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Gradient Parameter Estimation of a Class of Nonlinear Systems Based on the Maximum Likelihood Principle

Chen Zhang, Haibo Liu, and Yan Ji*
International Journal of Control, Automation, and Systems, vol. 20, no. 5, pp.1393-1404, 2022

Abstract : "This paper studies the maximum likelihood identification problems of the bilinear-in-parameter outputerror systems with colored noise. A hierarchical maximum likelihood gradient-based iterative (H-MLGI) algorithm, a filtering hierarchical maximum likelihood gradient-based iterative (F-H-MLGI) algorithm and a filtering hierarchical maximum likelihood multi-innovation gradient-based iterative (F-H-ML-MIGI) algorithm are developed for a bilinear-in-parameter output-error system by using the data filtering technique and multi-innovation identification theory. The analysis shows that compared with the H-MLGI algorithm, the F-H-MLGI algorithm can improve the parameter estimation accuracy. Additionally, the F-H-ML-MIGI can give more accurate parameter estimates than the F-H-MLGI algorithm and can track time-varying parameters based on the dynamical window data. The performances of the proposed identification algorithms are illustrated through simulation example. "

Keyword : Data filtering, gradient search, maximum likelihood, multi-innovation, parameter estimation.

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