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Hu, Xiao-Li
Publications (6 of 6) Show all publications
Hu, X.-L., Schön, T. & Ljung, L. (2009). Basic Convergence Results for Particle Filtering Methods: Theory for the Users. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Basic Convergence Results for Particle Filtering Methods: Theory for the Users
2009 (English)Report (Other academic)
Abstract [en]

This work extends our recent work on proving that the particle filter converge for unbounded function to a more general case. More specifically, we prove that the particle filter converge for unbounded functions in the sense of L p-convergence, for an arbitrary p greater than 1. Related to this, we also provide proofs for the case when the function we are estimating is bounded. In the process of deriving the main result we also established a new Rosenthal type inequality.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2009. p. 28
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2914
Keywords
Convergence, Particle filter, Nonlinear filtering, Dynamic systems
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-56208 (URN)LiTH-ISY-R-2914 (ISRN)
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-08-11Bibliographically approved
Hu, X.-L., Schön, T. & Ljung, L. (2008). A Basic Convergence Result for Particle Filtering. IEEE Transactions on Signal Processing, 56(4), 1337-1348
Open this publication in new window or tab >>A Basic Convergence Result for Particle Filtering
2008 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 56, no 4, p. 1337-1348Article in journal (Refereed) Published
Abstract [en]

The basic nonlinear filtering problem for dynamical systems is considered. Approximating the optimal filter estimate by particle filter methods has become perhaps the most common and useful method in recent years. Many variants of particle filters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still a clear-cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to infinity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result for a rather general class of unbounded functions. Furthermore, a general framework, including many of the particle filter algorithms as special cases, is given.

Keywords
Convergence of numerical methods, Nonlinear estimation, Particle filter, State estimation
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-11748 (URN)10.1109/TSP.2007.911295 (DOI)
Available from: 2008-05-07 Created: 2008-05-07 Last updated: 2017-12-13
Hu, X.-L. & Ljung, L. (2008). New Convergence Results for Least Squares Identification Algorithm. In: Proceedings of the 17th IFAC World Congress: . Paper presented at 17th IFAC World Congress, Seoul, South Korea, July, 2008 (pp. 5030-5035).
Open this publication in new window or tab >>New Convergence Results for Least Squares Identification Algorithm
2008 (English)In: Proceedings of the 17th IFAC World Congress, 2008, p. 5030-5035Conference paper, Published paper (Refereed)
Abstract [en]

The basic least squares method for identifying linear systems has been extensively studied. Conditions for convergence involve issues about noise assumptions and behavior of the sample covariance matrix of the regressors. Lai and Wei proved in 1982 convergence for essentially minimal conditions on the regression matrix: All eigenvalues must tend to infinity, and the logarithm of the largest eigenvalue must not tend to infinity faster than the smallest eigenvalue. In this contribution we revisit this classical result with respect to assumptions on the noise: How much unstructured disturbances can be allowed without affecting the convergence? The answer is that the norm of these disturbances must tend to infinity slower than the smallest eigenvalue of the regression matrix.

Keywords
System identification
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-44706 (URN)10.3182/20080706-5-KR-1001.00845 (DOI)77386 (Local ID)978-3-902661-00-5 (ISBN)77386 (Archive number)77386 (OAI)
Conference
17th IFAC World Congress, Seoul, South Korea, July, 2008
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-09-15
Hu, X.-L., Schön, T. & Ljung, L. (2007). A Basic Convergence Result for Particle Filtering. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>A Basic Convergence Result for Particle Filtering
2007 (English)Report (Other academic)
Abstract [en]

The basic nonlinear filtering problem for dynamical systems is considered. Approximating the optimal filter estimate by particle filter methods has become perhaps the most common and useful method in recent years. Many variants of particle filters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to infinity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result for a rather general class of unbounded functions. Furthermore, a general framework, including many of the particle filter algorithms as special cases, is given.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2007. p. 8
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2781
Keywords
Nonlinear filters, Particle filter, Convergence, Dynamic systems
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-56046 (URN)LiTH-ISY-R-2781 (ISRN)
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-08-12Bibliographically approved
Hu, X.-L., Schön, T. & Ljung, L. (2007). A Basic Convergence Result for Particle Filtering. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>A Basic Convergence Result for Particle Filtering
2007 (English)Report (Other academic)
Abstract [en]

The basic nonlinear filtering problem for dynamical systems is considered. Approximating the optimal filter estimate by particle filter methods has become perhaps the most common and useful method in recent years. Many variants of particle filters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to infinity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result for a rather general class of unbounded functions. Furthermore, a general framework, including many of the particle filter algorithms as special cases, is given.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2007. p. 13
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2824
Keywords
Nonlinear filters, Particle filter, Convergence, Dynamic systems
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-56140 (URN)LiTH-ISY-R-2824 (ISRN)
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-08-12Bibliographically approved
Hu, X.-L., Schön, T. & Ljung, L. (2007). A Robust Particle Filter for State Estimation - with Convergence Results. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>A Robust Particle Filter for State Estimation - with Convergence Results
2007 (English)Report (Other academic)
Abstract [en]

Particle filters are becoming increasingly important and useful for state estimation in nonlinear systems. Many filter versions have been suggested, and several results on convergence of filter properties have been reported. However, apparently a result on the convergence of the state estimate itself has been lacking. This contribution describes a general framework for particle filters for state estimation, as well as a robustified filter version. For this version a quite general convergence result is established. In particular, it is proved that the particle filter estimate convergences w.p.1 to the optimal estimate, as the number of particles tends to infinity.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2007. p. 8
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2822
Keywords
Nonlinear lters, particle lter, convergence, dynamic systems
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-56141 (URN)LiTH-ISY-R-2822 (ISRN)
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-10-08Bibliographically approved
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