Asymptotic Accuracy Analysis of Bias-Eliminating Least Squares Estimates for Identification of Errors in Variables Systems

Mei Hong, Torsten Söderström, and Wei Xing Zheng

October 2006

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 report, we investigate the asymptotic 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.

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