Adaptive filtering‐based multi‐innovation gradient algorithm for input nonlinear systems with autoregressive noise

Abstract

In this paper, by means of the adaptive filtering technique and the multi-innovation identification theory, an adaptive filtering-based multi-innovation stochastic gradient identification algorithm is derived for Hammerstein nonlinear systems with colored noise. The new adaptive filtering configuration consists of a noise whitening filter and a parameter estimator. The simulation results show that the proposed algorithm has higher parameter estimation accuracies and faster convergence rates than the multi-innovation stochastic gradient algorithm for the same innovation length. As the innovation length increases, the filtering-based multi-innovation stochastic gradient algorithm gives smaller parameter estimation errors than the recursive least squares algorithm

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

“…Chen and Ding applied the data filtering technique to identify the multi-input and single-output system based on the maximum likelihood recursive least squares algorithm [23]. Mao et al derived an adaptive filtering-based multi-innovation stochastic gradient algorithm for the input nonlinear system with autoregressive noise [24]. They introduced a linear filter to filter the input and output signals and decomposed the identification model into two subidentification models (i.e., a noise model and a system filtered model), which can improve the convergence rate and computation efficiency [25].…”

Auxiliary Model-Based Multi-Innovation Fractional Stochastic Gradient Algorithm for Hammerstein Output-Error Systems

“…The SG algorithm update the parameter estimate using the current data information, thus its computational complexity is low, but estimation accuracy needs to be improved. Based on the multi-innovation identification theory [44,45], a slide window of length p (i.e., innovation length) is built to improve the estimation performance of the SG algorithm, which contains the data information from the current time k to k − p + 1, i.e.,…”

“…Collect the input-output data u k and y k , form the basis function vector f (u k ) by (42), and the information vectors φk by (43), φs,k by (44) and φn,k by (45).…”

Identification algorithm of switched systems based on generalized auxiliary model

“…Thus, the stochastic gradient (SG) identification algorithm can be used to estimate the unknown parameters of (13) [23,24]. However, because the whole information vector Φ(t) of (13) contains unknown middle variables x(t − j), unmeasurable noise terms v(t − j) and uncertain label function μ i (t), we cannot directly use the common SG algorithm to confirm the parameters.…”