修正的最小二乘拟合波达方向估计方法

The Modified Method of DOA Estimation Based on Least Squares Fitting

首先分析了基于最小二乘拟合技术的多普勒信号波达方向估计方法原理 ,在此基础上 ,进一步讨论了采样时间相关矩阵发生亏秩对该方法的影响 ,即由于加权矢量的可选择自由度过大导致最优化问题出现病态。但可以证明 ,所有满足约束条件的加权矢量均可使最小二乘拟合问题收敛至相同的极值点 ,所以选择具有最小范数的加权矢量最优解是合理的。此外 ,对原问题进行降秩或秩恢复处理也可得到满意的收敛结果 ,文中对此作了详细讨论并给出了相应的修正步骤。最后给出的计算机仿真结果验证了所给修正方法的有效性。

The paper studies the effect of rank deficiency in sampling temporal correlation matrix by the LSF method for Doppler signal DOA estimation under the assumption that the array manifold is unknown. In many practical applications, the degree of feeedom for the optimal solution seeking is too hight, leading to an unwilling ill conditioned problem which degrades the LSF based method severely. The paper, proposes several preprocessing schemes for solving the potential poor convergence problem involved in the original optimization procedure. It is also shown that selecting a solution with minimum morm for the optimization is reasonable and feasible. In addition, some other techniques such as rank restoring and rank reducing which result in a successful convergence in beamspace are also presented. In these methods, good convergence can be achieved with some preprocessing techniques. Simulation results show that the given modification methods are very effective.\;