基于几何方法的结构化协方差矩阵估计  

Geometric Approach for Structured Covariance Matrix Estimation

作　　者：马全鑫 杜晓林 董军 李建波 田团伟 MA Quanxin;DU Xiaolin;DONG Jun;LI Jianbo;TIAN Tuanwei(School of Computer and Control Engineering,Yantai University,Yantai 264005,China;School of Communication and Information Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;School of Physics and Electronics,Henan University,Kaifeng 475001,China)

机构地区：[1]烟台大学计算机与控制工程学院,山东烟台264005 [2]重庆邮电大学通信与信息工程学院,重庆400065 [3]河南大学物理与电子学院,河南开封475001

出　　处：《雷达科学与技术》2023年第2期143-150,共8页Radar Science and Technology

基　　金：国家自然科学基金(No.61801415);重庆市教委科学技术研究项目(No.KJQN202100605)。

摘　　要：针对雷达在非均匀环境下难以获得足够数量样本估计协方差矩阵,致使干扰抑制性能下降的问题,遵循几何范式,本文提出了两种结构化干扰协方差矩阵(ICM)估计算法。具体而言,算法从一组训练数据出发,考虑不同的协方差矩阵结构信息(Persymmetric或Toeplitz结构),构造了两种结构样本协方差矩阵(SSCMs),通过利用正定矩阵空间特性并施加条件数上限约束,以ICM和SSCMs之间的Frobenius范数作为目标函数建立极小化问题,并对该问题进行转化,最终得到估计器的闭式解。在两种场景下的仿真结果表明了所提算法可更加精确地估计ICM,有效地提高了干扰抑制性能,且在小样本情况下的优化效果更为显著。It is difficult to obtain sufficient samples to estimate the covariance matrix in a heterogeneous environ⁃ment,which leads to the degradation of radar interference suppression performance.To solve this problem,following the geometric paradigm,two structured interference covariance matrix(ICM)estimation algorithms are proposed in this paper.Specifically,starting from a set of training data,two structured sample covariance matrices(SSCMs)are con⁃structed by considering different covariance matrix structure information(i.e.,Persymmetric or Toeplitz structure).By exploiting the characteristics of positive⁃definite matrix space and imposing an upper bound constraint on the condition number,the two minimization problems are established with the Frobenius norm between ICM and SSCMs as the objec⁃tive functions.The problems are transformed and the closed⁃form solutions of the estimators are finally obtained.The simulation results show that the proposed two algorithms can estimate the ICM more accurately compared with the refer⁃ence algorithms in the two scenarios,thereby effectively improving the interference suppression performance,and the optimization effect is more significant in the case of small samples.

关 键 词：几何方法 协方差矩阵估计 Persymmetric结构 Toeplitz结构 干扰抑制 

分 类 号：TN957[电子电信—信号与信息处理]