Hierarchical Least Squares Estimation Algorithm for Hammerstein–Wiener Systems

This letter focuses on identification problems of a Hammerstein-Wiener system with an output error linear element embedded between two static nonlinear elements. A hierarchical least squares algorithm is presented for the Hammerstein-Wiener system by using the auxiliary model identification idea and the hierarchical identification principle. The major contributions of the present study are that the identification model is formulated by using the auxiliary model identification idea (the estimate of the unknown internal variable is replaced with the output of an auxiliary model) and that the bilinear parameter vectors in the identification model are estimated by using the hierarchical identification principle. The proposed hierarchical identification approach is computationally more efficient than the existing over-parametrization method.

[1]  Feng Ding,et al.  Identification of Hammerstein nonlinear ARMAX systems , 2005, Autom..

[2]  Jian Li,et al.  Computationally Efficient Approaches to Aeroacoustic Source Power Estimation , 2011, IEEE Signal Processing Letters.

[3]  Feng Ding,et al.  Hierarchical Least Squares Identification for Linear SISO Systems With Dual-Rate Sampled-Data , 2011, IEEE Transactions on Automatic Control.

[4]  Gilney Damm,et al.  Nonlinear speed estimation of a GPS-free UAV , 2011, Int. J. Control.

[5]  Feng Ding,et al.  Auxiliary model-based least-squares identification methods for Hammerstein output-error systems , 2007, Syst. Control. Lett..

[6]  E. Bai.  An optimal two stage identification algorithm for Hammerstein-Wiener nonlinear systems , 1998 .

[7]  Yucai Zhu,et al.  Estimation of an N-L-N Hammerstein-Wiener model , 2002, Autom..

[8]  Tongwen Chen,et al.  Hierarchical least squares identification methods for multivariable systems , 2005, IEEE Transactions on Automatic Control.

[9]  Ruifeng Ding,et al.  Iterative parameter identification methods for nonlinear functions , 2012 .

[10]  Er-Wei Bai,et al.  Iterative identification of Hammerstein systems , 2007, Autom..

[11]  Mikko Kurimo,et al.  Missing-Feature Reconstruction With a Bounded Nonlinear State-Space Model , 2011, IEEE Signal Processing Letters.

[12]  Phong V. Vu,et al.  A Fast Wavelet-Based Algorithm for Global and Local Image Sharpness Estimation , 2012, IEEE Signal Processing Letters.

[13]  Jozef Vörös,et al.  Identification of Nonlinear Cascade Systems with Time-Varying Backlash , 2011 .

[14]  J. Voros.  AN ITERATIVE METHOD FOR HAMMERSTEIN-WIENER SYSTEMS PARAMETER IDENTIFICATION , 2004 .

[15]  Feng Ding,et al.  Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems , 2011, Comput. Math. Appl..

[16]  Er-Wei Bai,et al.  A blind approach to the Hammerstein-Wiener model identification , 2002, Autom..

[17]  D. Wang.  Brief paper: Lleast squares-based recursive and iterative estimation for output error moving average systems using data filtering , 2011 .

[18]  Feng Ding,et al.  Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems , 2008, Comput. Math. Appl..

[19]  Feng Ding,et al.  Parameter estimation with scarce measurements , 2011, Autom..