A Robust Adaptive Filter for a Complex Hammerstein System

Abstract

The Hammerstein adaptive filter using maximum correntropy criterion (MCC) has been shown to be more robust to outliers than the ones using the traditional mean square error (MSE) criterion. As there is no report on the robust Hammerstein adaptive filters in the complex domain, in this paper, we develop the robust Hammerstein adaptive filter under MCC to the complex domain, and propose the Hammerstein maximum complex correntropy criterion (HMCCC) algorithm. Thus, the new Hammerstein adaptive filter can be used to directly handle the complex-valued data. Additionally, we analyze the stability and steady-state mean square performance of HMCCC. Simulations illustrate that the proposed HMCCC algorithm is convergent in the impulsive noise environment, and achieves a higher accuracy and faster convergence speed than the Hammerstein complex least mean square (HCLMS) algorithm.

Modeling and identification for practical nonlinear process using neural fuzzy network–based Hammerstein system

“…Based on the perspective of identification algorithms used, there exist two categories of identification algorithms, namely, the recursive-based algorithm and the iterative-based algorithm. On the basis of the perspective of supplementary means, mainly including the multi-innovation principle (Cheng et al, 2018), particle filtering theory (Ji et al, 2021; Qian et al, 2019) and auxiliary model technique (Ding et al, 2006; Lyu et al, 2020). In accordance with the perspective of system simplification, the identification strategies are divided into hierarchical theory (Ding et al, 2018; Ji et al, 2020), the combined signal–based idea (Li and Jia, 2017; Li et al, 2017b), and key item separation technology (Chen et al, 2015).…”

Parameter identification for Hammerstein nonlinear system with polynomial and state space model

“…27 From the perspective of identification algorithms used, there exists three categories, namely, two-stage estimation algorithms, [28][29][30][31][32] recursive-based estimation algorithms, [33][34][35][36][37][38] and iterative-based estimation algorithms. 21,22,29,30 On the basis of the perspective of supplementary means, mainly including multi-innovation principle, 39 particle filtering theory, 40,41 and auxiliary model technique. 42,43 State space systems have been successfully applied to parameter identification for a long history with many theoretical formulations.…”

Multierror stochastic gradient algorithm for identification of a Hammerstein system with random noise and its application in the modeling of a continuous stirring tank reactor

“…For example, Ding et al proposed two hierarchical algorithms, 5,6 Wang et al proposed a key term separation least squares algorithm, 7 Vanbeylen proposed a blind maximum likelihood identification, 8 Meher et al used a hysteretic relay in feedback to identify a Hammerstein system with a more generalized linear subsystem, 9 Mete et al utilized classical and heuristic algorithms to identify a Hammerstein model with second-order Volterra nonlinearity, 10 Qian et al proposed a Hammerstein maximum complex correntropy criterion algorithm. 11 Among numerous algorithms, the information-theoretic approaches are becoming more widespread. [12][13][14] Compared with mean squares error (MSE) criterion, which concentrates on second order statistics, the information-theoretic criterion (e.g., minimum error entropy [MEE], 15 Renyi's entropy, 16,17 and fixed-point maximum correntropy 18 ) is related to various statistics behavior of the probability density function (pdf) of the error.…”

“…The parameter estimation of the Hammerstein system can be traced back to 1966, and many algorithms have been proposed. For example, Ding et al proposed two hierarchical algorithms, 5,6 Wang et al proposed a key term separation least squares algorithm, 7 Vanbeylen proposed a blind maximum likelihood identification, 8 Meher et al used a hysteretic relay in feedback to identify a Hammerstein system with a more generalized linear subsystem, 9 Mete et al utilized classical and heuristic algorithms to identify a Hammerstein model with second‐order Volterra nonlinearity, 10 Qian et al proposed a Hammerstein maximum complex correntropy criterion algorithm 11 …”