RECURSIVE EXTENDED COMPENSATED LEAST SQUARES BASED ALGORITHM FOR ERRORS-IN-VARIABLES IDENTIFICATION

Tomasz Larkowski, Jens G. Linden, Keith J. Burnham

2009

Abstract

An algorithm for the recursive identification of single-input single-output linear discrete-time time-invariant errors-in-variables system models in the case of white input and coloured output noise is presented. The approach is based on a bilinear parametrisation technique which allows the model parameters to be estimated together with the auto-correlation elements of the input/output noise sequences. In order to compensate for the bias in the recursively obtained least squares estimates, the extended bias compensated least squares method is used. An alternative for the online update of the associated pseudo-inverse of the extended observation covariance matrix is investigated, namely an approach based on the matrix pseudo-inverse lemma and an approach based on the recursive extended instrumental variables technique. A Monte-Carlo simulation study demonstrates the appropriateness and the robustness against noise of the proposed scheme.

References

  1. Björck, A°. (1996). Numerical Methods for Least Squares Problems. SIAM, Philadelphia.
  2. Ekman, M. (2005a). Identification of linear systems with errors in variables using separable nonlinear least squares. In Proc. of 16th IFAC World Congress, Prague, Czech Republic.
  3. Ekman, M. (2005b). Modeling and Control of Bilinear Systems: Applications to the Activated Sludge Process. PhD thesis, Uppsala University, Sweden.
  4. Ekman, M., Hong, M., and S öderström, T. (2006). A separable nonlinear least-squares approach for identification of linear systems with errors in variables. In 14th IFAC Symp. on System Identification, Newcastle, Australia.
  5. Feng, D., Zhang, H., Zhang, X., and Bao, Z. (2001). An extended recursive least-squares algorithm. Signal Proc., 81(5):1075-1081.
  6. Friedlander, B. (1984). The overdetermined recursive instrumental variable method. IEEE Trans. on Automatic Control, 29(4):353-356.
  7. Ikenoue, M., Kanae, S., Yang, Z., and Wada, K. (2008). Bias-compensation based method for errorsin-variables model identification. In Proc. of 17th IFAC World Congress, pages 1360-1365, Seul, South Korea.
  8. Larkowski, T., Linden, J. G., Vinsonneau, B., and Burnham, K. J. (2008). Identification of errors-in-variables systems via extended compensated least squares for the case of coloured output noise. In The 19th Int. Conf. on Systems Engineering, pages 71-76, Las Vegas, USA.
  9. Linden, J. G. (2008). Algorithms for recursive Frisch scheme identification and errors-in-variables filtering. PhD thesis, Coventry University, UK.
  10. Ljung, L. (1999). System Identification - Theory for the User. Prentice Hall PTR, New Jersey, USA, 2nd edition.
  11. Mahata, K. (2007). An improved bias-compensation approach for errors-in-variables model identification. Automatica, 43(8):1339-1354.
  12. Markovsky, I. and Van Huffel, S. (2007). Overview of total least-squares methods. Signal Proc., 87(10):2283- 2302.
  13. S öderström, T. (2007). Errors-in-variables methods in system identification. Automatica, 43(6):939-958.
Download


Paper Citation


in Harvard Style

Larkowski T., G. Linden J. and J. Burnham K. (2009). RECURSIVE EXTENDED COMPENSATED LEAST SQUARES BASED ALGORITHM FOR ERRORS-IN-VARIABLES IDENTIFICATION . In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO, ISBN 978-989-674-001-6, pages 142-147. DOI: 10.5220/0002211901420147


in Bibtex Style

@conference{icinco09,
author={Tomasz Larkowski and Jens G. Linden and Keith J. Burnham},
title={RECURSIVE EXTENDED COMPENSATED LEAST SQUARES BASED ALGORITHM FOR ERRORS-IN-VARIABLES IDENTIFICATION},
booktitle={Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},
year={2009},
pages={142-147},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002211901420147},
isbn={978-989-674-001-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,
TI - RECURSIVE EXTENDED COMPENSATED LEAST SQUARES BASED ALGORITHM FOR ERRORS-IN-VARIABLES IDENTIFICATION
SN - 978-989-674-001-6
AU - Larkowski T.
AU - G. Linden J.
AU - J. Burnham K.
PY - 2009
SP - 142
EP - 147
DO - 10.5220/0002211901420147