A unified framework for EIV identification methods when the measurement noises are mutually correlated

In this paper, the previously introduced Generalized Instrumental Variable Estimator (GIVE) is extended to the case of errors-in-variables models where the additive input and output noises are mutually correlated white processes. It is shown how many estimators proposed in the literature can be described as various special cases of a generalized instrumental variable framework. It is also investigated how to analyze the common situation where some of the equations that define the estimator are to hold exactly, and others to hold approximately in a least squares sense, providing a detailed study of the accuracy analysis.

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

[2]  Thomas Bak,et al.  Data Driven Modelling of the Dynamic Wake between Two Wind Turbines , 2012 .

[3]  T Söderström,et al.  Convergence of bias-eliminating least squares methods for errors-in-variables identification , 2005 .

[4]  Umberto Soverini,et al.  Identification of Errors-In-Variables Models with Mutually Correlated Input and Output Noises , 2012 .

[5]  Sabine Van Huffel,et al.  Total least squares and errors-in-variables modeling , 2007, Signal Process..

[6]  久也 藤岡.  European Control Conference ECC 97 , 1998 .

[7]  Roberto Diversi,et al.  Bias‐eliminating least‐squares identification of errors‐in‐variables models with mutually correlated noises , 2012 .

[8]  Chung-Yen Ong.  Frequency-Domain Maximum-Likelihood Adaptive Filtering , 1970 .

[9]  Torsten Söderström,et al.  Frequency domain maximum likelihood identification of noisy input–output models , 2014 .

[10]  P. Stoica,et al.  On nonexistence of the maximum likelihood estimate in blind multichannel identification , 2005, IEEE Signal Process. Mag..

[11]  Wei Xing Zheng,et al.  Convergence properties of bias‐eliminating algorithms for errors‐in‐variables identification , 2005 .

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

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

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

[15]  Torsten Söderström.  System identification for the errors-in-variables problem , 2010 .

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

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

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

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

[20]  John Swarbrooke,et al.  Case Study 18 – Las Vegas, Nevada, USA , 2007 .

[21]  S. Beghelli,et al.  A frequential approach for errors-in-variables models , 1997, 1997 European Control Conference (ECC).

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

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

[24]  Torsten Söderström,et al.  Errors-in-variables identification using a Generalized Instrumental Variable Estimation method , 2010, 49th IEEE Conference on Decision and Control (CDC).

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

[26]  Torsten Söderström,et al.  A generalised instrumental variable estimator for multivariable errors-in-variables identification problems , 2012, Int. J. Control.

[27]  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..

[28]  Torsten Söderström,et al.  A unified framework for EIV identification methods in the presence of mutually correlated noises , 2014 .

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

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

[31]  Wei Xing Zheng,et al.  A Simplified Form of the Bias-Eliminating Least Squares Method for Errors-in-Variables Identification , 2007, IEEE Transactions on Automatic Control.

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

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