Gradient-based variable forgetting factor RLS algorithm in time-varying environments
Gradient-based variable forgetting factor RLS algorithm in time-varying environments
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DOI：
10.1109/tsp.2005.851110
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发表时间：
2005-08-01
影响因子：
5.4
通讯作者：
So, CF
中科院分区：
文献类型：
--
作者：
Leung, SH;So, CF
本文提出了一种新的递推最小二乘（RLS）自适应算法的可变遗忘因子（VFF）控制机制。控制算法基本上是一个基于梯度的方法，其中的梯度是来自一个改进的均方误差分析的RLS。新的均方误差分析利用了相关矩阵的逆与自身的相关性，从而改进了理论结果，特别是在瞬态和稳态均方误差方面。结果表明，对于不同的遗忘因子和不同的模型阶数，理论分析与仿真结果接近。分析产生的均方误差的动态方程，可用于导出的均方误差的梯度的动态方程，以控制遗忘因子。当误差较大时，动态方程会产生正梯度，而当误差处于稳态时，动态方程会产生负梯度。与其他变遗忘因子算法相比，新的控制算法在不同信噪比下都能实现快速跟踪和较小的均方模型误差。
In this paper, a new control mechanism for the variable forgetting factor (VFF) of the recursive least square (RLS) adaptive algorithm is presented. The control algorithm is basically a gradient-based method of which the gradient is derived from an improved mean square error analysis of RLS. The new mean square error analysis exploits the correlation of the inverse of the correlation matrix with itself that yields improved theoretical results, especially in the transient and steady-state mean square error. It is shown that the theoretical analysis is close to simulation results for different forgetting factors and different model orders. The analysis yields a dynamic equation of mean square error that can be used to derive a dynamic equation of the gradient of mean square error to control the forgetting factor. The dynamic equation can produce a positive gradient when the error is large and a negative gradient when the error is in the steady state. Compared with other variable forgetting factor algorithms, the new control algorithm gives fast tracking and small mean square model error for different signal-to-noise ratios (SNRs).