Confidence Regions for Systems with Random and Uncertain Perturbations
The state estimation problem for statistically uncertain
systems with observation is investigated. A system is called statistically uncertain one if it contains random perturbations with incompletely known distributions, or it contains both random and nonrandom uncertain perturbations. Confidence estimates for the system states are studied.
It is shown that linear estimates are not optimal even for linear systems depended on Gaussian random erturbations with uncertain mean values. The nonlinear confidence estimates for the system state are constructed using a notion of a random information set. The properties of the estimates are studied.