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

•A new iterative state estimation algorithm for advection dominated flows with non-Gaussian uncertainty description of L∞-type.•The algorithm approximates this L∞-type bounding set by a union of possibly overlapping localized (in space) ellipsoids.•The resulting local state estimates are stitched together by the iterative d-ADN Schwartz method.•The efficacy of the proposed method is demonstrated with a set of numerical examples.