Data Filtering Based Recursive and Iterative Least Squares Algorithms for Parameter Estimation of Multi-Input Output Systems

Abstract

This paper discusses the parameter estimation problems of multi-input output-error autoregressive (OEAR) systems. By combining the auxiliary model identification idea and the data filtering technique, a data filtering based recursive generalized least squares (F-RGLS) identification algorithm and a data filtering based iterative least squares (F-LSI) identification algorithm are derived. Compared with the F-RGLS algorithm, the proposed F-LSI algorithm is more effective and can generate more accurate parameter estimates. The simulation results confirm this conclusion.

Coupled Least Squares Identification Algorithms for Multivariate Output-Error Systems

“…For the identification model in (5), Φ x (t) is the information matrix that consists of the unknown inner variables x(t − j)'s, so we construct an auxiliary model x a (t), and define the estimate of Φ x (t) aŝ…”

“…Multivariable systems are popular in industrial processes [1][2][3] and a number of successful methods have been developed to solve the identification and control problems of multivariable systems [4][5][6][7]. For example, Zhang and Hoagg used a candidate-pool approach to identify the feedback and feedforward transfer function matrices and presented a frequency-domain technique for identifying multivariable feedback and feedforward systems [8]; Salhi and Kamoun proposed a recursive algorithm to estimate the parameters of the dynamic linear part and the static nonlinear part of multivariable Hammerstein systems [9].…”

The Bias Compensation Based Parameter and State Estimation for Observability Canonical State-Space Models with Colored Noise

“…In industrial processes, the observation data are often corrupted by colored noises [29][30][31]. As we have known, the parameter estimates generated by the recursive least squares algorithm for the system with colored noise are biased.…”

“…Readθ g (k) andθ h (k) using Equation (29). Acquire the parameter estimatesĝ i (k) andĥ i (k) using Equations (41) and (42).…”

Auxiliary Model Based Multi-Innovation Stochastic Gradient Identification Algorithm for Periodically Non-Uniformly Sampled-Data Hammerstein Systems

“…Furthermore, the information vector ϕ i (k) contains unmeasurable noise-free outputs w i−j (k). A solution to this difficulty is to replace w i−j (k) with their estimatesŵ i−j (k) based on the auxiliary model identification idea [38][39][40]. Accordingly, define the estimate of ϕ i (k) as:…”