数据矩阵的特性映象及其线谱估计应用

许多信号处理问题归结为求解一线性方程组。对此线性方程组的系数矩阵进行可能的特性映象,比如低秩化和Toeplitz结构化的处理,可以明显地降低噪声的影响,提高信号参量估计的准确度。本文讨论了数据矩阵的特性映象,并给出了叠代映象系列收敛的简单而形象的证明。在线谱估计的应用中,从正弦波自相关函数的模型出发,推导了该情况下数据矩阵的特性映象算法。通过一实例的计算和比较,可以看出此方法显著地改善了谱估计的性能。

PROPERTY MAPPING OF DATA MATRICES AND ITS APPLICATION TO SPECTRAL LINE ESTIMATION

In many signal processing applications there is often a set of linear equations to-be solved. According to signal properties, certain property mappings can be used on the data ma trix in the set of linear equations so that the effect of noise would be reduced and the accuracy of signal parameter estimation would be improved. The paper is devoted to this subject and the convergence of the iterative property mapping process associated with a data matrix is directly proved.
Applying this method to spectral line estimation, the specific iterative property mapping algorithm is derived with a sinusoid autocorrelation model. A given numerical example illustrates the improvement of high resolution performance.