基于奇异值比值的正则化矩阵修正方法

Correction Method of Regularized Matrix Based on Ratio of Singular Value

针对雷达数据反演过程中存在的不适定性问题,基于岭估计方法分析,提出了一种基于奇异值比值的正则化矩阵修正方法。奇异值分解矩阵后,通过条件数法在奇异值矩阵中确定门限奇异值,将门限奇异值与各奇异值比值的平方根构造对角矩阵,将对角矩阵与左奇异值向量矩阵结合构造正则化矩阵。该方法能够加强对较小奇异值的修正,而减弱对较大奇异值的修正,从而保证了不适定问题解算结果的可靠性及计算精度。数值计算与误差分析结果证明了该方法的有效性。

A new correction method is presented for the ill-conditioned problems in radar data inversion process. After singular value decomposition of the matrix, the threshold of the singular value is selected by the conditional number method in the singular value matrix, and the ratio of the threshold singular value to each singular value is composed into a diagonal matrix. Then comnine the diagonal matrix with the left singular value vector matrix to construct the regularization matrix. The method adjusts the correction of each singular value by regularization parameter and the constructed diagonal matrix. Because the values in the singular value matrix are monotonically decreasing, the values in the constructed regularization matrix monotonically increase. Therefore, the correction for larger singular values will be weak, while the correction for smaller singular values will gradually change with the gradual decrease of singular values, ensuring the reliability of the numerical estimation and the calculation accuracy. The numerical calculations and error analysis demonstrate the effectiveness of the method.