Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems

Abstract

a b s t r a c tAccording to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided.

Filtering‐based iterative identification for multivariable systems

“…When n c = 0, the HGI algorithm reduces to an HGI algorithm for multivariable output-error MA systems in [18]. The HGI identification method is relatively easy to implement, but its convergence is slow.…”

“…The hierarchical identification is based on decomposition and can be applied to obtain the parameter estimates of the complex multivariable systems [16]. In this literature, Schranz et al [17] studied the hierarchical parameter identification problems in models of respiratory mechanics; Zhang et al [18] used the auxiliary model identification idea and the hierarchical gradient-based iterative (HGI) method for solving the parameter estimation problem of the multivariable output-error moving average (MA) systems; Han et al [19] presented a hierarchical least squares-based iterative algorithm for multivariable systems with additive MA noises by using the decomposition technique.The iterative algorithms update the parameter estimates using the bath data and can be applied to scalar systems and multivariable systems [20], linear systems and non-linear systems [21,22]. The filtering technique can extract the useful information from noisy measurement data for parameter estimation [23,24] and has been used in signal processing and communication [25][26][27], and neural network [28,29].…”

Hammerstein model identification of multivariable nonlinear systems in the presence of colored noises

“…Though these approaches seem quite suitable to represent many systems, but they might be inadequate for the real systems where the outputs are corrupted with some noises. Most of the identification approaches address the independently distributed noises or the so-called "white" noises, however, in recent years, attention to the colored noises is increased [6]- [12]. In these papers, some useful techniques for identification of single-input single-output (SISO) linear [6]- [8], SISO nonlinear [9], [10], and MIMO linear [11], [12] systems in the presence of colored noises are introduced.…”

Performance Analysis of the Auxiliary Model-Based Stochastic Gradient Parameter Estimation Algorithm for State-Space Systems with One-Step State Delay

“…The auxiliary model identification idea is effective for exploring new parameter estimation algorithm. Zhang et al presented a hierarchical gradient-based iterative parameter estimation algorithm for multivariable output error moving average systems [59]; Xiang et al proposed hierarchical least squares algorithms for single-input multiple-output systems based on the auxiliary model [46]; Han et al analyzed the performance analysis of the parameter estimation algorithm for multi-input systems based on the auxiliary model [21]. The main contributions of this paper are to transform the state-space system with one-step state delay into an input-output representation, to present an auxiliary model-based stochastic gradient (AM-SG) parameter estimation algorithm and to study the convergence of the AM-SG algorithm.…”