BLUE, BLUP and the Kalman filter: some new results
Abstract
In this contribution, we extend ‘Kalmanfilter’ theory by introducing a new BLUE–BLUP recursion of the partitioned measurement and dynamic models. Instead of working with known statevector means, we relax the model and assume these means to be unknown. The recursive BLUP is derived from first principles, in which a prominent role is played by the model’s misclosures. As a consequence of the mean statevector relaxing assumption, the recursion does away with the usual need of having to specify the initial statevector variance matrix. Next to the recursive BLUP, we introduce, for the same model, the recursive BLUE. This extension is another consequence of assuming the statevector means unknown. In the standard Kalman filter setup with known statevector means, such difference between estimation and prediction does not occur. It is shown how the two intertwined recursions can be combined into one general BLUE–BLUP recursion, the outputs of which produce for every epoch, in parallel, the BLUP for the random statevector and the BLUE for the mean of the statevector.
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