Multi‐innovation gradient parameter estimation for multivariable systems based on the maximum likelihood principle

Abstract

This article considers the parameter estimation problems of linear multivariable systems with unknown disturbances. For the parameter matrices in the multivariable systems, the model decomposition technique is used to reduce the computational complexity by decomposing the multivariable system into several subsystems with only the parameter vectors. By means of the negative gradient search, a decomposition-based maximum likelihood recursive extended stochastic gradient algorithm is derived. In order to improve the parameter estimation accuracy, by introducing the multi-innovation identification theory, a decomposition-based maximum likelihood multi-innovation extended stochastic gradient algorithm is proposed. The simulation results illustrate the effectiveness of the proposed algorithms.

Multi‐innovation gradient‐based iterative identification methods for feedback nonlinear systems by using the decomposition technique

“…21,22 The basic idea is to expand the scalar innovation to an innovation vector/matrix, such that the innovations and measurement data can be made full use of and the identification accuracy can be enhanced. 23 For example, Wang et al presented a hierarchical multi-innovation stochastic gradient algorithm for Volterra nonlinear systems with the non-Gaussian noises by combining with the logarithmic p-norms 1 ≤ p ≤ 2. 24 In the area of parameter estimation, the iterative technique are effective tools and have been widely applied to optimize the parameters of the estimated models.…”

“…The multi‐innovation identification theory is important in system identification 21,22 . The basic idea is to expand the scalar innovation to an innovation vector/matrix, such that the innovations and measurement data can be made full use of and the identification accuracy can be enhanced 23 . For example, Wang et al presented a hierarchical multi‐innovation stochastic gradient algorithm for Volterra nonlinear systems with the non‐Gaussian noises by combining with the logarithmic $$$ p $$$‐norms $$$ 1\le p\le 2 $$$ 24 .…”

“…8. Read out the parameter estimation vectors âk (t), bk (t) and qk (t) from θk (t) in Equation(23). 9.…”

Identification of dual‐rate sampled errors‐in‐variables systems with time delays

“…6 EIV systems have been frequently encountered in the fields of medical science, economics, and industry processes due to instrumental measurement errors or manual operation factors. 7,8 Traditional identification methods for systems considering only output measurement noise cannot be directly applied to EIV systems to obtain unbiased parameter estimates [9][10][11][12][13] such as the gradient-based and the LS-based identification methods. [14][15][16][17] Therefore, it is necessary to develop new identification methods for EIV systems.…”

Multi-innovation gradient estimation for multivariate systems with colored noise based on the maximum likelihood principle

“…Parameter estimation is an eternal topic in the field of identification and is the basis in controller design, dynamic systems modeling, and signal processing [3][4][5]. Different identification methods have been proposed for scalar systems and multivariable systems, such as the least squares methods [6,7], the iterative methods [8], the maximum likelihood methods [9], the orthogonal matching pursuit methods [10], and the robust identification methods [11]. In industrial control and application, multivariable systems are better prepared to describe the characteristics of process objects than scalar systems.…”