State estimation using model order reduction for unstable systems

✍ Scribed by C. Boess; A.S. Lawless; N.K. Nichols; A. Bunse-Gerstner

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 386 KB
• Volume: 46
• Category: Article
• ISSN: 0045-7930
• DOI: 10.1016/j.compfluid.2010.11.033

✦ Synopsis

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.