Abstract: FxLMS（Filtered-x Least Mean Square） has been used widely in AVC（Active Vibration Control） system. In practice, the signal produced by the sensors contains not only the signal but also interference, such as measurement noise or burst noise, which deteriorate the AVC system. In order to solve this problem, a new robust filtered-x LMS algorithm is proposed. A Tracking-Differentiator filter and a non-linear transformation function are designed to process the reference and error signals respectively. The updating formula of the filter coefficients in the proposed algorithm is derived from a new minimization criterion that minimizes the Euclidean norm of difference between the currently innovation vector and past vector. Compared with the existing algorithms, the proposed algorithm is more robust against interference to reference signals. Numerical simulation results show the effectiveness of the algorithm.

Key words: Filtered-x Least Mean Square（FxLMS） algorithm, Active Vibration Control（AVC）, impulsive noise, tracking-differentiator filter, non-linear transformation

摘要： FxLMS（Filtered-x Least Mean Square）算法在主动振动控制系统中有着广泛的应用，在实际系统中由于参考输入信号会混入诸如测量噪声、冲击噪声、野值等与参考信号不相关的干扰信号，这会导致系统更新稳定性性能变坏，甚至发散。针对这个问题，提出一种改进的FxLMS算法。新的算法利用跟踪微分滤波器和非线性变换函数分别对参考输入信号和反馈误差信号进行处理。同时，以滤波器更新向量的差值最小为优化条件推导出新的更新公式。通过在主动振动控制系统中与已有算法进行仿真比较，仿真结果证明在处于噪声干扰的情况下新的算法体现出更好的更新稳定性。

关键词: 滤波-x最小均方算法（FxLMS）, 主动振动控制, 冲击噪声, 跟踪微分滤波器, 非线性变换