Robust processing of heavy tails signals - comparison of approaches

This paper deals with robust estimation of AR parameters. We compare the performance of the LMS algorithm to the performance of two robust, adaptive algorithms: the LMAD algorithm of Shao and Nikias in which the error signal in the LMS algorithm is hard-limited before used to control the weights, and the LLMS algorithm in which the input process is soft-limited before the LMS algorithm is applied. The comparison is done in terms of rate of convergence and stability (steady state variance). We show that with a proper choice of limiting level, the LLMS algorithm outperforms the LMAD algorithms when applied to symmetric, α stable processes of 1 ≤ α ≤ 2.