Target localization in a multi-static passive radar system through convex optimization

We propose efficient target localization methods for a passive radar system using time-of-arrival (TOA) information of the signals received from multiple illuminators, where the position of the receiver is subject to random errors. Since the maximum likelihood (ML) formulation of this target localiz...

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Published in	Signal processing Vol. 102; pp. 207 - 215
Main Authors	Chalise, Batu K., Zhang, Yimin D., Amin, Moeness G., Himed, Braham
Format	Journal Article
Language	English
Published	Amsterdam Elsevier B.V 01.09.2014 Elsevier
Subjects	Applied sciences Convex optimization Detection, estimation, filtering, equalization, prediction Exact sciences and technology Information, signal and communications theory Miscellaneous Passive radar Radar signal processing Semi-definite relaxation Signal and communications theory Signal processing Signal, noise Target localization Telecommunications and information theory Semi-definite relaxation Passive radar Radar signal processing Convex optimization Target localization Performance evaluation Non convex programming Random error Multistatic radar Passive system Algorithm Convex programming Optimization Mean square error Arrival time Relaxation Simulation Signal processing Maximum likelihood Target detection Cramer Rao inequality Software radio
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ISSN	0165-1684 1872-7557
DOI	10.1016/j.sigpro.2014.02.023

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Abstract	We propose efficient target localization methods for a passive radar system using time-of-arrival (TOA) information of the signals received from multiple illuminators, where the position of the receiver is subject to random errors. Since the maximum likelihood (ML) formulation of this target localization problem is a non-convex optimization problem, semi-definite relaxation (SDR)-based optimization methods in general do not provide satisfactory performance. As a result, approximated ML optimization problems are proposed and solved with SDR plus bisection methods. For the case without position error, it is shown that the relaxation guarantees a rank-one solution. The optimization problem for the case with position error involves only a relaxation of a scalar quadratic term. Simulation results show that the proposed algorithms outperform existing methods and provide root mean-square error performance very close to the Cramer–Rao lower bound. •Efficient target localization methods exploiting time-of-arrival information are developed based on semi-definite relaxation (SDR).•The proposed methods provide root mean-square error (RMSE) performance that is close to the Cramer–Rao lower bound (CRLB) and outperform existing SDR-based target localization techniques.•The application to bistatic passive radar systems with multiple illuminators is new.•The computation complexity of the proposed methods is shown to be advantageous as compared to existing SDR-based methods.
AbstractList	We propose efficient target localization methods for a passive radar system using time-of-arrival (TOA) information of the signals received from multiple illuminators, where the position of the receiver is subject to random errors. Since the maximum likelihood (ML) formulation of this target localization problem is a non-convex optimization problem, semi-definite relaxation (SDR)-based optimization methods in general do not provide satisfactory performance. As a result, approximated ML optimization problems are proposed and solved with SDR plus bisection methods. For the case without position error, it is shown that the relaxation guarantees a rank-one solution. The optimization problem for the case with position error involves only a relaxation of a scalar quadratic term. Simulation results show that the proposed algorithms outperform existing methods and provide root mean-square error performance very close to the Cramer–Rao lower bound. •Efficient target localization methods exploiting time-of-arrival information are developed based on semi-definite relaxation (SDR).•The proposed methods provide root mean-square error (RMSE) performance that is close to the Cramer–Rao lower bound (CRLB) and outperform existing SDR-based target localization techniques.•The application to bistatic passive radar systems with multiple illuminators is new.•The computation complexity of the proposed methods is shown to be advantageous as compared to existing SDR-based methods.
Author	Amin, Moeness G. Himed, Braham Chalise, Batu K. Zhang, Yimin D.
Author_xml	– sequence: 1 givenname: Batu K. surname: Chalise fullname: Chalise, Batu K. organization: Wireless Communications and Positioning Laboratory, Center for Advanced Communications, Villanova University, Villanova, PA 19085, USA – sequence: 2 givenname: Yimin D. surname: Zhang fullname: Zhang, Yimin D. email: yimin.zhang@villanova.edu organization: Wireless Communications and Positioning Laboratory, Center for Advanced Communications, Villanova University, Villanova, PA 19085, USA – sequence: 3 givenname: Moeness G. surname: Amin fullname: Amin, Moeness G. organization: Wireless Communications and Positioning Laboratory, Center for Advanced Communications, Villanova University, Villanova, PA 19085, USA – sequence: 4 givenname: Braham surname: Himed fullname: Himed, Braham organization: Air Force Research Laboratory, AFRL/RYMD, Dayton, OH 45433, USA
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Keywords	Semi-definite relaxation Passive radar Radar signal processing Convex optimization Target localization Performance evaluation Non convex programming Random error Multistatic radar Passive system Algorithm Convex programming Optimization Mean square error Arrival time Relaxation Simulation Signal processing Maximum likelihood Target detection Cramer Rao inequality Software radio
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Snippet	We propose efficient target localization methods for a passive radar system using time-of-arrival (TOA) information of the signals received from multiple...
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SubjectTerms	Applied sciences Convex optimization Detection, estimation, filtering, equalization, prediction Exact sciences and technology Information, signal and communications theory Miscellaneous Passive radar Radar signal processing Semi-definite relaxation Signal and communications theory Signal processing Signal, noise Target localization Telecommunications and information theory
Title	Target localization in a multi-static passive radar system through convex optimization
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