Alpha稳定分布噪声环境下新的类RLS自适应算法

New RLS-like adaptive algorithm under alpha-stable noise conditions

给出在分数低阶Alpha稳定分布环境中一种新的类RLS自适应算法.由于Alpha稳定分布信号不存在有限的二阶和二阶以上矩,因此用最小p范数准则代替了传统的最小均方准则,并利用矩阵求逆定理提出一种直接递推的类RLS算法,避免了以往类RLS算法中的IRLS迭代计算,从而使算法的计算复杂度大大降低.最后对几种自适应算法进行仿真,并对其收敛特性进行了分析.结果表明,算法的收敛速度明显快于LMP和NLMP算法.

This paper introduces a new RLS-like adaptive algorithm for filtering alpha-stable noises. Unlike previously introduced stochastic gradient- type algorithms, the new adaptation algorithm minimizes the Lp norm of the error at the output of the adaptive filter instead of the usual Euclidean norm. The new algorithm is proposed by way of the matrix inversion lemma and convergence and greatly decreases computational complexity. Computer simulations are presented to compare the relative performances of the related algorithms, The results show that the convergence speed of the new RLS-like adaptive algorithm is much faster than that of the LMP and NLMP algorithms.