Technical Report 2008-008

Relations between Bias-Eliminating Least Squares, the Frisch Scheme and Extended Compensated Least Squares Methods for Identifying Errors-in-Variables Systems

Mei Hong and Torsten Söderström

March 2008

There are many methods for identifying errors-in-variables systems. Among them Bias-Eliminating Least Squares (BELS), the Frisch scheme and Extended Compensated Least Squares (ECLS) methods are attractive approaches because of their simplicity and good estimation accuracy. These three methods are all based on a bias-compensated least-squares (BCLS) principle. In this report, the relations between them are considered. In particular, the nonlinear equations utilized in these three methods are proved to be equivalent under different noise conditions. It is shown that BELS, Frisch and ECLS methods have the same asymptotic estimation accuracy providing the same extended vector is used.

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