Robust constrained recursive least M-estimate adaptive filtering algorithm

Recently, the constrained adaptive filtering algorithms with strong robustness to non-Gaussian noise have been widely studied. Among them, the robust constrained least mean M-estimate (CLMM) algorithm has significant performance in the background of impulse noise base on the well anti-impulse noise characteristic of the M-estimate function. However, there is an irreconcilable contradiction between the steadystate error and the convergence rate of CLMM. To solve this contradiction, this paper introduces the modified Huber function (MHF) into the constrained recursive least squares (CRLS) algorithm and develops the constrained recursive least M-estimate (CRLM) algorithm, which fully combines the superior convergence performance of CRLS and the anti-impulse noise characteristic of the MHF. We furthermore propose an enhanced version of the CRLM, namely robust CRLM (RCRLM), which is robust to round-off error. Then, We analyze the mean and mean square stability and transient, steady-state NMSD of the proposed RCRLM algorithm under some simplified assumptions. Simulation results in various non-Gaussian noise scenarios show that the proposed RCRLM is superior to some existing constraint algorithms in terms of convergence speed, steady-state error and tracking ability, and the theoretical analysis results are also verified. (c) 2021 Elsevier B.V. All rights reserved.