Computationally tractable robust moving horizon estimation using an approximate convex hull

When the model of the system under observation is not precisely known, state estimation and the subsequent prediction of system trajectories from this state estimate is subject to uncertainty. A useful method state estimation and prediction is to provide bounds within which the estimates are guaranteed to lie. When a model set is available, predictions can be made for every element of this set, with bounds derived from these predictions. The goal of this work is to reduce the computational complexity of a robust moving horizon estimation (MHE) method of this from. The main element of this method is the computation and use of a so called approximate convex hull that provides an approximate cover of the model set. Estimates and predictions need only be made for the models at the vertices of the approximate convex hull. An output bound is given that reflects the effect of the approximation error. Therefore, the method guarantees that the actual output is in the bound estimated by the robust MHE.