Auxiliary Model Based Least Squares Iterative Algorithms for Parameter Estimation of Bilinear Systems Using Interval-Varying Measurements

This paper focuses on the parameter estimation of a class of bilinear systems, for which the input-output representation is derived by eliminating the state variables in the systems. Based on the obtained identification model and the hierarchical identification principle, a hierarchical auxiliary model based least squares iterative algorithm is derived, to improve the computation efficiency and the parameter estimation accuracy by using the auxiliary model identification idea and the interval-varying input-output data. For comparison, an auxiliary model based least squares iterative algorithm is presented. The simulation results show that the proposed algorithm has better performance in estimating the parameters of bilinear systems.

[1]  R. Mohler,et al.  Bilinear system identification by Walsh functions , 1978 .

[2]  R. Mohler.  An Overview of Bilinear System Theory and Applications , 1980 .

[3]  B. Cheng,et al.  Analysis and parameter estimation of bilinear systems via block-pulse functions , 1982 .

[4]  M. Inagaki,et al.  Bilinear system identification by Volterra kernels estimation , 1984 .

[5]  Y. Shih,et al.  Analysis and parameter estimation of bilinear systems via Chebyshev polynomials , 1984 .

[6]  C. Hwang,et al.  Parameter identification of bilinear systems using the Galerkin method , 1985 .

[7]  Chyi Hwang,et al.  Analysis and parameter identification of bilinear systems via shifted Legendre polynomials , 1985 .

[8]  H.-Y. Chung,et al.  Analysis and parameter estimation of bilinear systems using Taylor operational matrices , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  P. Paraskevopoulos,et al.  A new orthogonal series approach to state space analysis of bilinear systems , 1994, IEEE Trans. Autom. Control..

[10]  M. Verhaegen,et al.  Identifying MIMO Wiener systems using subspace model identification methods , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[11]  Boualem Boashash,et al.  Identification of bilinear systems using bandlimited regression , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[12]  Heinz Unbehauen,et al.  Bilinear Continuous-Time Systems Identification via Hartley-Based Modulating Functions , 1998, Autom..

[13]  Nicholas Kalouptsidis,et al.  Identification of input-output bilinear systems using cumulants , 2001, IEEE Trans. Signal Process..

[14]  Michel Verhaegen,et al.  Subspace identification of multivariable linear parameter-varying systems , 2002, Autom..

[15]  A practical procedure of bilinear weighted core kinetics parameters computation for the purpose of experimental reactivity determination , 2002 .

[16]  Brett Ninness,et al.  Maximum-likelihood parameter estimation of bilinear systems , 2005, IEEE Transactions on Automatic Control.

[17]  Yovani Marrero-Ponce,et al.  Novel 3D bio-macromolecular bilinear descriptors for protein science: Predicting protein structural classes. , 2015, Journal of theoretical biology.

[18]  Feng Ding,et al.  Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle , 2015, Signal Process..

[19]  Xianqiang Yang,et al.  EM algorithm-based identification of a class of nonlinear Wiener systems with missing output data , 2015 .

[20]  Guangjie Han,et al.  Distributed Parameter Estimation for Mobile Wireless Sensor Network Based on Cloud Computing in Battlefield Surveillance System , 2015, IEEE Access.

[21]  Raja Muhammad Asif Zahoor,et al.  Two-stage fractional least mean square identification algorithm for parameter estimation of CARMA systems , 2015, Signal Process..

[22]  Dongqing Wang,et al.  Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models , 2016, Appl. Math. Lett..

[23]  Feng Ding,et al.  Parameter estimation algorithms for multivariable Hammerstein CARMA systems , 2016, Inf. Sci..

[24]  Kang-Hyun Jo,et al.  Output feedback fault-tolerant control for a class of discrete-time fuzzy bilinear systems , 2016 .

[25]  Shun-Hung Tsai,et al.  A Novel Fuzzy Identification Method Based on Ant Colony Optimization Algorithm , 2016, IEEE Access.

[26]  Patrick T. Brewick,et al.  An evaluation of data-driven identification strategies for complex nonlinear dynamic systems , 2016 .

[27]  Ying Liao,et al.  Parameter identification of nonlinear dynamic systems using an improved particle swarm optimization , 2016 .

[28]  Feng Ding,et al.  Adaptive filtering parameter estimation algorithms for Hammerstein nonlinear systems , 2016, Signal Process..

[29]  Dandan Meng.  Recursive Least Squares and Multi-innovation Gradient Estimation Algorithms for Bilinear Stochastic Systems , 2017, Circuits Syst. Signal Process..

[30]  Zhen Zhang,et al.  Maximum likelihood estimation method for dual-rate Hammerstein systems , 2017 .

[31]  Feng Ding,et al.  Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering , 2017, Digit. Signal Process..

[32]  Feng Ding,et al.  The Gradient-Based Iterative Estimation Algorithms for Bilinear Systems with Autoregressive Noise , 2017, Circuits, Systems, and Signal Processing.

[33]  Chong Chen,et al.  State of Charge Estimation of Battery Energy Storage Systems Based on Adaptive Unscented Kalman Filter With a Noise Statistics Estimator , 2017, IEEE Access.

[34]  F. Ding,et al.  Least-squares-based iterative and gradient-based iterative estimation algorithms for bilinear systems , 2017 .

[35]  F. Ding,et al.  Recasted models-based hierarchical extended stochastic gradient method for MIMO nonlinear systems , 2017 .

[36]  Feng Ding,et al.  Hierarchical Stochastic Gradient Algorithm and its Performance Analysis for a Class of Bilinear-in-Parameter Systems , 2017, Circuits Syst. Signal Process..

[37]  Feng Ding,et al.  The maximum likelihood least squares based iterative estimation algorithm for bilinear systems with autoregressive moving average noise , 2017, J. Frankl. Inst..

[38]  T. Hayat,et al.  Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique , 2017 .

[39]  Feng Ding,et al.  Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering , 2017, J. Frankl. Inst..