Parameter estimation via artificial data generation with the “two-stage” approach

In this paper, we consider one of the most classical estimation problem, that of identifying an unknown parameter in a given model from measurements of input/output data. We present a new method named the two-stage approach which provides efficient estimates. The method is based on the preliminary generation of artificial data, and it is fully non-Bayesian. In this way, it is possible to avoid the well known difficulties encountered when resorting to Kalman filtering techniques in parameter estimation.

[1]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[2]  Giorgio Picci,et al.  Identification, adaptation, learning : the science of learning models from data , 1996 .

[3]  Giorgio Picci,et al.  Identification, Adaptation, Learning , 1996 .

[4]  E. Kamen,et al.  Introduction to Optimal Estimation , 1999 .

[5]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[6]  A.H. Haddad,et al.  Applied optimal estimation , 1976, Proceedings of the IEEE.

[7]  J. Grizzle,et al.  The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systemsy , 1995 .

[8]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[9]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[10]  J. Grizzle,et al.  The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systems , 1992, 1992 American Control Conference.

[11]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[12]  Rudolph van der Merwe,et al.  The Unscented Kalman Filter , 2002 .

[13]  M. Boutayeb,et al.  Convergence analysis of the extended Kalman filter used as an observer for nonlinear deterministic discrete-time systems , 1997, IEEE Trans. Autom. Control..

[14]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice Using MATLAB , 2001 .

[15]  Lennart Ljung,et al.  The Extended Kalman Filter as a Parameter Estimator for Linear Systems , 1979 .

[16]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[17]  P. Khargonekar,et al.  H∞ control and filtering for sampled-data systems , 1993, IEEE Trans. Autom. Control..

[18]  J. Grizzle,et al.  Observer design for nonlinear systems with discrete-time measurements , 1995, IEEE Trans. Autom. Control..

[19]  Shirley Dex,et al.  JR 旅客販売総合システム(マルス)における運用及び管理について , 1991 .

[20]  Torsten P. Bohlin,et al.  Practical Grey-box Process Identification: Theory and Applications , 2006 .

[21]  Konrad Reif,et al.  The extended Kalman filter as an exponential observer for nonlinear systems , 1999, IEEE Trans. Signal Process..