基于截断核范数正则化的协方差矩阵估计

Truncated Nuclear Norm Regularization Based Covariance Matrix Estimation

非均匀杂波环境导致机载雷达用于协方差矩阵估计的样本不足。本文提出了一种基于截断核范数正则化(Truncated Nuclear Norm Regularization,TNNR)的协方差矩阵估计算法以满足小样本条件下机载雷达空时自适应处理(Space Time Adaptive Processing,STAP)应用。本文利用TNNR确保所估计杂波协方差矩阵(Clutter Covariance Matrix,CCM)的低秩特性,并将NP-hard问题转换为凸优化问题。不同于常规的秩最小化算法,如核范数松弛方法,本文所提出的TNNR算法仅最小化与矩阵的秩无关的较小奇异值的和,可以更加准确地约束矩阵的秩。在此基础上本文还利用CCM的块Toeplitz结构先验信息,可确保在连续域上进行信号建模,有效避免网格点失配问题。仿真结果表明本文所提出的算法在小样本条件下可更加准确地估计CCM且STAP性能更优。

The heterogeneous clutter environment leads to the shortage of samples for covariance matrix estimation of airborne radar.this paper proposes a novel covariance matrix estimation method based on truncated nuclear norm regularization(TNNR)for airborne space time adaptive processing(STAP)with small samples.Specifically,this paper exploits TNNR to ensure the low rank estimation of the clutter covariance matrix(CCM)and transforms the NP-hard problem to a convex optimization problem.Different from the general rank minimization approach,such as nuclear norm relaxation method,the proposed TNNR algorithm in this paper only minimizes the sum of small singular values,which are independent of the rank of a matrix,approximating the rank more accurately.Moreover,the paper also utilizes the prior knowledge of the block-Toeplitz structure of the CCM,which can ensure the model established in continuous domain,avoiding the off-grid problem effectively.The simulation results indicate that the proposed algorithm can estimate CCM more accurately and achieve better STAP performance.