Maximum Likelihood Parameter Estimation for ARMAX Models Based on Stochastic Gradient Algorithm

2018 ◽  
Author(s):  
Lun Li ◽  
Yan Pu ◽  
Jing Chen
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Stochastic Gradient ◽  
Gradient Algorithm ◽  
Stochastic Gradient Algorithm

scholarly journals Filtering-Based Parameter Identification Methods for Multivariable Stochastic Systems

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2254
Author(s):  
Huafeng Xia ◽  
Feiyan Chen
Keyword(s):  
Maximum Likelihood ◽  
Stochastic Systems ◽  
Stochastic Gradient ◽  
Gradient Algorithm ◽  
Parameter Estimates ◽  
Data Filtering ◽  
Model Decomposition ◽  
Stochastic Gradient Algorithm ◽  
Equation Error ◽  
Identification Theory

This paper presents an adaptive filtering-based maximum likelihood multi-innovation extended stochastic gradient algorithm to identify multivariable equation-error systems with colored noises. The data filtering and model decomposition techniques are used to simplify the structure of the considered system, in which a predefined filter is utilized to filter the observed data, and the multivariable system is turned into several subsystems whose parameters appear in the vectors. By introducing the multi-innovation identification theory to the stochastic gradient method, this study produces improved performances. The simulation numerical results indicate that the proposed algorithm can generate more accurate parameter estimates than the filtering-based maximum likelihood recursive extended stochastic gradient algorithm.

Partially coupled extended stochastic gradient algorithm for nonlinear multivariable output error moving average systems

2017 ◽  
Vol 34 (2) ◽  
pp. 629-647 ◽  
Author(s):  
Xuehai Wang ◽  
Feng Ding
Keyword(s):  
Parameter Estimation ◽  
Moving Average ◽  
Estimation Algorithm ◽  
Stochastic Gradient ◽  
Gradient Algorithm ◽  
Parameter Estimates ◽  
Multivariable Systems ◽  
Content Type ◽  
Stochastic Gradient Algorithm ◽  
Output Error

Purpose The purpose of this paper is to study the parameter estimation problem of nonlinear multivariable output error moving average systems. Design/methodology/approach A partially coupled extended stochastic gradient algorithm is presented for nonlinear multivariable systems by using the decomposition technique. Findings The proposed algorithm can realize the coupled computation of the parameter estimates between subsystems. Originality/value This paper develops a coupled parameter estimation algorithm for nonlinear multivariable systems and directly estimates the system parameters without over-parameterization.

An improved nonlinear innovation-based parameter identification algorithm for ship models

2021 ◽  
pp. 1-9
Author(s):  
Baigang Zhao ◽  
Xianku Zhang
Keyword(s):  
Parameter Identification ◽  
Test Data ◽  
Stochastic Gradient ◽  
Least Square ◽  
Gradient Algorithm ◽  
Model Parameters ◽  
Identification Algorithm ◽  
Process Innovations ◽  
Stochastic Gradient Algorithm ◽  
Tangent Function

Abstract To solve the problem of identifying ship model parameters quickly and accurately with the least test data, this paper proposes a nonlinear innovation parameter identification algorithm for ship models. This is based on a nonlinear arc tangent function that can process innovations on the basis of an original stochastic gradient algorithm. A simulation was carried out on the ship Yu Peng using 26 sets of test data to compare the parameter identification capability of a least square algorithm, the original stochastic gradient algorithm and the improved stochastic gradient algorithm. The results indicate that the improved algorithm enhances the accuracy of the parameter identification by about 12% when compared with the least squares algorithm. The effectiveness of the algorithm was further verified by a simulation of the ship Yu Kun. The results confirm the algorithm's capacity to rapidly produce highly accurate parameter identification on the basis of relatively small datasets. The approach can be extended to other parameter identification systems where only a small amount of test data is available.

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