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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。
In this paper, using the least-squares method, the singular value decomposition of the augmented matrix of the linear prediction equations of space front and backward is established, and the signal and noise subspace are established. Under the minimum F norm of the error augmentation matrix, it is proved that The augmented form of the predictive equation coefficient vector is located exactly within the noise subspace. The analysis of signal subspace perturbations shows that this method is superior to the modified method of spatial smoothing. Theoretical and simulation results show that this method can achieve good signal-to-noise ratio and good resolution of coherent signal sources.