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

TL;DR

This paper introduces a novel iterative localised state estimation algorithm for advection flows with non-Gaussian uncertainties, combining ellipsoidal approximations and domain decomposition to improve estimation accuracy.

Contribution

It develops a new method that approximates non-Gaussian uncertainties with ellipsoids and uses localized filters combined with an iterative stitching process.

Findings

Effective in handling non-Gaussian uncertainties in advection flows.

Improves state estimation accuracy through domain decomposition and iterative stitching.

Demonstrated success with numerical examples.

Abstract

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.