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Open AccessArticle

Variational Bayesian Iterative Estimation Algorithm for Linear Difference Equation Systems

1
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China
2
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 2G6, Canada
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1143; https://doi.org/10.3390/math7121143
Received: 30 October 2019 / Revised: 19 November 2019 / Accepted: 20 November 2019 / Published: 22 November 2019
(This article belongs to the Section Engineering Mathematics)
Many basic laws of physics or chemistry can be written in the form of differential equations. With the development of digital signals and computer technology, the research on discrete models has received more and more attention. The estimates of the unknown coefficients in the discretized difference equation can be obtained by optimizing certain criterion functions. In modern control theory, the state-space model transforms high-order differential equations into first-order differential equations by introducing intermediate state variables. In this paper, the parameter estimation problem for linear difference equation systems with uncertain noise is developed. By transforming system equations into state-space models and on the basis of the considered priors of the noise and parameters, a variational Bayesian iterative estimation algorithm is derived from the observation data to obtain the parameter estimates. The unknown states involved in the variational Bayesian algorithm are updated by the Kalman filter. A numerical simulation example is given to validate the effectiveness of the proposed algorithm. View Full-Text
Keywords: iterative algorithm; variational Bayesian; parameter estimation; Kalman filter iterative algorithm; variational Bayesian; parameter estimation; Kalman filter
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Ma, J.; Fei, Q.; Guo, F.; Xiong, W. Variational Bayesian Iterative Estimation Algorithm for Linear Difference Equation Systems. Mathematics 2019, 7, 1143.

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