| 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. |
- Gedon, Daniel, 1994-, et al.
(author)
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Deep State Space Models for Nonlinear System Identification
- 2021
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In: IFAC PapersOnLine. - : Elsevier. - 2405-8963. ; , s. 481-486
-
Conference paper (peer-reviewed)abstract
- Deep state space models (SSMs) are an actively researched model class for temporal models developed in the deep learning community which have a close connection to classic SSMs. The use of deep SSMs as a black-box identification model can describe a wide range of dynamics due to the flexibility of deep neural networks. Additionally, the probabilistic nature of the model class allows the uncertainty of the system to be modelled. In this work a deep SSM class and its parameter learning algorithm are explained in an effort to extend the toolbox of nonlinear identification methods with a deep learning based method. Six recent deep SSMs are evaluated in a first unified implementation on nonlinear system identification benchmarks.
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| 3. |
- Gerdin, Markus, 1977-, et al.
(author)
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On Parameter and State Estimation for Linear Differential-Algebraic Equations
- 2007
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In: Automatica. - Linköping : Elsevier. - 0005-1098 .- 1873-2836. ; 43:3, s. 416-425
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Journal article (peer-reviewed)abstract
- The current demand for more complex models has initiated a shift away from state-space models towards models described by differential-algebraic equations (DAEs). These models arise as the natural product of object-oriented modeling languages, such as Modelica. However, the mathematics of DAEs is somewhat more involved than the standard state-space theory. The aim of this work is to present a well-posed description of a linear stochastic differential-algebraic equation and more importantly explain how well-posed estimation problems can be formed. We will consider both the system identification problem and the state estimation problem. Besides providing the necessary theory we will also explain how the procedures can be implemented by means of efficient numerical methods.
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| 4. |
- 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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| 5. |
- 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
-
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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| 6. |
- Ljung, Lennart, et al.
(author)
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Deep Learning and System Identification
- 2020
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In: IFAC Papersonline. - : Elsevier BV. - 2405-8963. ; , s. 1175-1181
-
Conference paper (peer-reviewed)abstract
- Deep learning is a topic of considerable interest today. Since it deals with estimating - or learning - models, there are connections to the area of System Identification developed in the Automatic Control community. Such connections are explored and exploited in this contribution. It is stressed that common deep nets such as feedforward and cascadeforward nets are nonlinear ARX (NARX) models, and can thus be easily incorporated in System Identification code and practice. The case of LSTM nets is an example of NonLinear State-Space (NLSS) models.
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| 7. |
- Chen, Tianshi, et al.
(author)
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Decentralization of Particle Filters Using Arbitrary State Decomposition
- 2010
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In: Proceedings of the 49th IEEE Conference on Decision and Control. - 9781424477456 ; , s. 7383-7388
-
Conference paper (peer-reviewed)abstract
- In this paper, a new particle filter (PF) which we refer to as the decentralized PF (DPF) is proposed. By first decomposing the state into two parts, the DPF splits the filtering problem into two nested sub-problems and then handles the two nested sub-problems using PFs. The DPF has an advantage over the regular PF that the DPF can increase the level of parallelism of the PF. In particular, part of the resampling in the DPF bears a parallel structure and thus can be implemented in parallel. The parallel structure of the DPF is created by decomposing the state space, differing from the parallel structure of the distributed PFs which is created by dividing the sample space. This difference results in a couple of unique features of the DPF in contrast with the existing distributed PFs. Simulation results from a numerical example indicates that the DPF has a potential to achieve the same level of performance as the regular PF, in a shorter execution time.
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| 8. |
- Chen, Tianshi, et al.
(author)
-
Decentralized Particle Filter with Arbitrary State Decomposition
- 2011
-
In: IEEE Transactions on Signal Processing. - : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 59:2, s. 465-478
-
Journal article (peer-reviewed)abstract
- In this paper, a new particle filter (PF) which we refer to as the decentralized PF (DPF) is proposed. By first decomposing the state into two parts, the DPF splits the filtering problem into two nested subproblems and then handles the two nested subproblems using PFs. The DPF has the advantage over the regular PF that the DPF can increase the level of parallelism of the PF. In particular, part of the resampling in the DPF bears a parallel structure and can thus be implemented in parallel. The parallel structure of the DPF is created by decomposing the state space, differing from the parallel structure of the distributed PFs which is created by dividing the sample space. This difference results in a couple of unique features of the DPF in contrast with the existing distributed PFs. Simulation results of two examples indicate that the DPF has a potential to achieve in a shorter execution time the same level of performance as the regular PF.
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| 9. |
- 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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| 10. |
- Hu, Xiao-Li, et al.
(author)
-
Basic Convergence Results for Particle Filtering Methods: Theory for the Users
- 2009
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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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