Comparison of linear and nonlinear methods of confidence estimation for statistically uncertain systems

In this paper, we consider a problem of confidence sets design for the estimation problem with observations in the system that contains both random perturbations with given distributions and uncertain perturbations with information completely defined by the domain of their possible values. Two approaches are compared: the first is based on application of a posteriori distributions and relations of the Kalman filter for systems with uncertain parameters, the other is connected with design of optimal confidence sets. It was shown that nonlinear estimates are better for the estimation problem under consideration.