Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems

Abstract

This paper studies the parameter identification problems for multivariable output-error-like systems with colored noises. Based on the hierarchical identification principle, the original system is decomposed into several subsystems. However, each subsystem contains the same parameter vector, which leads to redundant computation. By taking the average of the parameter estimation vectors of each subsystem, a partially-coupled subsystem recursive generalized extended least squares (PC-S-RGELS) algorithm is presented to cut down the redundant parameter estimates. Furthermore, a partially-coupled recursive generalized extended least squares (PC-RGELS) algorithm is presented to further reduce the computational cost and the redundant estimates by using the coupling identification concept. Finally, an example indicates the effectiveness of the derived algorithms.

Adaptive parameter estimation for a general dynamical system with unknown states

“…This paper aims to design a state filter for the time‐delay system with unknown parameters from observation information. The basis idea is to propose an interactive parameter and state estimation algorithm based on the hierarchical identification principle . More specific details are in the following sections.…”

“…The basis idea is to propose an interactive parameter and state estimation algorithm based on the hierarchical identification principle. 36,37 More specific details are in the following sections.…”

Moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear systems

“…The problem we face is that the parameter matrix A u (t) and vector b are unknown. Therefore, the state estimation in Equations (28) to (30) cannot be realized. The solution is that using the parameter estimates…”

“…Then, the estimate u,k (t) of A u (t) can be obtained by u,k (t) ∶= k (t) +M k (t)u(t). Replacing A u (t) and b in Equations (28) to (30) with their estimates u,k (t) andb k (t), and replacing the unknown information vector v (t), the parameter vector v in Equations (28) to (30) with their estimateŝv ,k (t) in Equation (17) and̂v ,k (t) in Equation (20) givê…”

“…25,26 The iterative algorithm processes a batch of measurement data and makes efficient use of the measurement data at each iteration. [27][28][29] Hence, some iterative methods can be used for finding the solutions to some matrix equations 30,31 and for deriving new signal modeling 32,33 and parameter identification algorithms. 34,35 On the basis of the iterative schemes, this paper aims to design a dynamical moving data window (MDW) to update the collected data to identify the bilinear system.…”