一种基于算子理论的去相关LMS自适应滤波算法

针对输入信号向量序列之间的相关性将显著降低LMS算法的性能这一问题，从算子的角度出发，提出了一种新的去相关LMS自适应滤波算法。通过将最新输入向量向以前所有时刻的输入向量序列所张成的线性空间的零空间作正交投影，达到提取新信息的目的，并以提取的新息作为LMS算法的更新方向向量。仿真分析表明，新算法具有收敛速度快、输出误差小以及对信噪比不敏感等特点，并且采用较低的滤波器阶数即可得到良好的滤波效果，同时提高算法的运算效率。

Decorrelation-based least mean square adaptive filtering algorithm based on theory of operators

To resolve the performance-worsening problem of the least mean square (LMS) algorithm caused by the correlation among the input signal vector sequence, this paper proposed a new decorrelation-based LMS algorithm based on theory of ope-rators. The algorithm extracted the innovation process by projecting the latest input signal vector into the null space of the linear space generated by all the previous input signal vectors orthogonally, and took the innovation process as the updating direction vector. Simulation results show that the new algorithm has characteristics as following: fast convergence, small output errors and insensitive to the signal to noise ratio. Further more, the filter adopting the new algorithm can obtain a satisfactory filtering effect and an improving operational efficiency as well by choosing a lower filter order.