A Comparison of Set Estimation Methods for Output Error Models with Bounded Errors

The computation of bounds on parameters, rather than point estimates and covariances, is considered for discrete time output error models which are linear in the parameters. The additive noise is assumed to be unknown but bounded in an l_∞ norm by a given constant. In the case for given input-output data, the set of all admissible parameters consistent with the given model equation and the noise bound, is a convex polytope. In this paper we attempt to estimate optimally by means of minimizing the parameter uncertainty intervals. Therefore, we compare ellipsoidal bounding with orthotopic bounding (linear programming) and a simulation example is given to illustrate the results.