Description
The Fast Kalman filter applies only to systems with sparse matrices (Lange, 2001), since HWB is an inversion method to solve sparse linear equations (Wolf, 1978).
The ordinary Kalman filter is optimal for general systems. However, an optimal Kalman filter is probably stable only if Kalman's observability and controllability conditions are also satisfied (Kalman, 1960). These conditions are challenging to continuously maintain for a large system which means that even an optimal Kalman filter may diverge towards false solutions. Fortunately, the stability of an optimal Kalman filter can be controlled by monitoring its error variances if these can be reliably estimated. Their precise computation is, however, much more demanding than the optimal filtering itself but the FKF method may provide the required speed-up also in this respect.
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