The modified extended Kalman filter based recursive estimation for Wiener nonlinear systems with process noise and measurement noise

Abstract

This article develops the modified extended Kalman filter based recursive estimation algorithms for Wiener nonlinear systems with process noise and measurement noise. The prior estimate of the linear block output is computed based on the auxiliary model, and the posterior estimate is updated by designing a modified extended Kalman filter. A multi-innovation gradient algorithm and a recursive least squares algorithm are derived to estimate the parameters of the linear subsystem, respectively. The simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.

Estimation of wiener nonlinear systems with measurement noises utilizing correlation analysis and Kalman filter

“…8,9 The Wiener models, which are composed of a linear filter and a static nonlinearity, are a class of output nonlinear systems, and they have been proved to be useful as nonlinear models for many practical applications, such as continuous stirred tank reactors, 10,11 solid oxide fuel cell, 12 pH neutralization process, 13 wind power forecasting, 14 and so on. Over the past few decades, a lot of effective approaches have been developed for dealing with the problem of the Wiener systems identification, including over parameterization algorithm, 15 subspace method, 16,17 frequency-type method, 18 exciting signals-based techniques, 19,20 iterative algorithm, [21][22][23] auxiliary model-based multi-innovation method, [24][25][26] and least squares method. 27 Since noises widely exist in actual industrial processes, and are often colored noise, which play a vital influence on system identification, thus it is very significant to focus on the Wiener systems with noises.…”

“…Wang et al developed a modified extended Kalman filter-based recursive estimate algorithm for Wiener nonlinear systems corrupted by process noises and measurement noises. 24 Considering the robust identification issue for time-varying Wiener output-error systems, the adaptive filtering recursive identification scheme was carried out. 28 By combining the least square technique, the adjustable model, and the Kalman filter principal, Salhi and Kamoun put forward recursive parameter and state estimate scheme for estimating multivariable Wiener models.…”

Joint parameter and time-delay estimation for a class of Wiener models based on a new orthogonal least squares algorithm

“…In order to obtain a unique estimation, Vörös proposed the key term separation principle to simplify the model equation [3], Wang employed the uniqueness assumption on a Wiener system with colored noise [6]. Moreover, Wang et al developed a modified extended Kalmam filter-based recursive estimation algorithms for Wiener models, in which the nonlinear part was approximated by the first order Taylor expansion, and then the parameters of the linear and nonlinear part were hierarchically identified by the least squares and the extended Kalman filters, respectively [8]. A more general method is the inverse representation method, assuming that the output nonlinear function have an inverse, which is proposed to break out of the limitation of white input in the stochastic method.…”

Identification of the nonlinear systems based on the kernel functions

“…System identification is theory of establishing the mathematical models of dynamical systems by measuring the system inputs and outputs 1‐3 . System modeling and parameter estimation are the basis of all the control problems, 4‐9 so it is significant to build an appropriate model for system prediction and control 10‐15 . Many identification methods have been developed for linear systems, but most practical systems have nonlinear characteristics in nature.…”