改进的变步长自适应滤波及Eckart加权抑噪算法

针对已有的变步长自适应滤波算法对噪声干扰敏感的问题,提出改进的变步长最小均方误差自适应算法,该算法对误差的自相关时间均值估计做遗忘加权补偿,并改步长因子固定范围约束为动态变化约束,一方面克服了单纯采用自相关时间均值估计调整步长所导致的步长因子快速衰减,获得了较快的收敛速度；另一方面相比基于Sigmoid函数的变步长算法,具有更平滑的步长变化和更低的稳态失调噪声.在改进算法中引入Eckart加权进一步抑制了自适应滤波器权系数伪峰,采用滑动窗遗忘加权降低了计算复杂度.将新算法及其Eckart加权应用于自适应时延估计仿真实验,结果表明：相比于已有的2种参数固定条件下的变步长自适应滤波算法,改进算法获得了更好的高斯噪声和突变噪声干扰下的时变时延跟踪性能.

Modified variable step-size adaptive filtering and Eckart weighted denoising algorithm

The performance of the existing variable step-size least mean square(LMS) adaptive filtering algorithm is highly sensitive to the noise disturbance.In order to solve this problem,a modified variable step-size LMS-type algorithm was proposed.The modified algorithm compensates the time-averaged estimation of the autocorrelation of error with forgetting weight,and replaces the fixed step-size range restriction by dynamic change restriction.The modified algorithm overcomes the fast attenuation of step-size and obtains faster convergence rate.In addition,comparing to another variable step-size algorithm based on Sigmoid function,the modified algorithm is provided with smoother step-size variation and lower steady-state offset noise.Moreover,Eckart weighted method is introduced into the algorithm to restrain fake peaks of adaptive filter’s coefficient vector,and the use of sliding forgetting-weighted window reduces the computational complexity.The results of the simulation on tracking time-varying delay indicated that,the modified algorithm and its Eckart weighted method achieved superior performance for cases of Gaussian noise and impulsive noise interference,comparing to the existing step-size LMS algorithm being of fixed parameters.