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Maximum likelihood least squares‐based iterative methods for output‐error bilinear‐parameter models with colored noises
Author(s) -
Chen Mengting,
Ding Feng,
Lin Rongming,
Ng Teng Yong,
Zhang Yanliang,
Wei Wei
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5081
Subject(s) - least squares function approximation , bilinear interpolation , non linear least squares , algorithm , iterative method , mathematics , nonlinear system , estimation theory , total least squares , identification (biology) , basis (linear algebra) , colored , mathematical optimization , statistics , physics , botany , geometry , quantum mechanics , estimator , singular value decomposition , biology , materials science , composite material
Summary This article is concerned with the parameter identification of output‐error bilinear‐parameter models with colored noises from measurement data. An auxiliary model least squares‐based iterative method is developed through the overparameterization model. It examines the difficulty of estimating the overparameterized vector, which usually presents a heavy computational burden in the identification process. To overcome this drawback, a parameter separation technique is introduced and the nonlinear model is reformulated as a refined identification model through eliminating the crossmultiplying terms. In this regard, a parameter separation least squares‐based iterative (PS‐LSI) algorithm is derived by avoiding estimating the redundant parameters. On the basis of the PS‐LSI algorithm, we derive a maximum likelihood least squares‐based iterative method to further improve the numerical accuracy. The identification is dependent on the formulation of a pseudolinear regression relationship, which contains two linear prefilters constructed from the system and noise models. The performance of this proposed method is confirmed by the numerical simulations as well as direct comparisons with other existing algorithms.