Set-membership Estimation using Ellipsoidal Ensembles

This paper is about a set-membership based state- and parameter estimation approach for nonlinear dynamic systems under the assumption that all measurement errors are bounded. In detail, we propose an outer approximation method, where the set of states and parameters that is consistent with the incoming measurement bounds is over-approximated by an intersection of ellipsoids. We introduce computationally tractable methods for propagating such ellipsoidal ensembles through dynamic systems and construct an associated recursive estimation algorithm. We also show how to select the past measurements such that the intersection problem remains tractable on long time horizons. The proposed approach is illustrated by applying it to a batch membrane process.