Author(s)

M. Verlaan & A.W. Heemink

Abstract

In theory K aim an filters can be used to solve many on-line data assimilation problems. However, for models resulting from the discretization of partial differential equations the number of state variables is usually very large, leading to a huge computational burden. Therefore approximation of the Kalman filter equations is in general necessary. In this paper two new algorithms are proposed, that extend the idea of the Reduced Rank Square Root filter [15] for use with non-linear models. The algorithms are based on a low rank approximation of the error covari- ance matrix and use a square root representation of the error covariance. For both algorithms the tangent linear model is not needed. The first al- gorithm proposed is accurate up to first order terms, which is comparable to the extended Kalman filter

Keywords