A covariance matching approach for identifying errors-in-variables systems

The errors-in-variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise. Several estimation methods have been proposed for identifying dynamic errors-in-variables models. In this paper a covariance matching approach is proposed to solve the identification problem. It applies for general types of input signals. The method utilizes a small set of covariances of the measured input-output data. This property applies also for some other methods, such as the Frisch scheme and the bias-eliminating least squares method. Algorithmic details for the proposed method are provided. User choices, for example specification of which input-output covariances to utilize, are discussed in some detail. The method is evaluated by using numerical examples, and is shown to have competitive properties as compared to alternative methods.

[1]  T. Söderström.  ON COMPUTING THE CRAMER-RAO BOUND AND COVARIANCE MATRICES FOR PEM ESTIMATES IN LINEAR STATE SPACE MODELS , 2006 .

[2]  M. Mossberg,et al.  Errors-in-variables identification through covariance matching: Analysis of a colored measurement noise case , 2008, 2008 American Control Conference.

[3]  István Berkes,et al.  On the convergence of ∑_{}(_{}) , 2009 .

[4]  Feng Ding,et al.  Hierarchical gradient-based identification of multivariable discrete-time systems , 2005, Autom..

[5]  Feng Ding,et al.  Performance analysis of estimation algorithms of nonstationary ARMA processes , 2006, IEEE Transactions on Signal Processing.

[6]  W. Zheng.  Transfer function estimation from noisy input and output data , 1998 .

[7]  Torsten Söderström,et al.  A SEPARABLE NONLINEAR LEAST-SQUARES APPROACH FOR IDENTIFICATION OF LINEAR SYSTEMS WITH ERRORS IN VARIABLES , 2006 .

[8]  Gene H. Golub,et al.  The differentiation of pseudo-inverses and non-linear least squares problems whose variables separate , 1972, Milestones in Matrix Computation.

[9]  G. Golub,et al.  Separable nonlinear least squares: the variable projection method and its applications , 2003 .

[10]  Torsten Söderström,et al.  Using continuous-time modeling for errors-in-variables identification , 2006 .

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

[12]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[13]  Umberto Soverini,et al.  The frisch scheme in dynamic system identification , 1990, Autom..

[14]  Torsten Söderström,et al.  Relations between Bias-Eliminating Least Squares, the Frisch scheme and Extended Compensated Least Squares methods for identifying errors-in-variables systems , 2009, Autom..

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

[16]  Mats Ekman,et al.  IDENTIFICATION OF LINEAR SYSTEMS WITH ERRORS IN VARIABLES USING SEPARABLE NONLINEAR LEAST-SQUARES , 2005 .

[17]  Lennart Ljung,et al.  Theory and Practice of Recursive Identification , 1983 .

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

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

[20]  Max Donath,et al.  American Control Conference , 1993 .

[21]  Petre Stoica,et al.  On the convergence of pseudo-linear regression algorithms , 1985 .

[22]  Sabine Van Huffel,et al.  Recent advances in total least squares techniques and errors-in-variables modeling , 1997 .

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

[24]  Feng Ding,et al.  Hierarchical least squares identification methods for multivariable systems , 2005, IEEE Trans. Autom. Control..