How to Select the Best Sensors for TDOA and TDOA/AOA Localization?
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摘要
This paper focuses on the sensor subset optimization problem in time difference of arrival(TDOA) passive localization scenario. We seek for the best sensor combination by formulating a non-convex optimization problem, which is to minimize the trace of covariance matrix of localization error under the condition that the number of selected sensors is given. The accuracy metric is described by the localization error covariance matrix of classical closed-form solution, which is introduced to convert the TDOA nonlinear equations into pseudo linear equations. The non-convex optimization problem is relaxed to a standard semi-definite program(SDP) and efficiently solved in a short time. In addition, we extend the sensor selection method to a mixed TDOA and angle of arrival(AOA) localization scenario with the presence of sensor position errors. Simulation results validate that the performance of the proposed sensor selection method is very close to the exhaustive search method.
This paper focuses on the sensor subset optimization problem in time difference of arrival(TDOA) passive localization scenario. We seek for the best sensor combination by formulating a non-convex optimization problem, which is to minimize the trace of covariance matrix of localization error under the condition that the number of selected sensors is given. The accuracy metric is described by the localization error covariance matrix of classical closed-form solution, which is introduced to convert the TDOA nonlinear equations into pseudo linear equations. The non-convex optimization problem is relaxed to a standard semi-definite program(SDP) and efficiently solved in a short time. In addition, we extend the sensor selection method to a mixed TDOA and angle of arrival(AOA) localization scenario with the presence of sensor position errors. Simulation results validate that the performance of the proposed sensor selection method is very close to the exhaustive search method.
This paper focuses on the sensor subset optimization problem in time difference of arrival(TDOA) passive localization scenario. We seek for the best sensor combination by formulating a non-convex optimization problem, which is to minimize the trace of covariance matrix of localization error under the condition that the number of selected sensors is given. The accuracy metric is described by the localization error covariance matrix of classical closed-form solution, which is introduced to convert the TDOA nonlinear equations into pseudo linear equations. The non-convex optimization problem is relaxed to a standard semi-definite program(SDP) and efficiently solved in a short time. In addition, we extend the sensor selection method to a mixed TDOA and angle of arrival(AOA) localization scenario with the presence of sensor position errors. Simulation results validate that the performance of the proposed sensor selection method is very close to the exhaustive search method.
引文
[1]K.C.Ho and M.Sun,“Passive Source Localization Using Time Differences of Arrival and Gain Ratios of Arrival,”IEEE Trans.Signal Process.,vol.56,no.2,2008,pp.464-477.
[2]B.Hao,Z.Li,J.Si,W.Yin,and Y.Ren,“Passive Multiple Disjoint Sources Localization Using TDOAs and GROAs in the Presence of Sensor Location Uncertainties,”Proc.IEEE International Conference on Communications(IEEE ICC),2012,pp.47-52.
[3]B.Hao,Z.Li,P.Qi,L.Guan,“Effective Bias Reduction Methods for Passive Source Localization using TDOA and GROA,”Science China Information Sciences,vol.56,no.7,2013,pp.1-12.
[4]S.Liu,M.Rao,Y.Tao,L.Liu,P.Zhang,“A Virtual TDOA Localization Scheme of Chinese DTMBSignal in Radio Monitoring Networks,”China Communications,vol.12,no.11,2015,pp.164-176.
[5]T.Zhang,A.F.Molisch,Y.Shen,Q.Zhang,Hao Feng,M.Z.Win,“Joint Power and Bandwidth Allocation in Wireless Cooperative Wireless Localization Networks,”IEEE Trans.Wireless commun.,vol.15,no.10,2016,pp.6527-6540.
[6]T.Wang,Y.Shen,M.Z.Win,“A General Analytical Framework of Scheduling Algorithms for Network Navigation,”Proc.IEEE International Conference on Communications(IEEE ICC),Sydney,Australia,pp.4583-4588,Jun.2014.
[7]K.Witrisal,et al.,“High-Accuracy Localization for Assisted Living 5G systems will turn multipath channels from foe to friend,”IEEE Signal Process.Mag.,vol.33,no.2,2016,pp.59-70.
[8]Z.Li,L.Guan,C.Li,A.Radwan,“A Secure Intelligent Spectrum Control Strategy for Future THz Mobile Heterogeneous Networks,”IEEE Commun.Mag.,vol.56,no.6,2018,pp.116-123.
[9]S.Chen and J.Zhao,“The Requirements,Challenges and Technologies for 5G of Terrestrial Mobile Telecommunication,”IEEE Commun.Mag.,vol.52,no.5,2014,pp.36-43.
[10]Y.Wang and K.C.Ho,“An Asymptotically Efficient Estimator in Closed-Form for 3-D AOA Localization Using a Sensor Network,”IEEE Trans.Wireless Commun.,vol.14,no.12,2015,pp.6524-6535.
