前后向线性预测全最小二乘方法实现高分辨空间谱估计方法研究

The Study on High Resolution Spatial Spectrum Estimation Based on Total Least Square Method of Forward and Backward Linear Prediction

本文利用全最小二乘方法,对空间阵元前、后向线性预测方程的增广矩阵进行奇异值分解,建立信号、噪声子空间,在误差增广矩阵F范数最小的准则下,证明了预测方程系数矢量的增阶形式刚好位于噪声子空间内。信号子空间的扰动分析表明,这种方法优于修正的空间平滑方法。理论与模拟结果证明这种方法可以实现低信噪比、相干信号源的良好分辨。

This paper utillizes the Total Least Square method to decompose the data augmented matrix from spatial array's forward and backward linear prediction equticns into singular values and vectors to erect Signal and Noise Subspace.On the norms of minimum F-norm of error augmented matrix, it is proved that the augment-order forms of prediction equation coefficients locate Noise Subspace exactly.It is proved by the perturbation analysis of Signal Subspace that the performances of the method presented here are better than the improved spatial smoothing techniques.Theory and simulation results have proved and certificated that this method is able to excellently resolve the coherent signal sources of lower ratio of signal and noise.