» Download Article

Authors
Mei Hong; Torsten Soderstrom; Wei Xing Zheng

Identifier
10.3182/20060329-3-AU-2901.00024

Index Terms
system identification,errors-in-variables,bias-eliminating least squares,accuracy analysis

Abstract
The bias-eliminating least squares (BELS) method is one of the consistent estimators for identifying dynamic errors-in-variables systems. The attraction of the BELS method lies in its good accuracy and its modest computational cost. In this paper, we investigate the accuracy properties of the BELS estimates. It is shown that the estimated system parameters and the estimated noise variances are asymptotically Gaussian distributed. An explicit expression for the normalized covariance matrix of the estimated parameters is derived and supported by some numerical examples.

References

[1] Fernando, K. V. and H. Nicholson (1985). Identification
     of linear systems with input and output
    noise: the Koopmans-Levin method. IEE Proceedings,
     Part D 132(1), 30-36.
[2] Hong, M., T. Söderström and W. X. Zheng (2005). Accuracy
     analysis of bias-eliminating least squares
    estimates for identification of errors-in-variables
    systems. Technical Report No: 2005-021.
[3] Pintelon, R. and J. Schoukens (2001). System Identification.
     A Frequency Domain Approach. IEEE
    Press. New York, NY, USA.
[4] Söderström, T. (1981). Identification of stochastic linear
     systems in presence of input noise. Automatica
     17(5), 713-725.
[5] Söderström, T. (2005). Accuracy analysis of the Frisch
    estimates for identifying errors-in-variables systems.
     In: Proc. 44th IEEE CDC/ECC 2005.
    Seville, Spain. To appear.
[6] Söderström, T. and P. Stoica (1989). System Identification
    . Prentice Hall Int., Hemel Hempstead, UK.
[7] Söderström, T., M. Hong and W. X. Zheng (2005).
    Convergence properties of bias-eliminating algorithms
     for errors-in-variables identification. Int.
    J. Adaptive Control Signal Processing. To appear.
[8] Söderström, T., U. Soverini and K. Mahata
    (2002). Perspectives on errors-in-variables estimation
     for dynamic systems. Signal Processing
    82(8), 1139-1154.
[9] Van Huffel, S. and Lemmerling, Ph., editors. (2002).
    Total Least Squares and Errors-in-Variables
    Modelling. Analysis, Algorithms and Applications
    . Kluwer. Dordrecht, The Netherlands.
[10] Zheng, W. X. (1998). Transfer function estimation
     form noisy input and output data. Int. J. Adaptive
     Control Signal Processing 12(4), 365-380.
[11] Zheng, W. X. and C. B. Feng (1989). Unbiased parameter
      estimation of linear systems in presence
     of input and output noise. Int. J. Adaptive Control
     Signal Processing 3(3), 231-251.