基于截断修正平滑l_0范数的MIMO雷达目标参数估计
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摘要
在多输入多输出(MIMO)雷达中,针对平滑l0范数(SL0)因感知矩阵的病态性而导致其失效的问题,提出了一种基于截断修正SL0的MIMO雷达目标参数估计方法。该方法在对MIMO雷达感知矩阵进行截断奇异值分解(TSVD)处理的基础上,将保留的奇异值以均值为截断门限,分成较大和较小的两部分,分别采用不同的修正准则进行修正;然后经奇异值分解(SVD)反变换获得非病态感知矩阵,利用该非病态感知矩阵通过SL0算法对MIMO雷达目标参数进行估计,从而显著提高了MIMO雷达目标参数估计的精度和速度。仿真结果验证了该方法的有效性。
Because of the ill-posed sensing matrix,the smoothed l_0norm( SL0) algorithm fails to estimate target parameter in multiple input multiple output( MIMO) radars. To solve this problem,the truncated modified smoothed l_0 norm algorithm for MIMO radars is proposed. Based on the truncated singular value decomposition algorithm( TSVD),the retained singular values of sensing matrix are divided into the larger and smaller by the mean value of singular values. Then,the two groups of the singular values are modified by using different modified criterion. From the modified singular values,the SVD inverse transform is utilized to obtain a non ill-posed sensing matrix. Finally,the SL0 algorithm can be used to reconstruct the target signals in the MIMO radar by taking advantage of the obtained non ill-posed sensing matrix. Therefore,the target parameters can be fast estimated with high accuracy for MIMO radar. The validity of the proposed method is demonstrated with the numerical simulations.
Because of the ill-posed sensing matrix,the smoothed l_0norm( SL0) algorithm fails to estimate target parameter in multiple input multiple output( MIMO) radars. To solve this problem,the truncated modified smoothed l_0 norm algorithm for MIMO radars is proposed. Based on the truncated singular value decomposition algorithm( TSVD),the retained singular values of sensing matrix are divided into the larger and smaller by the mean value of singular values. Then,the two groups of the singular values are modified by using different modified criterion. From the modified singular values,the SVD inverse transform is utilized to obtain a non ill-posed sensing matrix. Finally,the SL0 algorithm can be used to reconstruct the target signals in the MIMO radar by taking advantage of the obtained non ill-posed sensing matrix. Therefore,the target parameters can be fast estimated with high accuracy for MIMO radar. The validity of the proposed method is demonstrated with the numerical simulations.
引文
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[10]HANSEN P C.Rank-deficient and discrete ill-posed problems:numerical aspects of linear inversion[M].Philadelphia,PA:SIAM,1997.
[11]冯俊杰,张弓,方文青.基于SL0范数的改进稀疏信号重构算法[J].数据采集与处理,2016,31(1):178-183.FENG Junjie,ZHANG Gong,FANG Wenqing.Improved sparse signal reconstruction algorithm based on SL0 norm[J].Journal of Data Acquisition and Processing,2016,31(1):178-183.(in Chinese)
[12]TAN X,ROBERTS W,LI J,et al.Sparse learning via iterative minimization with application to MIMO radar imaging[J].IEEE Transactions on Signal Processing,2011,59(3):1088-1101.
[13]冯遵德.II类病态系统分析理论及其应用研究[D].山东:山东科技大学,2006.FENG Zunde.Research on analysis theory and application for II ill-condition system[D].Shandong:Shandong University of Science and Technology,2006.(in Chinese)
[2]FISHLER E,HAIMOVICH A,BLUM R,et al.Spatial diversity in radars-models and detection performance[J]IEEE Transactions on Signal Processing,2006,54(3):823-838.
[3]段沛沛,李辉.压缩感知稀疏表示在雷达目标识别中的应用[J].电讯技术,2016,56(1):20-25.DUAN Peipei,LI Hui.Application of compressed sensing sparse representation in radar target recognition[J].Telecommunication Engineering,2016,56(1):20-25.(in Chinese)
[4]LI J,STOICA P.MIMO radar with collocated antennas[J].IEEE Signal Processing Magazine,2007,24(5):106-114.
[5]DONOHO D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[6]YAO Y,ATHINA P,VINCENT P.Measurement matrix design for compressive sensing based MIMO radar[J].IEEE Transactions on Signal Processing,2011,59(11):5338-5352.
[7]GONG P,SHAO Z.Target estimation by iterative reweighted lqminimization for MIMO radar[J].Signal Processing,2014,101(C):35-41.
[8]MOHIMANI G H,BABAIE-ZADEH M,JUTTEN C.Fast sparse representation using smoothed l0norm[J].IEEETransactions on Signal Processing,2007,46(6):1-12.
[9]FENG J J,ZHANG G,WEN F Q.MIMO radar imaging based on smoothed l0norm[J].Mathematical Problems in Engineering,2015,2015(8):1-10.
[10]HANSEN P C.Rank-deficient and discrete ill-posed problems:numerical aspects of linear inversion[M].Philadelphia,PA:SIAM,1997.
[11]冯俊杰,张弓,方文青.基于SL0范数的改进稀疏信号重构算法[J].数据采集与处理,2016,31(1):178-183.FENG Junjie,ZHANG Gong,FANG Wenqing.Improved sparse signal reconstruction algorithm based on SL0 norm[J].Journal of Data Acquisition and Processing,2016,31(1):178-183.(in Chinese)
[12]TAN X,ROBERTS W,LI J,et al.Sparse learning via iterative minimization with application to MIMO radar imaging[J].IEEE Transactions on Signal Processing,2011,59(3):1088-1101.
[13]冯遵德.II类病态系统分析理论及其应用研究[D].山东:山东科技大学,2006.FENG Zunde.Research on analysis theory and application for II ill-condition system[D].Shandong:Shandong University of Science and Technology,2006.(in Chinese)