least squares estimator contains a subvector that converges almost surely to the correct parameters of the exponentials. |
| doi_str_mv | 10.1109/TIT.2005.853311 |
| format | Article |
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We consider both the case where the number of exponential signals is underestimated, and the case where the number of exponential signals is overestimated. In the case where the number of exponential signals is underestimated, we prove the almost sure convergence of the least squares estimates (LSE) to the parameters of the dominant exponentials. In the case where the number of exponential signals is overestimated, the estimated parameter vector obtained by the least squares estimator contains a subvector that converges almost surely to the correct parameters of the exponentials.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2005.853311</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>2-D parameter estimation ; Additive noise ; Applied sciences ; Communication channels ; Consistency ; Convergence ; Detection, estimation, filtering, equalization, prediction ; Electric noise ; Error analysis ; Estimates ; Estimators ; Exact sciences and technology ; Gaussian noise ; Information, signal and communications theory ; Least squares approximation ; Least squares estimation ; Least squares method ; Mathematical analysis ; Maximum likelihood detection ; Maximum likelihood estimation ; model-order selection ; Parameter estimation ; Performance analysis ; random fields ; Signal and communications theory ; Signal, noise ; Signaling ; strong consistency ; Telecommunications and information theory ; Two dimensional ; two-dimensional (2-D) exponentials ; Vectors (mathematics) ; White noise</subject><ispartof>IEEE transactions on information theory, 2005-09, Vol.51 (9), p.3314-3321</ispartof><rights>2005 INIST-CNRS</rights><rights>Copyright Institute of Electrical and Electronics Engineers, Inc. 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We consider both the case where the number of exponential signals is underestimated, and the case where the number of exponential signals is overestimated. In the case where the number of exponential signals is underestimated, we prove the almost sure convergence of the least squares estimates (LSE) to the parameters of the dominant exponentials. In the case where the number of exponential signals is overestimated, the estimated parameter vector obtained by the least squares estimator contains a subvector that converges almost surely to the correct parameters of the exponentials.</description><subject>2-D parameter estimation</subject><subject>Additive noise</subject><subject>Applied sciences</subject><subject>Communication channels</subject><subject>Consistency</subject><subject>Convergence</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Electric noise</subject><subject>Error analysis</subject><subject>Estimates</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>Gaussian noise</subject><subject>Information, signal and communications theory</subject><subject>Least squares approximation</subject><subject>Least squares estimation</subject><subject>Least squares method</subject><subject>Mathematical analysis</subject><subject>Maximum likelihood detection</subject><subject>Maximum likelihood estimation</subject><subject>model-order selection</subject><subject>Parameter estimation</subject><subject>Performance analysis</subject><subject>random fields</subject><subject>Signal and communications theory</subject><subject>Signal, noise</subject><subject>Signaling</subject><subject>strong consistency</subject><subject>Telecommunications and information theory</subject><subject>Two dimensional</subject><subject>two-dimensional (2-D) exponentials</subject><subject>Vectors (mathematics)</subject><subject>White noise</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kTFvFDEQhS0EEkegpqCxkEiqvYy9nl27RCGBSCelyFVpLK93lji6sw97D8i_j08XKRIF1WhmvvdGo8fYRwFLIcCcr6_XSwmAS41tK8QrthCIfWM6VK_ZAkDoxiil37J3pTzUVqGQC3Z3O-cUf3KfYgllpugfeZr4fE88_abccBdHvo8j5ZFmytsQaeSr28sDJJtvnP7uUqQ4B7cpPET-5z7MxGMKhd6zN1Od0ofnesLWV5frix_N6ub79cXXVeOVlHMjO6VQIuGgESY_6r7XAw6qJdeingi8NF5PRshRO6pjLdTQK8B-GFxv2hN2drTd5fRrT2W221A8bTYuUtoXa4TqlETQlTz9Lyk19AidquDnf8CHtM-xPmGFQQNCCqjQ-RHyOZWSabK7HLYuP1oB9pCIrYnYQyL2mEhVfHm2dcW7zZRd9KG8yHpALc3h_KcjF4joZa2Mga5tnwDToZJB</recordid><startdate>20050901</startdate><enddate>20050901</enddate><creator>Kliger, M.</creator><creator>Francos, J.M.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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We consider both the case where the number of exponential signals is underestimated, and the case where the number of exponential signals is overestimated. In the case where the number of exponential signals is underestimated, we prove the almost sure convergence of the least squares estimates (LSE) to the parameters of the dominant exponentials. In the case where the number of exponential signals is overestimated, the estimated parameter vector obtained by the least squares estimator contains a subvector that converges almost surely to the correct parameters of the exponentials.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2005.853311</doi><tpages>8</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | 2-D parameter estimation Additive noise Applied sciences Communication channels Consistency Convergence Detection, estimation, filtering, equalization, prediction Electric noise Error analysis Estimates Estimators Exact sciences and technology Gaussian noise Information, signal and communications theory Least squares approximation Least squares estimation Least squares method Mathematical analysis Maximum likelihood detection Maximum likelihood estimation model-order selection Parameter estimation Performance analysis random fields Signal and communications theory Signal, noise Signaling strong consistency Telecommunications and information theory Two dimensional two-dimensional (2-D) exponentials Vectors (mathematics) White noise |
| title | Strong consistency of the over- and underdetermined LSE of 2-D exponentials in white noise |
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