A discrete time Kalman filter algorithm for large scale problems

GERMÁN ARIEL TORRES

Santiago de Chile

Workshop; I SAEMC-IAI, STIC-AMSUD Workshop; 2007

Centro de Modelamiento Matemático (CMM)

Data assimilation is the process of feeding a partially unknown prediction model with available information coming from observations, with the objective of correcting and improving the modeled results. One of the most important mathematical tools to perform data assimilation is the Kalman filter. The Kalman filter is esentially an algorithm of prediction-correction type that is optimal in the sense of minimizing the trace of the covariance matrix of the errors. Unfortunately the computational cost of applying the filter to large scale problems is enormous, and the programming of the filter is highly dependent on the model and the format of the data involved. The first objective of this paper is to present a set of Fortran 90 modules in order to implement reduced rank square root versions of the Kalman Filter, adapted for assimilation of a very big amount of variables. The second objective is to present a Kalman filter implementation whose code can be independent from model and observations, and as easy as possible for the user. A detailed description of the algorithms, structure and examples of use are given.