一种基于对数函数的改进变步长LMS算法研究

Study on An improved step size factor of variable LMS algorithm

为提高超弱光纤光栅反射信号光电检测电路的测量精度,提出一种新的变步长LMS算法去除光电探测器信号中的高斯噪声。针对基于对数函数的变步长LMS(Least Mean Square)算法其步长因子易受噪声干扰,导致其步长因子取值在最优解附近波动的问题。根据高斯白噪声相关性差的特性,使用相关特性改进步长因子的更新公式,降低不相关噪声对稳态误差的影响。通过理论分析和MATLAB软件仿真结果对比分析改进前后收敛速度和稳态误差,本算法在低信噪比条件下稳态误差减小三分之一,收敛速度更快,具有更好的抗噪、滤波性能,有效抑制了超弱光纤光栅反射信号检测的噪声。

In order to improve the measurement accuracy of the photoelectric detection circuit of the ultra-weak FBG reflection signal.A new variable step LMS algorithm is proposed to remove Gaussian noise from photodetector signal.Aim at the problem that the step size factor of variable LMS algorithm based on logarithmic function is easy to be disturbed by noise,lead to the step size factor waveing among the optimal solution.According to the bad correlation of white Gaussian noise,using correlation characteristic to improve the update formula of step size to reduce the impact of noise.The theory analyze and simulation comparative analysis of convergence rate and steady-state error before and after improvement show that this algorithm’s steady-state error reduced by one third and has better ability of resist noise and smoothing in low SNR environment.The noise of the reflection signal detection of the ultra weak fiber grating is effectively suppressed.