Filtered multi‐innovation‐based iterative identification methods for multivariate equation‐error ARMA systems

Abstract

This paper focuses on the parameter estimation issues of multivariate equation-error autoregressive moving average systems. By applying the gradient search and the multi-innovation theory, we derive a multi-innovation gradient based iterative (MI-GI) algorithm. In order to improve the computational efficiency and the parameter estimation accuracy, a filtering and decomposition based gradient iterative (F-D-GI) algorithm is presented by using the data filtering technique and the decomposition technique. The key is to choose an appropriate filter to filter the input-output data and to transform an original system into several subsystems. Compared with the MI-GI algorithm, the F-D-GI algorithm can generate more accurate parameter estimates. Finally, an illustrative example is provided to indicate the effectiveness of the proposed algorithms.

A coupled recursive least squares algorithm for multivariable systems and its computational amount analysis by using the coupling identification concept

“…Furthermore, the proposed method can be extended to study the parameter identification problems of other linear or nonlinear stochastic multivariable systems with colored noises [109][110][111][112][113][114][115] and can be applied to chemical process control systems. In the future work, the further investigation is to combine the identification algorithms proposed in this article with other methods, [116][117][118][119][120][121][122] such as the multi-innovation identification theory, to enhance their ability to track time-varying parameters and to improve the efficient data utilization. Furthermore, combining the coupling identification concept with other identification methods [123][124][125][126][127][128] such as the Bayesian approach, the maximum likelihood method and the Kalman filter technique to study more complex parameter identification problems is also an interesting research direction in the future.…”

Filtered generalized iterative parameter identification for equation‐error autoregressive models based on the filtering identification idea

“…The proposed iterative algorithms in this article can combine other identification approaches [70][71][72][73][74][75] to investigate new parameter estimation methods of some stochastic systems with colored noises [76][77][78][79][80][81] and can be applied to signal processing and chemical process control. [82][83][84][85][86][87] The calculation amount of the F-GLSI algorithm in ( 71)-( 85) at each iteration is displayed in Table 2, and the steps of computing the parameter estimates are as follows.…”

A filtering‐based recursive extended least squares algorithm and its convergence for finite impulse response moving average systems

“…The proposed F-RELS algorithm for finite impulse response systems in this article can combine other parameter identification algorithms [73][74][75][76][77][78] to develop new estimation methods of different linear and nonlinear stochastic systems [79][80][81][82][83][84] and can be applied to signal processing and process control systems [85][86][87][88][89][90][91] . The steps involved in the F-RELS algorithm are listed in the following.…”