Maximum likelihood extended gradient‐based estimation algorithms for the input nonlinear controlled autoregressive moving average system with variable‐gain nonlinearity

2021 ◽  
Author(s):  
Ximei Liu ◽  
Yamin Fan
Keyword(s):  
Maximum Likelihood ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Variable Gain ◽  
Estimation Algorithms ◽  
Average System ◽  
Gradient Based

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.

Parameter Estimation Algorithms for Hammerstein–Wiener Systems With Autoregressive Moving Average Noise

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Yanjiao Wang ◽  
Feng Ding
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Data Filtering ◽  
Estimation Algorithms ◽  
Gradient Based ◽  
Wiener Systems ◽  
Filtering Technique ◽  
Identification Theory

Hammerstein–Wiener (H–W) systems are a class of typical nonlinear systems. This paper studies the gradient-based parameter estimation algorithms for H–W nonlinear systems based on the multi-innovation identification theory and the data filtering technique. The proposed methods include a generalized extended stochastic gradient (GESG) algorithm, a multi-innovation GESG (MI-GESG) algorithm, a data filtering based GESG (F-GESG) algorithm and a data filtering based MI-GESG algorithm. Finally, the computational efficiency of the proposed algorithms are analyzed and compared. The simulation example verifies the theoretical results.

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