Model Order Selection in Errors-in-Variables System Identification

Abstract This work studies the problem of model order selection in errors-in-variables (EIV) system identification. Two criteria, the final correlated prediction error (FCPE) criterion and the final correlated output error (FCOE) criterion are developed for estimating the order of EIV systems. The criteria are extensions of the final prediction error (FPE) criterion and the final output error (FOE) criterion. To eliminate the influence of the input noise in FPE criterion and FOE criterion, the idea of the new criteria is to correlate the prediction error and the output error with the output signal respectively. Simulations are used to illustrate the performance of the criteria.

[1]  Torsten Söderström,et al.  Identification of stochastic linear systems in presence of input noise , 1981, Autom..

[2]  Wei Xing Zheng,et al.  A bias correction method for identification of linear dynamic errors-in-variables models , 2002, IEEE Trans. Autom. Control..

[3]  H. Akaike.  Statistical predictor identification , 1970 .

[4]  Chun-Bo Feng,et al.  Unbiased parameter estimation of linear systems in the presence of input and output noise , 1989 .

[5]  Torsten Söderström,et al.  On model order determination for errors-in-variables estimation , 2012 .

[6]  H. Akaike.  Fitting autoregressive models for prediction , 1969 .

[7]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[8]  H. Akaike.  A new look at the statistical model identification , 1974 .

[9]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[10]  Rik Pintelon,et al.  Frequency-Domain, Errors-in-Variables Estimation of Linear Dynamic Systems Using Data From Overlapping Subrecords , 2008, IEEE Transactions on Instrumentation and Measurement.

[11]  Torsten Söderström,et al.  Errors-in-variables methods in system identification , 2018, Autom..

[12]  Petre Stoica,et al.  Combined instrumental variable and subspace fitting approach to parameter estimation of noisy input-output systems , 1995, IEEE Trans. Signal Process..

[13]  Herbert J. A. F. Tulleken,et al.  Generalized binary noise test-signal concept for improved identification-experiment design , 1990, Autom..

[14]  Torsten Söderström,et al.  Perspectives on errors-in-variables estimation for dynamic systems , 2002, Signal Process..

[15]  Yucai Zhu.  Multivariable process identification for mpc: the asymptotic method and its applications , 1998 .

[16]  Yucai Zhu,et al.  A Method of ARX Model Estimation of Errors-in-Variables Systems , 2015 .

[17]  R. Pintelon,et al.  Frequency Domain Errors-In-Variables Identification of a Time-Varying, Discrete Time System , 2011 .

[18]  Umberto Soverini,et al.  The Frisch scheme in algebraic and dynamic identification problems , 2008, Kybernetika.

[19]  Torsten Söderström,et al.  A generalized instrumental variable estimation method for errors-in-variables identification problems , 2011, Autom..

[20]  Torsten Söderström,et al.  Extending the Frisch scheme for errors‐in‐variables identification to correlated output noise , 2008 .

[21]  Umberto Soverini,et al.  A New Criterion in EIV Identification and Filtering Applications , 2003 .

[22]  Umberto Soverini,et al.  Identification of ARX and ARARX Models in the Presence of Input and Output Noises , 2010, Eur. J. Control.