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...
| Main Authors: | , |
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| Format: | Journal Article |
| Published: |
Springer - Verlag
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/43062 |
| _version_ | 1848756586935222272 |
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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. |
| first_indexed | 2025-11-14T09:14:34Z |
| format | Journal Article |
| id | curtin-20.500.11937-43062 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:14:34Z |
| publishDate | 2013 |
| publisher | Springer - Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |