Variance properties of a two-step ARX estimation procedure

In this contribution we discuss some variance properties of a two-step ARX estimation scheme. An expression for the co-variance of the final low order model is calculated and it is discussed how one should minimize this covariance. The implication of the results is that identification of the dynamics of a system could very easily be performed with standard linear least squares (two times), even if the measurement noise is heavily colored. We also show a numerical example, where this two-step estimation scheme gives a variance which is close (but not equal) to the the Cramèr-Rao lower bound. Moreover, we show that the point estimate of the covariance is close to the one obtained through Monte Carlo simulations.