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Article: Proper orthogonal decomposition method to nonlinear filtering problems in medium-high dimension
Title | Proper orthogonal decomposition method to nonlinear filtering problems in medium-high dimension |
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Authors | |
Keywords | Nonlinear filtering problems Duncan- Mortensen-Zakai equation Proper orthogonal decomposition Real-time algorithm |
Issue Date | 2020 |
Publisher | Institute of Electrical and Electronics Engineers. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9 |
Citation | IEEE Transactions on Automatic Control, 2020, v. 65 n. 4, p. 1613-1624 How to Cite? |
Abstract | In this paper, we investigate the proper orthogonal decomposition (POD) method to numerically solve the forward Kolmogorov equation (FKE). Our method aims to explore the low-dimensional structures in the solution space of the FKE and to develop efficient numerical methods. As an important application and our primary motivation to study the POD method to FKE, we solve the nonlinear filtering (NLF) problems with a real-time algorithm proposed in cite{YauYau:2008} combined with the POD method. This algorithm is referred as POD algorithm in this paper. Our POD algorithm consists of off-line and on-line stages. In the off-line stage, we construct a small number of POD basis functions that capture the dynamics of the system and compute propagation of the POD basis functions under the FKE operator. In the on-line stage, we synchronize the coming observations in a real-time manner. Its convergence analysis has also been discussed. Some numerical experiments of the NLF problems are performed to illustrate the feasibility of our algorithm and to verify the convergence rate. Our numerical results show that the POD algorithm provides considerable computational savings over existing numerical |
Persistent Identifier | http://hdl.handle.net/10722/272215 |
ISSN | 2023 Impact Factor: 6.2 2023 SCImago Journal Rankings: 4.501 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Wang, Z | - |
dc.contributor.author | Luo, X | - |
dc.contributor.author | Yau, SST | - |
dc.contributor.author | Zhang, Z | - |
dc.date.accessioned | 2019-07-20T10:37:55Z | - |
dc.date.available | 2019-07-20T10:37:55Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | IEEE Transactions on Automatic Control, 2020, v. 65 n. 4, p. 1613-1624 | - |
dc.identifier.issn | 0018-9286 | - |
dc.identifier.uri | http://hdl.handle.net/10722/272215 | - |
dc.description.abstract | In this paper, we investigate the proper orthogonal decomposition (POD) method to numerically solve the forward Kolmogorov equation (FKE). Our method aims to explore the low-dimensional structures in the solution space of the FKE and to develop efficient numerical methods. As an important application and our primary motivation to study the POD method to FKE, we solve the nonlinear filtering (NLF) problems with a real-time algorithm proposed in cite{YauYau:2008} combined with the POD method. This algorithm is referred as POD algorithm in this paper. Our POD algorithm consists of off-line and on-line stages. In the off-line stage, we construct a small number of POD basis functions that capture the dynamics of the system and compute propagation of the POD basis functions under the FKE operator. In the on-line stage, we synchronize the coming observations in a real-time manner. Its convergence analysis has also been discussed. Some numerical experiments of the NLF problems are performed to illustrate the feasibility of our algorithm and to verify the convergence rate. Our numerical results show that the POD algorithm provides considerable computational savings over existing numerical | - |
dc.language | eng | - |
dc.publisher | Institute of Electrical and Electronics Engineers. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9 | - |
dc.relation.ispartof | IEEE Transactions on Automatic Control | - |
dc.subject | Nonlinear filtering problems | - |
dc.subject | Duncan- Mortensen-Zakai equation | - |
dc.subject | Proper orthogonal decomposition | - |
dc.subject | Real-time algorithm | - |
dc.title | Proper orthogonal decomposition method to nonlinear filtering problems in medium-high dimension | - |
dc.type | Article | - |
dc.identifier.email | Zhang, Z: zhangzw@hku.hk | - |
dc.identifier.authority | Zhang, Z=rp02087 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1109/TAC.2019.2927322 | - |
dc.identifier.scopus | eid_2-s2.0-85082779441 | - |
dc.identifier.hkuros | 298667 | - |
dc.identifier.volume | 65 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 1613 | - |
dc.identifier.epage | 1624 | - |
dc.identifier.isi | WOS:000522918700018 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0018-9286 | - |