Localised sequential state estimation for advection dominated flows with non-Gaussian uncertainty description

This paper presents a new iterative state estimation algorithm for advection dominated flows with non-Gaussian uncertainty description of L∞-type: uncertain initial condition and model error are assumed to be pointwise bounded in space and time, and the observation noise has uncertain but bounded second moments. The algorithm approximates this L∞-type bounding set by a union of possibly overlapping ellipsoids, which are localised (in space) on a number of sub-domains. On each sub-domain the state of the original system is estimated by the standard L2-type filter (e.g. Kalman minimax filter) which uses Gaussian/ellipsoidal uncertainty description and observations (if any) which correspond to this sub-domain. The resulting local state estimates are stitched together by the iterative d-ADN Schwarz method to reconstruct the state of the original system. The efficacy of the proposed method is demonstrated with a set of numerical examples.