Analysis and parameter estimation of nonlinear systems with Hammerstein model using Taylor series approach

1988 ◽  
Vol 35 (12) ◽  
pp. 1539-1541 ◽  
Author(s):  
Chung Hung-Yuan ◽  
Sun York-Yih
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Taylor Series ◽  
Hammerstein Model

scholarly journals Noise Reduction in the Swept Sine Identification Procedure of Nonlinear Systems

2021 ◽  
Vol 11 (16) ◽  
pp. 7273
Author(s):  
Pietro Burrascano ◽  
Matteo Ciuffetti
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Additive Noise ◽  
Laboratory Data ◽  
Model Identification ◽  
Estimation Procedure ◽  
Parameters Estimation ◽  
Hammerstein Model ◽  
Model Parameters ◽  
Identification Procedure

The Hammerstein model identification technique based on swept sine excitation signals proved in numerous applications to be particularly effective for the definition of a model for nonlinear systems. In this paper we address the problem of the robustness of this model parameter estimation procedure in the presence of noise in the measurement step. The relationship between the different functions that enter the identification procedure is analyzed to assess how the presence of additive noise affects model parameters estimation. This analysis allows us to propose an original technique to mitigate the effects of additive noise in order to improve the accuracy of model parameters estimation. The different aspects addressed in the paper and the technique for mitigating the effects of noise on the accuracy of parameter estimation are verified on both synthetic and experimental data acquired with an ultrasonic system. The results of both simulations and experiments on laboratory data confirm the correctness of the assumptions made and the effectiveness of the proposed mitigation methodology.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

A New Integrated Algorithm of Structure Determination and Parameter Estimation for Nonlinear Systems Identification

1999 ◽  
Author(s):  
Wang Xiao Wang ◽  
Jianyin Xie
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Structure Determination ◽  
Model Identification ◽  
Identification Algorithm ◽  
Householder Transformation ◽  
Systems Identification ◽  
Value Decomposition ◽  
Svd Method ◽  
Nonlinear Systems Identification

Abstract A new integrated algorithm of structure determination and parameter estimation is proposed for nonlinear systems identification in this paper, which is based on the Householder Transformation (HT), Givens and Modified Gram-Schmidt (MGS) algorithms. While being used for the polynomial and rational NARMAX model identification, it can select the model terms while deleting the unimportant ones from the assumed full model, avoiding the storage difficulty as the CGS identification algorithm does which is proposed by Billings et. al., and is numerically more stable. Combining the H algorithm with the modified bidiagonalization least squares (MBLS) algorithm and the singular value decomposition (SVD) method respectively, two algorithms referred to as the MBLSHT and SVDHT ones are proposed for the polynomial and rational NARMAX model identification. They are all numerically more stable than the HT or Givens or MGS algorithm given in this paper, and the MBLSHT algorithm has the best performance. A higher precision for the parameter estimation can thus be obtained by them, as supported b simulation results.

scholarly journals An EKF-Based Fixed-Point Iterative Filter for Nonlinear Systems

Sensors ◽  
2019 ◽  
Vol 19 (8) ◽  
pp. 1893
Author(s):  
Feng ◽  
Feng ◽  
Wen
Keyword(s):  
Fixed Point ◽  
Kalman Filter ◽  
Nonlinear Systems ◽  
Iterative Method ◽  
Taylor Series ◽  
Nonlinear Filtering ◽  
Higher Order ◽  
Point Function ◽  
State Estimate ◽  
Linearized System

In this paper, a fixed-point iterative filter developed from the classical extended Kalman filter (EKF) was proposed for general nonlinear systems. As a nonlinear filter developed from EKF, the state estimate was obtained by applying the Kalman filter to the linearized system by discarding the higher-order Taylor series items of the original nonlinear system. In order to reduce the influence of the discarded higher-order Taylor series items and improve the filtering accuracy of the obtained state estimate of the steady-state EKF, a fixed-point function was solved though a nested iterative method, which resulted in a fixed-point iterative filter. The convergence of the fixed-point function is also discussed, which provided the existing conditions of the fixed-point iterative filter. Then, Steffensen’s iterative method is presented to accelerate the solution of the fixed-point function. The final simulation is provided to illustrate the feasibility and the effectiveness of the proposed nonlinear filtering method.

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