O. Barrero M. and B.L.R. De Moor (Belgium)
Data Assimilation, Kalman Filtering, Large Scale Systems,Square Root Algorithm
For systems with a relatively small order the Kalman fil ter provides an optimal solution to many data assimilation problems. However, for large scale systems that arise from discretizing partial differential equations, the number of computations and the required storage for the Kalman filter become prohibitive. Also numerical difficulties may arise from propagation of errors, due to finite machine precision computations. Often they result in the violation of the re quirement that the error covariance matrix should be posi tive semi-definite. In this paper we will discuss the Singular Square Root Algorithm (SQRT) to compute a Kalman filter gain for large scale systems, which solves in a reasonable manner the problems mentioned above.
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