Parameter estimation algorithm for multivariable controlled autoregressive autoregressive moving average systems

Abstract

This paper investigates parameter estimation problems for multivariable controlled autoregressive autoregressive moving average (M-CARARMA) systems. In order to improve the performance of the standard multivariable generalized extended stochastic gradient (M-GESG) algorithm, we derive a partially coupled generalized extended stochastic gradient algorithm by using the auxiliary model. In particular, we divide the identification model into several subsystems based on the hierarchical identification principle and estimate the parameters using the coupled relationship between these subsystems. The simulation results show that the new algorithm can give more accurate parameter estimates of the M-CARARMA system than those of the M-GESG algorithm.

Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems

“…Referring to the decomposition methods in [51,52,71], let ψ T i (s) ∈ R n 0 be the ith row of the information matrix ψ(s), that is…”

“…The coupled identification methods have been derived to identify the parameters of multivariable systems and were first presented in [50]. The basic idea of the coupling identification concept is to decompose the original system into several subsystems, and to estimate the parameters based on the coupled parameter relationships between these subsystems [51][52][53].…”

Partially coupled gradient estimation algorithm for multivariable equation‐error autoregressive moving average systems using the data filtering technique

“…2. Collect the input and output data u(t) and y(t), and construct the information vector φ(t) using (37), formφ(t) using (34), read ϕ i (t) from (35), and constructΩ(t) by (36). 3.…”

Recursive coupled projection algorithms for multivariable output‐error‐like systems with coloured noises

“…The hierarchical identification principle [16,17] and the coupling identification concept [8,18] are essential in the field of the parameter identification of multivariable systems. The hierarchical identification is dividing the original multivariable system into several subsystems with fewer parameters and estimating these subsystems, respectively.…”