COMPUTATIONAL ASPECTS FOR RECURSIVE FRISCH SCHEME SYSTEM IDENTIFICATION

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

Abstract

The implementation of a recursive algorithm for the estimation of parameters of a linear single-input singleoutput errors-in-variables system is re-considered. The objective is to reduce the computational complexity in order to reduce the computation time per recursion, which, in turn, will allow a wider applicability of the recursive algorithm. The technique of stationary iterative methods for least squares is utilised, in order to reduce the complexity from cubic to quadratic order with respect to the model parameters to be estimated. A numerical simulation underpins the theoretically obtained results.

References

  1. Beghelli, S., Guidorzi, R. P., and Soverini, U. (1990). The Frisch scheme in dynamic system identification. Automatica, 26(1):171-176.
  2. Björck, A°. (1996). Numerical Methods for Least Squares Problems. SIAM, Philadelphia.
  3. Diversi, R., Guidorzi, R., and Soverini, U. (2006). YuleWalker equations in the Frisch scheme solution of errors-in-variables identification problems. In Proc.
  4. 17th Int. Symp. on Math. Theory of Networks and Systems, pages 391-395.
  5. Feng, Y. T. and Owen, D. R. J. (1996). Conjugate gradient methods for solving the smallest eigenpair of large symmetric eigenvalue problems. Int. J. for Numerical Methods in Engineering, 39:2209-2229.
  6. Hong, M., S öderström, T., Soverini, U., and Diversi, R. (2007). Comparison of three Frisch methods for errors-in-variables identification. Technical Report 2007-021, Uppsala University, Uppsala, Sweden.
  7. Linden, J. G., Larkowski, T., and Burnham, K. J. (2008a). An improved recursive Frisch scheme identification algorithm. In Proc. 19th Int. Conf. on Systems Engineering, pages 65-70, Las Vegas, USA.
  8. Linden, J. G., Vinsonneau, B., and Burnham, K. J. (2007). Fast algorithms for recursive Frisch scheme system identification. In Proc. CD-ROM 22nd IAR & ACD Workshop, Grenoble, France.
  9. Linden, J. G., Vinsonneau, B., and Burnham, K. J. (2008b). Gradient-based approaches for recursive Frisch scheme identification. In Preprints of the 17th IFAC World Congress, pages 1390-1395, Seoul, Korea.
  10. Ljung, L. (1999). System Identification - Theory for the user. PTR Prentice Hall Information and System Sciences Series. Prentice Hall, New Jersey, 2nd edition.
  11. Sagara, S. and Wada, K. (1977). On-line modified leastsquares parameter estimation of linear discrete dynamic systems. Int. J. Control, 25(3):329-343.
  12. S öderström, T. (2006). Statistical analysis of the Frisch scheme for identifying errors-in-variables systems. Technical report 2006-002, Uppsala University, Department of Information Technology, Uppsala, Sweden.
  13. S öderström, T. (2007a). Accuracy analysis of the Frisch scheme for identifying errors-in-variables systems. IEEE Trans. Autom. Contr., 52(6):985-997.
  14. S öderström, T. (2007b). Errors-in-variables methods in system identification. Automatica, 43(6):939-958.
  15. Zheng, W. X. and Feng, C. B. (1989). Unbiased parameter estimation of linear systems in the presence of input and output noise. Int. J. of Adaptive Control and Signal Proc., 3:231-251.
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Paper Citation


in Harvard Style

G. Linden J., Larkowski T. and Burnham K. (2009). COMPUTATIONAL ASPECTS FOR RECURSIVE FRISCH SCHEME SYSTEM 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 136-141. DOI: 10.5220/0002211401360141


in Bibtex Style

@conference{icinco09,
author={Jens G. Linden and Tomasz Larkowski and Keith J. Burnham},
title={COMPUTATIONAL ASPECTS FOR RECURSIVE FRISCH SCHEME SYSTEM IDENTIFICATION},
booktitle={Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},
year={2009},
pages={136-141},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002211401360141},
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 - COMPUTATIONAL ASPECTS FOR RECURSIVE FRISCH SCHEME SYSTEM IDENTIFICATION
SN - 978-989-674-001-6
AU - G. Linden J.
AU - Larkowski T.
AU - Burnham K.
PY - 2009
SP - 136
EP - 141
DO - 10.5220/0002211401360141