# American Institute of Mathematical Sciences

March  2014, 34(3): 1061-1078. doi: 10.3934/dcds.2014.34.1061

## Analysis of the 3DVAR filter for the partially observed Lorenz'63 model

 1 Warwick Mathematics Institute, University of Warwick, CV4 7AL, United Kingdom, United Kingdom, United Kingdom

Received  December 2012 Revised  April 2013 Published  August 2013

The problem of effectively combining data with a mathematical model constitutes a major challenge in applied mathematics. It is particular challenging for high-dimensional dynamical systems where data is received sequentially in time and the objective is to estimate the system state in an on-line fashion; this situation arises, for example, in weather forecasting. The sequential particle filter is then impractical and ad hoc filters, which employ some form of Gaussian approximation, are widely used. Prototypical of these ad hoc filters is the 3DVAR method. The goal of this paper is to analyze the 3DVAR method, using the Lorenz '63 model to exemplify the key ideas. The situation where the data is partial and noisy is studied, and both discrete time and continuous time data streams are considered. The theory demonstrates how the widely used technique of variance inflation acts to stabilize the filter, and hence leads to asymptotic accuracy.
Citation: Kody Law, Abhishek Shukla, Andrew Stuart. Analysis of the 3DVAR filter for the partially observed Lorenz'63 model. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 1061-1078. doi: 10.3934/dcds.2014.34.1061
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