一种新型跟踪离散1/f噪声信号递归RLS算法

Novel Recursive Least Squares algorithm for tracking discrete-time 1/f noise signal

给出了一个对离散1/f噪声信号进行跟踪简单修正的RLS算法。正规RLS算法或快速RLS算法在有限运算精度条件下的收敛性和失调性没有本质区别,它们在有限迭代次数后必定会导致RLS滤波器权系数发散,特别是在跟踪非平稳信号时更是如此。鉴于此,通过引入一个非线性函数对RLS滤波器输入数据的逆自相关阵予以修正。实验表明该算法具有良好的跟踪非平稳信号以及具有混沌特性的1/f噪声信号的能力,能有效降低跟踪的平均误差以及方差,且能根据输入数据的变化快速调整滤波器系数,性能比正规RLS算法好。对于跟踪fBm噪声过程如何动态调节记忆因子的问题,推导了记忆因子与输入信号的自相关矩阵特征值之间的一个关系表达式,这为采用RLS算法动态调整记忆因子来跟踪fBm过程提供了理论依据。

A simple improved RLS algorithm is given to track a discrete-time noised 1/f signal. Formal RLS algorithm or rapid computing RLS algorithm in the limited accuracy under the conditions of disorder and convergence is no essential difference, they are limited in the number of iterations and the RLS filter will lead to weight divergence, particularly in tracking non-stationary signals even more so. In view of this, this paper introduces a non-linear fimction of RLS filter input data from the inverse correlation matrix to be amended. Experiments show that the algorithm has a good track non-stationary signals as well as the characteristics of chaos with the 1/f noise of the signal capabilities. It can effectively reduce the tracking error, as well as the average variance, and can input data in accordance with the rapid changes in the adjustment of filter coefficients. Performance is better than the regular RLS algorithm. FBm noise for tracking the dynamic process of adjustment factor memory, this paper derives an expression of relation between memory factor and input signal autocorrelation matrix, providing theoretical basis for the RLS algorithm which is used to dynamically adjust the memory factor to track the fBm process.