[11]Y.Zhao,Z.Li,B.Hao,J.Si,P.Wan,“Bias Reduced Method for TDOA and AOA Localization in the Presence of Sensor Errors,”Proc IEEE International Conference on Communications(IEEEICC),2017,pp.1-6.
[12]F.Gao and A.B.Gershman,“A Generalized ESPRIT Approach to Direction-of-Arrival Estimation,”IEEE Signal Process.Lett.,vol.12,no.3,2005,pp.254-257.
[13]A.Noroozi,M.A.Sebt,“Spherical Interpolation Method of Emitter Localisation using Weighted Least Squares,”IET Signal Process.,vol.10,no.8,2016,pp.841-854.
[14]L.M.Kaplan,“Global Node Selection for Localization in a Distributed Sensor Network,”IEEETrans.Aerosp.Electron.Syst.,vol.42,no.1,2006,pp.113-135.
[15]K.W.K.Lui,H.C.So,“A Study of Two-dimensional Sensor Placement using Time Difference of Arrival Measurements,”Digital Signal Processing,vol.19,no.4,2009,pp.650-659.
[16]H.Jamali-Rad,A.Simonetto,G.Leus,“Sparsity-Aware Sensor Selection:Centralized and Distributed Algorithms,”IEEE Signal Process.Lett.,vol.21,no.2,2014,pp.217-220.
[17]H.Jamali-Rad,A.Simonetto,X.Ma,G.Leus,“Distributed Sparsity-Aware Sensor Selection,”IEEE Trans.Signal Process.,vol.63,no.22,2015,pp.5951-5964.
[18]S.Joshi and S.Boyd,“Sensor Selection via Convex Optimization,”IEEE Trans.Signal Process.,vol.57,no.2,2009,pp.451-462.
[19]S.Liu,S.P.Chepuri,M.Fardad,E.Masazade,G.Leus,and P.K.Varshney,“Sensor Selection for Estimation with Correlated Measurement Noise,”IEEE Trans.Signal Process.,vol.64,no.13,2016,pp.3509-3522.
[20]S.P.Chepuri and G.Leus,“Sparsity-Promoting Sensor Selection for Nonlinear Measurement Models,”IEEE Trans.Signal Process.,vol.63,no.3,2015,pp.684-698.
[21]H.Wang,K.Yao,G.Pottie,D.Estrin,“Entropy-based Sensor Selection Heuristic for Target Localization,”Proc.IEEE International Symposium on Information Processing in Sensor Networks,2004,pp.36-45.
[22]S.Rao,S.P.Chepuri,and G.Leus,“Greedy Sensor Selection for Nonlinear Models,”Proc.IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing(CAMSAP),2015,pp.241-244.
[23]X.Hu and M.L.Fowler,“Sensor Selection for Multiple Sensor Emitter Location Systems,”Proc.IEEE Aerospace Conference,2008,pp.1-10.
[24]K.C.Ho and W.Xu,“An Accurate Algebraic Solution for Moving Source Location Using TDOA and FDOA Measurements,”IEEE Trans.Signal Process.,vol.52,no.9,2004,pp.2453-2463.
[25]M.Grant,S.Boyd,and Y.Ye,“CVX Version 1.1.Matlab Software for Disciplined Convex Programming 2007,”Available:www.stanford.edu/~boyd/cvx/.
[26]B Hao,Y.Zhao,Z.Li and P.Wan,“A Sensor Selection Method for TDOA and AOA localization in the Presence of Sensor Errors,”Proc.IEEE/CICInternational Conference on Communications in China(IEEE/CIC ICCC),2017,pp.1-6.Biographies
[2]B.Hao,Z.Li,J.Si,W.Yin,and Y.Ren,“Passive Multiple Disjoint Sources Localization Using TDOAs and GROAs in the Presence of Sensor Location Uncertainties,”Proc.IEEE International Conference on Communications(IEEE ICC),2012,pp.47-52.
[3]B.Hao,Z.Li,P.Qi,L.Guan,“Effective Bias Reduction Methods for Passive Source Localization using TDOA and GROA,”Science China Information Sciences,vol.56,no.7,2013,pp.1-12.
[4]S.Liu,M.Rao,Y.Tao,L.Liu,P.Zhang,“A Virtual TDOA Localization Scheme of Chinese DTMBSignal in Radio Monitoring Networks,”China Communications,vol.12,no.11,2015,pp.164-176.
[5]T.Zhang,A.F.Molisch,Y.Shen,Q.Zhang,Hao Feng,M.Z.Win,“Joint Power and Bandwidth Allocation in Wireless Cooperative Wireless Localization Networks,”IEEE Trans.Wireless commun.,vol.15,no.10,2016,pp.6527-6540.
