Optimal Design of the Adaptive Normalized Matched Filter Detector using Regularized Tyler Estimators

Handle URI:
http://hdl.handle.net/10754/626097
Title:
Optimal Design of the Adaptive Normalized Matched Filter Detector using Regularized Tyler Estimators
Authors:
Kammoun, Abla ( 0000-0002-0195-3159 ) ; Couillet, Romain; Pascal, Frederic; Alouini, Mohamed-Slim ( 0000-0003-4827-1793 )
Abstract:
This article addresses improvements on the design of the adaptive normalized matched filter (ANMF) for radar detection. It is well-acknowledged that the estimation of the noise-clutter covariance matrix is a fundamental step in adaptive radar detection. In this paper, we consider regularized estimation methods which force by construction the eigenvalues of the covariance estimates to be greater than a positive regularization parameter ρ. This makes them more suitable for high dimensional problems with a limited number of secondary data samples than traditional sample covariance estimates. The motivation behind this work is to understand the effect and properly set the value of ρthat improves estimate conditioning while maintaining a low estimation bias. More specifically, we consider the design of the ANMF detector for two kinds of regularized estimators, namely the regularized sample covariance matrix (RSCM), the regularized Tyler estimator (RTE). The rationale behind this choice is that the RTE is efficient in mitigating the degradation caused by the presence of impulsive noises while inducing little loss when the noise is Gaussian. Based on asymptotic results brought by recent tools from random matrix theory, we propose a design for the regularization parameter that maximizes the asymptotic detection probability under constant asymptotic false alarm rates. Provided Simulations support the efficiency of the proposed method, illustrating its gain over conventional settings of the regularization parameter.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Kammoun A, Couillet R, Pascal F, Alouini M-S (2017) Optimal Design of the Adaptive Normalized Matched Filter Detector using Regularized Tyler Estimators. IEEE Transactions on Aerospace and Electronic Systems: 1–1. Available: http://dx.doi.org/10.1109/taes.2017.2766538.
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
IEEE Transactions on Aerospace and Electronic Systems
Issue Date:
25-Oct-2017
DOI:
10.1109/taes.2017.2766538
Type:
Article
ISSN:
0018-9251
Sponsors:
Couillet’s work is supported by the ANR Project RMT4GRAPH (ANR-14-CE28-0006).
Additional Links:
http://ieeexplore.ieee.org/document/8082486/
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKammoun, Ablaen
dc.contributor.authorCouillet, Romainen
dc.contributor.authorPascal, Fredericen
dc.contributor.authorAlouini, Mohamed-Slimen
dc.date.accessioned2017-11-02T09:09:33Z-
dc.date.available2017-11-02T09:09:33Z-
dc.date.issued2017-10-25en
dc.identifier.citationKammoun A, Couillet R, Pascal F, Alouini M-S (2017) Optimal Design of the Adaptive Normalized Matched Filter Detector using Regularized Tyler Estimators. IEEE Transactions on Aerospace and Electronic Systems: 1–1. Available: http://dx.doi.org/10.1109/taes.2017.2766538.en
dc.identifier.issn0018-9251en
dc.identifier.doi10.1109/taes.2017.2766538en
dc.identifier.urihttp://hdl.handle.net/10754/626097-
dc.description.abstractThis article addresses improvements on the design of the adaptive normalized matched filter (ANMF) for radar detection. It is well-acknowledged that the estimation of the noise-clutter covariance matrix is a fundamental step in adaptive radar detection. In this paper, we consider regularized estimation methods which force by construction the eigenvalues of the covariance estimates to be greater than a positive regularization parameter ρ. This makes them more suitable for high dimensional problems with a limited number of secondary data samples than traditional sample covariance estimates. The motivation behind this work is to understand the effect and properly set the value of ρthat improves estimate conditioning while maintaining a low estimation bias. More specifically, we consider the design of the ANMF detector for two kinds of regularized estimators, namely the regularized sample covariance matrix (RSCM), the regularized Tyler estimator (RTE). The rationale behind this choice is that the RTE is efficient in mitigating the degradation caused by the presence of impulsive noises while inducing little loss when the noise is Gaussian. Based on asymptotic results brought by recent tools from random matrix theory, we propose a design for the regularization parameter that maximizes the asymptotic detection probability under constant asymptotic false alarm rates. Provided Simulations support the efficiency of the proposed method, illustrating its gain over conventional settings of the regularization parameter.en
dc.description.sponsorshipCouillet’s work is supported by the ANR Project RMT4GRAPH (ANR-14-CE28-0006).en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.relation.urlhttp://ieeexplore.ieee.org/document/8082486/en
dc.rights(c) 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.en
dc.subjectRegularized Tylers estimatoren
dc.subjectAdaptive Normalized Mached Filteren
dc.subjectrobust detectionen
dc.subjectRandom Matrix Theoryen
dc.subjectOptimal designen
dc.titleOptimal Design of the Adaptive Normalized Matched Filter Detector using Regularized Tyler Estimatorsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalIEEE Transactions on Aerospace and Electronic Systemsen
dc.eprint.versionPost-printen
dc.contributor.institutionLaboratoire des Signaux et Systémes (L2S, UMR CNRS 8506) CentraleSupélec-CNRS-Université Paris-Sud, 91192 Gif-sur-Yvette, Franceen
kaust.authorKammoun, Ablaen
kaust.authorAlouini, Mohamed-Slimen
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