Data Filtering-Based Multi-innovation Stochastic Gradient Algorithm for Nonlinear Output Error Autoregressive Systems

Abstract

This paper discusses the parameter estimation problems of nonlinear output error autoregressive systems and presents a data filtering-based multi-innovation stochastic gradient algorithm for improving the parameter estimation accuracy of the stochastic gradient algorithm by combining the multi-innovation identification theory and the data filtering technique. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the multi-innovation stochastic gradient algorithm. The simulation results confirm this conclusion.

A novel data filtering based multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems

“…For example, Wills et al used the particle filtering and smoothing techniques and the expectation maximization algorithm to propose a maximum-likelihood identification algorithm for Hammerstein-Wiener models where both colored process noise and white measurement noise are considered [15]; Li presented a maximum likelihood estimation algorithm for Hammerstein controlled autoregressive ARMA systems by using the Newton iteration [16]. Particularly, Ding proposed the multi-innovation identification theory by expanding the scalar innovation to an innovation vector [17] and employed it to present a multi-innovation gradient identification algorithm for nonlinear output error autoregressive systems [18].…”

“…The data filtering is usually used to get rid of the outliers and weaken the influence of noises to better extract the characteristic data in the digital signal processing, and has been applied to identify the model parameters [19][20][21]. For example, Scarpiniti et al presented an adaptive filter which is used for the identification of Wiener-type nonlinear systems and a learning algorithm was derived based on a gradient descent approach [22]; Ding et al introduced a recursive least squares parameter estimation algorithm for linear autoregressive moving average systems using the data filtering and the auxiliary model identification idea [23] for Hammerstein systems using the over-parametrization model based method [24]; Wang and Tang proposed a gradient based iterative algorithm by filtering the input-output data and transferring the model into two regression identification models for linear-inparameters output error autoregressive systems [25].…”

Parameter estimation for nonlinear systems by using the data filtering and the multi-innovation identification theory

“…Some identification methods for systems with colored noise are based on the data filtering technique [28,29]. Particularly, Li and Shi investigated the robust H-infinity filtering problem for nonlinear stochastic systems with uncertainties and random delays [23]; Zhang and Cui presented a bias compensation based recursive least squares identification algorithm for ARX-like systems with colored noise by means of the prefilter idea and the bias compensation principle [40]; Wang and Tang proposed a RLS estimation algorithm for a class of linear-in-parameters output error moving average systems which can represent both linear and nonlinear systems [36].…”

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

“…The multi-innovation identification theory is an important branch of system identification [10,11,12], the innovation is the useful information that can improve the accuracy of the parameter estimation or the state estimation [13,14]. In this aspect, Mao and Ding presented a multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems [15]; Jin et al proposed a multi-innovation least squares identification algorithm for multivariable output-error systems with scarce measurements [16]; Wang and Zhu presented a multi-innovation stochastic gradient algorithm for a class of linear-inparameter systems [17].…”