Some asymptotic properties of multivariable models identified by equation error techniques

In this paper some interesting properties are derived for simple equation error identification techniques, least squares and basic instrumental variable methods, applied to a class of linear time-invariant time-discrete multivariable models. The system at hand is not supposed to be contained in the chosen model set. Assuming that the input is unit variance white noise, it is shown that the Markov parameters of the system are estimated asymptotically unbiased over a certain interval around t = 0.