scholarly journals The Hierarchical Iterative Identification Algorithm for Multi-Input-Output-Error Systems with Autoregressive Noise

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Jiling Ding
Keyword(s):  
Least Squares ◽  
Identification Problem ◽  
Parameter Estimates ◽  
Identification Algorithm ◽  
Input Output ◽  
Iterative Identification ◽  
Hierarchical Identification ◽  
Output Error ◽  
Gradient Based ◽  
Simulation Results

This paper considers the identification problem of multi-input-output-error autoregressive systems. A hierarchical gradient based iterative (H-GI) algorithm and a hierarchical least squares based iterative (H-LSI) algorithm are presented by using the hierarchical identification principle. A gradient based iterative (GI) algorithm and a least squares based iterative (LSI) algorithm are presented for comparison. The simulation results indicate that the H-LSI algorithm can obtain more accurate parameter estimates than the LSI algorithm, and the H-GI algorithm converges faster than the GI algorithm.

scholarly journals Decomposition Least-Squares-Based Iterative Identification Algorithms for Multivariable Equation-Error Autoregressive Moving Average Systems

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 609 ◽  
Author(s):  
Lijuan Wan ◽  
Ximei Liu ◽  
Feng Ding ◽  
Chunping Chen
Keyword(s):  
Least Squares ◽  
Moving Average ◽  
Identification Problem ◽  
Autoregressive Moving Average ◽  
Parameter Estimates ◽  
Identification Algorithm ◽  
Hierarchical Identification ◽  
Iterative Search ◽  
Time Varying Parameters ◽  
Equation Error

This paper is concerned with the identification problem for multivariable equation-error systems whose disturbance is an autoregressive moving average process. By means of the hierarchical identification principle and the iterative search, a hierarchical least-squares-based iterative (HLSI) identification algorithm is derived and a least-squares-based iterative (LSI) identification algorithm is given for comparison. Furthermore, a hierarchical multi-innovation least-squares-based iterative (HMILSI) identification algorithm is proposed using the multi-innovation theory. Compared with the LSI algorithm, the HLSI algorithm has smaller computational burden and can give more accurate parameter estimates and the HMILSI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.

scholarly journals Least-Squares-Based Iterative Identification Algorithm for Wiener Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Lincheng Zhou ◽  
Xiangli Li ◽  
Feng Pan
Keyword(s):  
Nonlinear Systems ◽  
Least Squares ◽  
Iterative Algorithm ◽  
Identification Problem ◽  
Identification Algorithm ◽  
Separation Principle ◽  
Iterative Identification ◽  
Simulation Results ◽  
Information Vector ◽  
Simplified Form

This paper focuses on the identification problem of Wiener nonlinear systems. The application of the key-term separation principle provides a simplified form of the estimated parameter model. To solve the identification problem of Wiener nonlinear systems with the unmeasurable variables in the information vector, the least-squares-based iterative algorithm is presented by replacing the unmeasurable variables in the information vector with their corresponding iterative estimates. The simulation results indicate that the proposed algorithm is effective.

scholarly journals Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 558 ◽  
Author(s):  
Hao Ma ◽  
Jian Pan ◽  
Lei Lv ◽  
Guanghui Xu ◽  
Feng Ding ◽  
...  
Keyword(s):  
Least Squares ◽  
Computational Cost ◽  
Original System ◽  
Parameter Estimates ◽  
Recursive Algorithms ◽  
Parameter Vector ◽  
Identification Problems ◽  
Hierarchical Identification ◽  
Output Error ◽  
Parameter Identification Problems

This paper studies the parameter identification problems for multivariable output-error-like systems with colored noises. Based on the hierarchical identification principle, the original system is decomposed into several subsystems. However, each subsystem contains the same parameter vector, which leads to redundant computation. By taking the average of the parameter estimation vectors of each subsystem, a partially-coupled subsystem recursive generalized extended least squares (PC-S-RGELS) algorithm is presented to cut down the redundant parameter estimates. Furthermore, a partially-coupled recursive generalized extended least squares (PC-RGELS) algorithm is presented to further reduce the computational cost and the redundant estimates by using the coupling identification concept. Finally, an example indicates the effectiveness of the derived algorithms.

scholarly journals Least-Squares Based and Gradient Based Iterative Parameter Estimation Algorithms for a Class of Linear-in-Parameters Multiple-Input Single-Output Output Error Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Cheng Wang ◽  
Tao Tang ◽  
Dewang Chen
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Iterative Algorithm ◽  
Parameter Estimates ◽  
Iterative Search ◽  
Estimation Algorithms ◽  
Single Output ◽  
Multiple Input ◽  
Gradient Based ◽  
Simulation Results

The identification of a class of linear-in-parameters multiple-input single-output systems is considered. By using the iterative search, a least-squares based iterative algorithm and a gradient based iterative algorithm are proposed. A nonlinear example is used to verify the effectiveness of the algorithms, and the simulation results show that the least-squares based iterative algorithm can produce more accurate parameter estimates than the gradient based iterative algorithm.

scholarly journals Parameter and State Estimator for State Space Models

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ruifeng Ding ◽  
Linfan Zhuang
Keyword(s):  
State Space ◽  
State Equation ◽  
The State ◽  
Parameter Estimates ◽  
Identification Algorithm ◽  
State Variables ◽  
Input Output ◽  
State Estimator ◽  
Output Data ◽  
Canonical State

This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.

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