BLUE, BLUP and the Kalman filter: some new results

In this contribution, we extend ‘Kalman-filter’ theory by introducing a new BLUE–BLUP recursion of the partitioned measurement and dynamic models. Instead of working with known state-vector means, we relax the model and assume these means to be unknown. The recursive BLUP is derived from first princ...

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Main Authors: Teunissen, Peter, Khodabandeh, A.
Format: Journal Article
Published: Springer - Verlag 2013
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/43062
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author Teunissen, Peter
Khodabandeh, A.
author_facet Teunissen, Peter
Khodabandeh, A.
author_sort Teunissen, Peter
building Curtin Institutional Repository
collection Online Access
description In this contribution, we extend ‘Kalman-filter’ theory by introducing a new BLUE–BLUP recursion of the partitioned measurement and dynamic models. Instead of working with known state-vector 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 state-vector relaxing assumption, the recursion does away with the usual need of having to specify the initial state-vector variance matrix. Next to the recursive BLUP, we introduce, for the same model, the recursive BLUE. This extension is another consequence of assuming the state-vector means unknown. In the standard Kalman filter set-up with known state-vector 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 state-vector and the BLUE for the mean of the state-vector.
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spelling curtin-20.500.11937-430622017-09-13T15:54:28Z BLUE, BLUP and the Kalman filter: some new results Teunissen, Peter Khodabandeh, A. BLUE–BLUP recursion Best linear unbiased estimation (BLUE) Kalman filter Best linear unbiased prediction (BLUP) Misclosures Minimum mean squared error (MMSE) In this contribution, we extend ‘Kalman-filter’ theory by introducing a new BLUE–BLUP recursion of the partitioned measurement and dynamic models. Instead of working with known state-vector 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 state-vector relaxing assumption, the recursion does away with the usual need of having to specify the initial state-vector variance matrix. Next to the recursive BLUP, we introduce, for the same model, the recursive BLUE. This extension is another consequence of assuming the state-vector means unknown. In the standard Kalman filter set-up with known state-vector 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 state-vector and the BLUE for the mean of the state-vector. 2013 Journal Article http://hdl.handle.net/20.500.11937/43062 10.1007/s00190-013-0623-6 Springer - Verlag fulltext
spellingShingle BLUE–BLUP recursion
Best linear unbiased estimation (BLUE)
Kalman filter
Best linear unbiased prediction (BLUP)
Misclosures
Minimum mean squared error (MMSE)
Teunissen, Peter
Khodabandeh, A.
BLUE, BLUP and the Kalman filter: some new results
title BLUE, BLUP and the Kalman filter: some new results
title_full BLUE, BLUP and the Kalman filter: some new results
title_fullStr BLUE, BLUP and the Kalman filter: some new results
title_full_unstemmed BLUE, BLUP and the Kalman filter: some new results
title_short BLUE, BLUP and the Kalman filter: some new results
title_sort blue, blup and the kalman filter: some new results
topic BLUE–BLUP recursion
Best linear unbiased estimation (BLUE)
Kalman filter
Best linear unbiased prediction (BLUP)
Misclosures
Minimum mean squared error (MMSE)
url http://hdl.handle.net/20.500.11937/43062