The robustness analysis of DLMP algorithm under the fractional lower-order α-stable distribution environments

The direct least mean p-norm (DLMP) algorithm is a robust algorithm for time delay estimation under both Gaussian and fractional lower-order α-stable noise conditions. This paper briefly reviews the fundamental theory of α-stable distribution, abstracts two important theorems of fractional lower-order statistics, and under the Gaussian signal assumption, analyzes the convergence property of the DLMP algorithm, including the convergence property of the cost function, the unbiasness of the estimator and the appropriate selection of the convergence parameter μ. The improved performance of DLMP algorithm is clearly demonstrated through comprehensive simulations and detailed data analysis for estimating the latency changes of evoked potential (EP) signals.In the case of p=2, it is presented that DLMP algorithm keeps consistent with DLMS algorithm, which is based on second-order statistics, involving the cost function, the unbiasness of the estimator and the selection of the convergence parameter. Therefore, this paper proves that DLMP algorithm is a generalization of DLMS algorithm in α-stable distribution noisy environments.