Highly Robust Complex Covariance Estimators with Applications to Sensor Array Processing
Many applications in signal processing require the estimation of mean and covariance matrices of multivariate complex-valued data. Often, the data are non-Gaussian and are corrupted by outliers or impulsive noise. To mitigate this, robust estimators are employed. However, existing robust estimation...
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| Veröffentlicht in: | IEEE open journal of signal processing 2023-01, Vol.4, p.1-18 |
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| creator | Fishbone, Justin A. Mili, Lamine |
| description | Many applications in signal processing require the estimation of mean and covariance matrices of multivariate complex-valued data. Often, the data are non-Gaussian and are corrupted by outliers or impulsive noise. To mitigate this, robust estimators are employed. However, existing robust estimation techniques employed in signal processing, such as M -estimators, provide limited robustness in the multivariate case. For this reason, this paper introduces the signal processing community to the highly robust class of multivariate estimators called multivariate S -estimators. The paper extends multivariate S estimation theory to the complex-valued domain. The theoretical performances of S -estimators are explored and compared with M -estimators through the practical lens of the minimum variance distortionless response (MVDR) beamformer, and the empirical finite-sample performances of the estimators are explored through the practical lens of direction-of-arrival (DOA) estimation using the multiple signal classification (MUSIC) algorithm. |
| doi_str_mv | 10.1109/OJSP.2023.3261806 |
| format | Article |
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Often, the data are non-Gaussian and are corrupted by outliers or impulsive noise. To mitigate this, robust estimators are employed. However, existing robust estimation techniques employed in signal processing, such as M -estimators, provide limited robustness in the multivariate case. For this reason, this paper introduces the signal processing community to the highly robust class of multivariate estimators called multivariate S -estimators. The paper extends multivariate S estimation theory to the complex-valued domain. The theoretical performances of S -estimators are explored and compared with M -estimators through the practical lens of the minimum variance distortionless response (MVDR) beamformer, and the empirical finite-sample performances of the estimators are explored through the practical lens of direction-of-arrival (DOA) estimation using the multiple signal classification (MUSIC) algorithm.</description><identifier>ISSN: 2644-1322</identifier><identifier>EISSN: 2644-1322</identifier><identifier>DOI: 10.1109/OJSP.2023.3261806</identifier><identifier>CODEN: IOJSAF</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Algorithms ; Beamforming ; Complex elliptically symmetric distribution ; complex-valued S-estimator ; covariance and shape matrix estimation ; Covariance matrices ; Covariance matrix ; Direction of arrival ; Electric breakdown ; Estimation ; Estimators ; Lenses ; Multivariate analysis ; Outliers (statistics) ; Probability density function ; robust estimation of multivariate location and scatter ; Robustness ; Sensor arrays ; Signal classification ; Signal processing ; Sq-estimator ; Symmetric matrices</subject><ispartof>IEEE open journal of signal processing, 2023-01, Vol.4, p.1-18</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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Often, the data are non-Gaussian and are corrupted by outliers or impulsive noise. To mitigate this, robust estimators are employed. However, existing robust estimation techniques employed in signal processing, such as M -estimators, provide limited robustness in the multivariate case. For this reason, this paper introduces the signal processing community to the highly robust class of multivariate estimators called multivariate S -estimators. The paper extends multivariate S estimation theory to the complex-valued domain. The theoretical performances of S -estimators are explored and compared with M -estimators through the practical lens of the minimum variance distortionless response (MVDR) beamformer, and the empirical finite-sample performances of the estimators are explored through the practical lens of direction-of-arrival (DOA) estimation using the multiple signal classification (MUSIC) algorithm.</description><subject>Algorithms</subject><subject>Beamforming</subject><subject>Complex elliptically symmetric distribution</subject><subject>complex-valued S-estimator</subject><subject>covariance and shape matrix estimation</subject><subject>Covariance matrices</subject><subject>Covariance matrix</subject><subject>Direction of arrival</subject><subject>Electric breakdown</subject><subject>Estimation</subject><subject>Estimators</subject><subject>Lenses</subject><subject>Multivariate analysis</subject><subject>Outliers (statistics)</subject><subject>Probability density function</subject><subject>robust estimation of multivariate location and scatter</subject><subject>Robustness</subject><subject>Sensor arrays</subject><subject>Signal classification</subject><subject>Signal processing</subject><subject>Sq-estimator</subject><subject>Symmetric matrices</subject><issn>2644-1322</issn><issn>2644-1322</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>ESBDL</sourceid><sourceid>RIE</sourceid><sourceid>DOA</sourceid><recordid>eNpNUdFqGzEQPEoLDUk-INAHQZ_tald3OunRmLRJCSTULeRNKLqVI3M5XSU5if--5zoEP-0yzMwOO1V1AXwOwPW325-ruzlyFHOBEhSXH6oTlHU9A4H48Wj_XJ3nvOGcYwMwASfV_VVYP_Y79is-bHNhy_g09vQ6zWebgh0csctcwpMtMWX2EsojW4xjH5wtIQ6ZlchWNOSY2CIlu2N3KTrKOQzrs-qTt32m87d5Wv35fvl7eTW7uf1xvVzczFzNRZlZ67um9sIjWhQgmpo6LRvrqWs77FqEtpYWgFBq75pGS9BKNooLD-KhVeK0uj74dtFuzJimrGlnog3mPxDT2thUguvJKOig1dwL17lakrOk2oa0Vw6VBmUnr68HrzHFv1vKxWziNg1TfIPTVxERtJ5YcGC5FHNO5N-vAjf7Psy-D7Pvw7z1MWm-HDSBiI74XAGXSvwD-muGBg</recordid><startdate>20230101</startdate><enddate>20230101</enddate><creator>Fishbone, Justin A.</creator><creator>Mili, Lamine</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Often, the data are non-Gaussian and are corrupted by outliers or impulsive noise. To mitigate this, robust estimators are employed. However, existing robust estimation techniques employed in signal processing, such as M -estimators, provide limited robustness in the multivariate case. For this reason, this paper introduces the signal processing community to the highly robust class of multivariate estimators called multivariate S -estimators. The paper extends multivariate S estimation theory to the complex-valued domain. 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| source | IEEE Open Access Journals; DOAJ Directory of Open Access Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Algorithms Beamforming Complex elliptically symmetric distribution complex-valued S-estimator covariance and shape matrix estimation Covariance matrices Covariance matrix Direction of arrival Electric breakdown Estimation Estimators Lenses Multivariate analysis Outliers (statistics) Probability density function robust estimation of multivariate location and scatter Robustness Sensor arrays Signal classification Signal processing Sq-estimator Symmetric matrices |
| title | Highly Robust Complex Covariance Estimators with Applications to Sensor Array Processing |
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