The maximum likelihood least squares based iterative estimation algorithm for bilinear systems with autoregressive moving average noise

2017 ◽  
Vol 354 (12) ◽  
pp. 4861-4881 ◽  
Author(s):  
Meihang Li ◽  
Ximei Liu ◽  
Feng Ding
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Moving Average ◽  
Estimation Algorithm ◽  
Bilinear Systems ◽  
Autoregressive Moving Average ◽  
Iterative Estimation

scholarly journals Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Weili Xiong ◽  
Wei Fan ◽  
Rui Ding
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Least Squares ◽  
Moving Average ◽  
Estimation Algorithm ◽  
Autoregressive Moving Average ◽  
Parameter Estimates ◽  
Persistent Excitation ◽  
Estimation Algorithms ◽  
Parameter Estimation Algorithm

This paper studies least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.

Decomposition based least squares iterative estimation algorithm for output error moving average systems

2014 ◽  
Vol 31 (4) ◽  
pp. 709-725 ◽  
Author(s):  
Wenge Zhang
Keyword(s):  
Least Squares ◽  
Design Methodology ◽  
Moving Average ◽  
Estimation Algorithm ◽  
Identification Algorithm ◽  
Iterative Identification ◽  
Iterative Estimation ◽  
Content Type ◽  
Engineering Computation ◽  
Parameter Estimation Algorithm

Purpose – The purpose of this paper is to solve the heavy computational problem of parameter estimation algorithm. Design/methodology/approach – Presents a decomposition least squares based iterative identification algorithm. Findings – Can estimate the parameters for linear or pseudo-linear systems and have lower computational burden. Originality/value – This paper adopts a decomposition technique to solve engineering computation problems and offers a potential and efficient algorithm.

scholarly journals Highly efficient maximum-likelihood identification methods for bilinear systems with colored noises

2021 ◽  
Author(s):  
Meihang Li ◽  
Ximei Liu ◽  
Yamin Fan
Keyword(s):  
Maximum Likelihood ◽  
Computational Efficiency ◽  
Moving Average ◽  
Bilinear Systems ◽  
Autoregressive Moving Average ◽  
State Variables ◽  
Likelihood Principle ◽  
Identification Methods ◽  
Highly Efficient ◽  
Gradient Based

Abstract As a special class of nonlinear systems, bilinear systems can naturally describe many industrial production process. This paper mainly discussed the highly efficient iterative identification methods for bilinear systems with autoregressive moving average noise. Firstly, the input-output representation of the bilinear systems is derived through eliminating the unknown state variables in the model. Then based on the maximum-likelihood principle and the negative gradient search principle, a maximum-likelihood gradient-based iterative (ML-GI) algorithm is proposed to identify the parameters of the bilinear systems with colored noises. For further improving the computational efficiency, the original identification model is divided into three sub-identification models with smaller dimensions and fewer parameters, and a hierarchical maximum-likelihood gradient-based iterative (H-ML-GI) algorithm is derived by using the hierarchical identification principle. A gradient-based iterative (GI) algorithm is given for comparison. Finally, the algorithms are verified by a simulation example. The simulation results show that the proposed algorithms are effective for identifying bilinear systems with colored noises and the H-ML-GI algorithm has a higher computational efficiency and a faster convergence rate than the ML-GI algorithm and the GI algorithm.

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