State estimation using model order reduction for unstable systems

Boess, C., Lawless, A. S. ORCID: https://orcid.org/0000-0002-3016-6568, Nichols, N. K. ORCID: https://orcid.org/0000-0003-1133-5220 and Bunse-Gerstner, A. (2011) State estimation using model order reduction for unstable systems. Computers & Fluids, 46 (1). pp. 155-160. ISSN 0045-7930 doi: 10.1016/j.compfluid.2010.11.033

Abstract/Summary

The problem of state estimation occurs in many applications of fluid flow. For example, to produce a reliable weather forecast it is essential to find the best possible estimate of the true state of the atmosphere. To find this best estimate a nonlinear least squares problem has to be solved subject to dynamical system constraints. Usually this is solved iteratively by an approximate Gauss–Newton method where the underlying discrete linear system is in general unstable. In this paper we propose a new method for deriving low order approximations to the problem based on a recently developed model reduction method for unstable systems. To illustrate the theoretical results, numerical experiments are performed using a two-dimensional Eady model – a simple model of baroclinic instability, which is the dominant mechanism for the growth of storms at mid-latitudes. It is a suitable test model to show the benefit that may be obtained by using model reduction techniques to approximate unstable systems within the state estimation problem.

Additional Information	Special issue: 10th ICFD Conference Series on Numerical Methods for Fluid Dynamics (ICFD 2010)
Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/24144
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO) Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	State estimation; Gauss–Newton methods; Variational data assimilation; Unstable models; Balanced truncation
Additional Information	Special issue: 10th ICFD Conference Series on Numerical Methods for Fluid Dynamics (ICFD 2010)
Publisher	Elsevier
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