Statistical analysis of the Frisch scheme for identifying errors-in-variables systems

Several estimation methods have been proposed for identifying errors-in-variables systems, where both input and output measurements are corrupted by noise. One of the promising approaches is the so called Frisch scheme. This paper provides an accuracy analysis of the Frisch scheme applied to system identification. The estimates of the system parameters and the noise variances are shown to be asymptotically Gaussian distributed. An explicit expression for the covariance matrix of the asymptotic distribution is given as well. Numerical simulations support the theoretical results. A comparison with the Cramer-Rao lower bound is also given in examples, and it is shown that the Frisch scheme gives a performance close to the Cramer-Rao bound for large signal-to-noise ratios.