Adaptive filtering under multi-peak noise

Abstract

In this paper, we assume the multi-peak noise in adaptive filtering follows a multimodal probability distribution (MPD), and model it as a Gaussian mixture model (GMM). Then a new gradient ascent algorithm is proposed based on the maximum likelihood function. Under the MPD assumption, multiple means and variances of the modes can be estimated by the expectation-maximization (EM) algorithm, and a corresponding closed-form solution can be obtained. Since the GMM can exactly approximate multi-peak probability density function (PDF), the closed-form solution of the proposed MPD algorithm can approximate the optimal solution of the adaptive filtering problem under multi-peak additive noise. According to the interaction between the distance and magnitudes of adjacent peaks, multi-peak noise can be divided into significant multi-peak (SMP) noise, hidden multi-peak (HMP) noise (e.g., Rayleigh), and invisible multi-peak (IMP) noise (e.g., Uniform). Simulations demonstrate that the proposed MPD algorithm outperforms the maximum correntropy criterion (MCC) and minimum error entropy (MEE) under SMP and HMP noise, and outperforms the least mean fourth (LMF) under IMP noise. The experimental steady-state errors align well with the theoretical values.