[6]T.Wang,Y.Shen,M.Z.Win,“A General Analytical Framework of Scheduling Algorithms for Network Navigation,”Proc.IEEE International Conference on Communications(IEEE ICC),Sydney,Australia,pp.4583-4588,Jun.2014.
[7]K.Witrisal,et al.,“High-Accuracy Localization for Assisted Living 5G systems will turn multipath channels from foe to friend,”IEEE Signal Process.Mag.,vol.33,no.2,2016,pp.59-70.
[8]Z.Li,L.Guan,C.Li,A.Radwan,“A Secure Intelligent Spectrum Control Strategy for Future THz Mobile Heterogeneous Networks,”IEEE Commun.Mag.,vol.56,no.6,2018,pp.116-123.
[9]S.Chen and J.Zhao,“The Requirements,Challenges and Technologies for 5G of Terrestrial Mobile Telecommunication,”IEEE Commun.Mag.,vol.52,no.5,2014,pp.36-43.
[10]Y.Wang and K.C.Ho,“An Asymptotically Efficient Estimator in Closed-Form for 3-D AOA Localization Using a Sensor Network,”IEEE Trans.Wireless Commun.,vol.14,no.12,2015,pp.6524-6535.
[11]Y.Zhao,Z.Li,B.Hao,J.Si,P.Wan,“Bias Reduced Method for TDOA and AOA Localization in the Presence of Sensor Errors,”Proc IEEE International Conference on Communications(IEEEICC),2017,pp.1-6.
[12]F.Gao and A.B.Gershman,“A Generalized ESPRIT Approach to Direction-of-Arrival Estimation,”IEEE Signal Process.Lett.,vol.12,no.3,2005,pp.254-257.
[13]A.Noroozi,M.A.Sebt,“Spherical Interpolation Method of Emitter Localisation using Weighted Least Squares,”IET Signal Process.,vol.10,no.8,2016,pp.841-854.
[14]L.M.Kaplan,“Global Node Selection for Localization in a Distributed Sensor Network,”IEEETrans.Aerosp.Electron.Syst.,vol.42,no.1,2006,pp.113-135.
[15]K.W.K.Lui,H.C.So,“A Study of Two-dimensional Sensor Placement using Time Difference of Arrival Measurements,”Digital Signal Processing,vol.19,no.4,2009,pp.650-659.
[16]H.Jamali-Rad,A.Simonetto,G.Leus,“Sparsity-Aware Sensor Selection:Centralized and Distributed Algorithms,”IEEE Signal Process.Lett.,vol.21,no.2,2014,pp.217-220.
[17]H.Jamali-Rad,A.Simonetto,X.Ma,G.Leus,“Distributed Sparsity-Aware Sensor Selection,”IEEE Trans.Signal Process.,vol.63,no.22,2015,pp.5951-5964.
[18]S.Joshi and S.Boyd,“Sensor Selection via Convex Optimization,”IEEE Trans.Signal Process.,vol.57,no.2,2009,pp.451-462.
[19]S.Liu,S.P.Chepuri,M.Fardad,E.Masazade,G.Leus,and P.K.Varshney,“Sensor Selection for Estimation with Correlated Measurement Noise,”IEEE Trans.Signal Process.,vol.64,no.13,2016,pp.3509-3522.
[20]S.P.Chepuri and G.Leus,“Sparsity-Promoting Sensor Selection for Nonlinear Measurement Models,”IEEE Trans.Signal Process.,vol.63,no.3,2015,pp.684-698.
[21]H.Wang,K.Yao,G.Pottie,D.Estrin,“Entropy-based Sensor Selection Heuristic for Target Localization,”Proc.IEEE International Symposium on Information Processing in Sensor Networks,2004,pp.36-45.
[22]S.Rao,S.P.Chepuri,and G.Leus,“Greedy Sensor Selection for Nonlinear Models,”Proc.IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing(CAMSAP),2015,pp.241-244.
[23]X.Hu and M.L.Fowler,“Sensor Selection for Multiple Sensor Emitter Location Systems,”Proc.IEEE Aerospace Conference,2008,pp.1-10.
[24]K.C.Ho and W.Xu,“An Accurate Algebraic Solution for Moving Source Location Using TDOA and FDOA Measurements,”IEEE Trans.Signal Process.,vol.52,no.9,2004,pp.2453-2463.
[25]M.Grant,S.Boyd,and Y.Ye,“CVX Version 1.1.Matlab Software for Disciplined Convex Programming 2007,”Available:www.stanford.edu/~boyd/cvx/.
[26]B Hao,Y.Zhao,Z.Li and P.Wan,“A Sensor Selection Method for TDOA and AOA localization in the Presence of Sensor Errors,”Proc.IEEE/CICInternational Conference on Communications in China(IEEE/CIC ICCC),2017,pp.1-6.Biographies