Subspace System Identification of the Kalman Filter
Some proofs concerning a subspace identification algorithm are presented. It is proved that the Kalman filter gain and the noise innovations process can be identified directly from known input and output data without explicitly solving the Riccati equation. Furthermore, it is in general and for colo...
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| Format: | Article |
| Language: | English |
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Norwegian Society of Automatic Control
2003-07-01
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| Series: | Modeling, Identification and Control |
| Subjects: | |
| Online Access: | http://www.mic-journal.no/PDF/2003/MIC-2003-3-1.pdf |
| _version_ | 1818835380968882176 |
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| author | David Di Ruscio |
| author_facet | David Di Ruscio |
| author_sort | David Di Ruscio |
| collection | DOAJ |
| description | Some proofs concerning a subspace identification algorithm are presented. It is proved that the Kalman filter gain and the noise innovations process can be identified directly from known input and output data without explicitly solving the Riccati equation. Furthermore, it is in general and for colored inputs, proved that the subspace identification of the states only is possible if the deterministic part of the system is known or identified beforehand. However, if the inputs are white, then, it is proved that the states can be identified directly. Some alternative projection matrices which can be used to compute the extended observability matrix directly from the data are presented. Furthermore, an efficient method for computing the deterministic part of the system is presented. The closed loop subspace identification problem is also addressed and it is shown that this problem is solved and unbiased estimates are obtained by simply including a filter in the feedback. Furthermore, an algorithm for consistent closed loop subspace estimation is presented. This algorithm is using the controller parameters in order to overcome the bias problem. |
| first_indexed | 2024-12-19T02:49:48Z |
| format | Article |
| id | doaj.art-631234d036f94972bec7e1a49e461cc2 |
| institution | Directory Open Access Journal |
| issn | 0332-7353 1890-1328 |
| language | English |
| last_indexed | 2024-12-19T02:49:48Z |
| publishDate | 2003-07-01 |
| publisher | Norwegian Society of Automatic Control |
| record_format | Article |
| series | Modeling, Identification and Control |
| spelling | doaj.art-631234d036f94972bec7e1a49e461cc22022-12-21T20:38:41ZengNorwegian Society of Automatic ControlModeling, Identification and Control0332-73531890-13282003-07-0124312515710.4173/mic.2003.3.1Subspace System Identification of the Kalman FilterDavid Di RuscioSome proofs concerning a subspace identification algorithm are presented. It is proved that the Kalman filter gain and the noise innovations process can be identified directly from known input and output data without explicitly solving the Riccati equation. Furthermore, it is in general and for colored inputs, proved that the subspace identification of the states only is possible if the deterministic part of the system is known or identified beforehand. However, if the inputs are white, then, it is proved that the states can be identified directly. Some alternative projection matrices which can be used to compute the extended observability matrix directly from the data are presented. Furthermore, an efficient method for computing the deterministic part of the system is presented. The closed loop subspace identification problem is also addressed and it is shown that this problem is solved and unbiased estimates are obtained by simply including a filter in the feedback. Furthermore, an algorithm for consistent closed loop subspace estimation is presented. This algorithm is using the controller parameters in order to overcome the bias problem.http://www.mic-journal.no/PDF/2003/MIC-2003-3-1.pdfIdentification methodsSubspace methods Stochastic systemsSampled data systems |
| spellingShingle | David Di Ruscio Subspace System Identification of the Kalman Filter Modeling, Identification and Control Identification methods Subspace methods Stochastic systems Sampled data systems |
| title | Subspace System Identification of the Kalman Filter |
| title_full | Subspace System Identification of the Kalman Filter |
| title_fullStr | Subspace System Identification of the Kalman Filter |
| title_full_unstemmed | Subspace System Identification of the Kalman Filter |
| title_short | Subspace System Identification of the Kalman Filter |
| title_sort | subspace system identification of the kalman filter |
| topic | Identification methods Subspace methods Stochastic systems Sampled data systems |
| url | http://www.mic-journal.no/PDF/2003/MIC-2003-3-1.pdf |
| work_keys_str_mv | AT daviddiruscio subspacesystemidentificationofthekalmanfilter |