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Maximum Likelihood Identification Methods

Author: LiJunHong
Tutor: DingFeng
School: Jiangnan University
Course: Control Theory and Control Engineering
Keywords: parameter estimation maximum likelihood linear systems nonlinearsystems recursive identification
CLC: TP13
Type: PhD thesis
Year: 2013
Downloads: 72
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Abstract


The maximum likelihood identification is an identification method based on prob-ability and statistics theory. The parameter estimates are obtained by maximizing thelikelihood function of the observation data conditioned on the unknown parameter. Ithas excellent statistical properties and is widely used in many fields. However, the studyon the maximum likelihood identification method is still limited. This dissertation com-bines the maximum likelihood principle, the data filtering technique and the hierarchicalidentification principle to propose more efcient maximum likelihood methods for linearsystems and Hammerstein nonlinear systems, and has significant theoretical significancefor enriching the system identification theory. The main contributions of this dissertationare summarized as follows:1. For the finite impulse response autoregressive moving average systems, the max-imum likelihood recursive least squares (ML-RLS) algorithm is presented. In order todecrease the computational burden, a filtering based maximum likelihood recursive leastsquares (F-ML-RLS) estimation algorithm is developed. By filtering the input-outputdata with a filter, the original system is decomposed into two identification models withlower dimensions. The proposed filtered algorithm can interactively estimate the param-eters of the two models and can obtain high estimation accuracy.2. For the output error moving average systems, a maximum likelihood gradientbased iterative estimation (ML-GI) algorithm and a maximum likelihood gradient basediterative estimation algorithm over a finite data window (ML-GI-FDW) are proposed byusing the iterative identification technique. The iterative identification can make fully useof the system data and improve the identification accuracy. The ML-GI-FDW algorithmcan identify the time-varying parameters.3. For the input nonlinear finite impulse response moving average systems, a max-imum likelihood recursive least squares and a stochastic gradient (ML-SG) algorithmare derived. In order to accelerate the convergence rate, a maximum likelihood multi-innovation stochastic gradient (ML-MISG) algorithm is developed. The ML-MISG algo-rithm can improve the identification performance by expanding the innovation length.4. For the input nonlinear output error moving average system, a maximum likeli-hood least squares based iterative (ML-LSI) algorithm and a maximum likelihood leastsquares based iterative algorithm over finite data window (ML-LSI-FDW) are proposed.Compared with the recursive extended least squares (RELS) algorithm, the proposedalgorithms have higher estimation accuracy.5. In order to alleviate the computational burden of the over-parametrization method, a hierarchical maximum likelihood least squares based iterative (H-ML-LSI) algorithmand a gradient based iterative (H-ML-GI) algorithm are developed for the input nonlin-ear Box-Jenkins systems. Compared with the over-parametrization method, the proposedhierarchical algorithms can identify the parameters of the nonlinear static subsystem andthe linear dynamic subsystem, and can decrease computational burden.

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