| 1. |
- Hu, Xiao-Li, et al.
(author)
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A Basic Convergence Result for Particle Filtering
- 2007
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In: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems. - Linköping : Linköping University Electronic Press. - 9783902661289 ; , s. 288-293
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Conference paper (peer-reviewed)abstract
- 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.
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| 2. |
- Hu, Xiao-Li, et al.
(author)
-
A General Convergence Result for Particle Filtering
- 2011
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In: IEEE Transactions on Signal Processing. - Linköping : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 59:7, s. 3424-3429
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Journal article (peer-reviewed)abstract
- The particle filter has become an important tool in solving nonlinear filtering problems for dynamic systems. This correspondence extends our recent work, where we proved that the particle filter converges for unbounded functions, using L4-convergence. More specifically, the present contribution is that we prove that the particle filter converge for unbounded functions in the sense of Lp-convergence, for an arbitrary p ≥ 2.
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| 3. |
- Hu, Xiao-Li, et al.
(author)
-
A Robust Particle Filter for State Estimation - with Convergence Results
- 2007
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In: Proceedings of the 46th IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 9781424414987 - 9781424414970 ; , s. 312-317
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Conference paper (peer-reviewed)abstract
- 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.
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| 4. |
- Hu, Xiao-Li, et al.
(author)
-
A Basic Convergence Result for Particle Filtering
- 2008
-
In: IEEE Transactions on Signal Processing. - 1053-587X .- 1941-0476. ; 56:4, s. 1337-1348
-
Journal article (peer-reviewed)abstract
- 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.
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| 5. |
- Hu, Xiao-Li, et al.
(author)
-
Basic Convergence Results for Particle Filtering Methods: Theory for the Users
- 2009
-
Reports (other academic/artistic)abstract
- 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.
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| 6. |
- Hu, Xiao-Li, et al.
(author)
-
New Convergence Results for Least Squares Identification Algorithm
- 2009
-
Reports (other academic/artistic)abstract
- 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.
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| 7. |
- Hu, Xiao-Li, 1975-, et al.
(author)
-
New Convergence Results for Least Squares Identification Algorithm
- 2008
-
In: Proceedings of the 17th IFAC World Congress. - 9783902661005 ; , s. 5030-5035
-
Conference paper (peer-reviewed)abstract
- 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.
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