scholarly journals Combined Parameter and State Estimation Algorithms for Multivariable Nonlinear Systems Using MIMO Wiener Models

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Houda Salhi ◽  
Samira Kamoun
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
State Estimation ◽  
Internal Variables ◽  
Decomposition Technique ◽  
Parameter Estimation Problem ◽  
Filter Theory ◽  
Estimation Algorithms ◽  
Wiener Models ◽  
Multivariable Nonlinear Systems

This paper deals with the parameter estimation problem for multivariable nonlinear systems described by MIMO state-space Wiener models. Recursive parameters and state estimation algorithms are presented using the least squares technique, the adjustable model, and the Kalman filter theory. The basic idea is to estimate jointly the parameters, the state vector, and the internal variables of MIMO Wiener models based on a specific decomposition technique to extract the internal vector and avoid problems related to invertibility assumption. The effectiveness of the proposed algorithms is shown by an illustrative simulation example.

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.

State and Parametric Estimation of Nonlinear Systems Described by Wiener Sate-Space Mathematical Models

2015 ◽  
pp. 107-145 ◽  
Author(s):  
Houda Salhi ◽  
Samira Kamoun
Keyword(s):  
Nonlinear Systems ◽  
Mathematical Models ◽  
State Estimation ◽  
Estimation Algorithm ◽  
The State ◽  
Parametric Estimation ◽  
State Variables ◽  
Estimation Algorithms ◽  
And Performance ◽  
The Stability

This chapter deals with the description, the parametric estimation, the state estimation, and the parametric and state estimation conjointly of nonlinear systems. The focus is on the class of nonlinear systems, which are described by Wiener state-space discrete-time mathematical models. Thus, the authors develop a new recursive parametric estimation algorithm, which is based on least squares techniques. The stability conditions of the developed parametric estimation scheme are analyzed using the Lyapunov method. The state estimation problem of the considered nonlinear systems is formulated. Thus, the authors propose a recursive state estimation algorithm, which is based on Kalman Filter. A new recursive algorithm is proposed, which permits one to estimate conjointly the parameters and the state variables of nonlinear systems described by Wiener mathematical models, with unknown parameters and state variables. The efficiency and performance of the proposed recursive estimation algorithms are tested on numerical simulation examples.

Adaptive filtering parameter estimation algorithms for Hammerstein nonlinear systems

2016 ◽  
Vol 128 ◽  
pp. 417-425 ◽  
Author(s):  
Yawen Mao ◽  
Feng Ding ◽  
Ahmed Alsaedi ◽  
Tasawar Hayat
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Adaptive Filtering ◽  
Estimation Algorithms

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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