  This paper presents a new iterative state estimation algorithm for advection
dominated flows with non-Gaussian uncertainty description of $L^\infty$-type:
uncertain initial condition and model error are assumed to be pointvise bounded
in space and time, and the observation noise has uncertain but bounded second
moments. The algorithm approximates this $L^\infty$-type bounding set by a
union of possibly overlapping ellipsoids, which are localized (in space) on a
number of sub-domains. On each sub-domain the state of the original system is
estimated by the standard $L^2$-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 Schwartz method to reconstruct the
state of the original system. The efficacy of the proposed method is
demonstrated with a set of numerical examples.

Optimization and Control