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Vol: 54(68) No: 2 / June 2009 An Errors-in-variables Parameter Estimation Method with Observation Separation Levente Hunyadi Budapest University of Technology and Economics, Department of Automation and Applied Informatics, 1111 Budapest, Goldmann György tér 3., Hungary, phone: +36 1 463-2870, e-mail: hunyadi,vajk@aut.bme.hu, web: http://www.aut.bme.hu/portal/hunyadi István Vajk Budapest University of Technology and Economics, Department of Automation and Applied Informatics, 1111 Budapest, Goldmann György tér 3., Hungary, e-mail: vajk@aut.bme.hu Keywords: errors-in-variables, parameter estimation, data separation, principal components analysis Abstract In many practical application fields, including control systems, signal processing, communications and econometrics, the usual assumption that the system output is observed with errors whereas the input is fully available does not hold. On the contrary, in an errors-in-variables context not only outputs but also inputs are observed with errors. Different estimation methods have been devised to simultaneously derive process as well as noise parameters under these circumstances. This paper proposes an algorithmic framework which introduces a preliminary separation step to group observations before they are subject to parameter estimation. As estimates are derived independently for the two groups of observations, it is possible to use some distance metrics to compare them. Minimizing these metrics over a noise space, it is possible to arrive at noise parameter estimates. Once noise parameter estimates are available, a maximum likelihood estimator may be applied over the entire observation set to compute model parameter estimates. References [1] Juan C. Agüero and Graham C. Goodwin. Identifiability of errors in variables dynamic systems. Automatica, 44(2):371–382, 2008. [2] Roberto Diversi and Roberto Guidorzi and Umberto Soverini. A new criterion in EIV identification and filtering applications. Proc. of 13th IFAC Symposium on System Identification, pages 1993–1998, 2003. [3] Peter de Groen. An Introduction to Total Least Squares. Nieuw Archief voor Wiskunde, 4(14):237–253, 1996. [4] Mei Hong and Torsten Söderström and Umberto Soverini and Roberto Diversi. Comparison of three Frisch methods for errors-in-variables identification. Proc. of 17th IFAC World Congress, pages 420–425, Seoul, Korea, 2008. [5] Mei Hong and Torsten Söderström and Wei Xing Zheng. A simplified form of the bias-eliminating least squares method for errors-in-variables identification. Technical report, Department of Information Technology, Uppsala University, 2006. report number: 2006-040. [6] Ivan Markovsky and Alexander Kukush and Sabine Van Huffel. On errors-in-variables with unknown noise variance ratio. Proc. of 14th IFAC Symposium on System Identification, pages 172–177, 2006. [7] Torsten Söderström. Errors-in-variables methods in system identification. Automatica, 43:939–958, 2007. [8] Stéphane Thil and Marion Gilson and Hugues Garnier. On instrumental variable-based methods for errors-in-variables model identification. Proc. of 17th IFAC World Congress, pages 420–425, Seoul, Korea, 2008. [9] Stéphane Thil and Mei Hong and Torsten Söderström and Marion Gilson and Hugues Garnier. Statistical Analysis of a Third-Order Cumulants Based Algorithm for Discrete-Time Errors-in-Variables Identification. Proc. of 17th IFAC World Congress, pages 420–425, Seoul, Korea, 2008. [10] István Vajk. Identification methods in a unified framework. Automatica, 41(8):1385–1393, 2005. [11] István Vajk and Jenő Hetthéssy. Efficient estimation of errors-in-variables models. 17th IFAC World Congress, Seoul, Korea, 2008. [12] Wei Xing Zheng. A Bias Correction Method for Identification of Linear Dynamic Errors-in-Variables Models. IEEE Transactions on Automatic Control, 47(7):1142–1147, 2002. |