State estimation using model order reduction for unstable systems

• Published in: Computers & fluids Vol. 46; no. 1; pp. 155 - 160
• Main Authors: Boess, C., Lawless, A.S., Nichols, N.K., Bunse-Gerstner, A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2011
• Subjects: Approximation; Balanced truncation; Dynamical systems; Estimates; Fluid flow; Fluids; Gauss–Newton methods; Mathematical models; Model reduction; State estimation; Unstable models; Variational data assimilation; Balanced truncation; Unstable models; Gauss–Newton methods; State estimation; Variational data assimilation
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2010.11.033

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.