Sampling-based algorithm for filtering using Markov chain approximations
In this paper, the filtering problem for a large class of continuous-time, continuous-state stochastic dynamical systems is considered. Inspired by recent advances in asymptotically-optimal sampling-based motion planning algorithms, such as the PRM* and the RRT*, an incremental sampling-based algori...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2013
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| Online Access: | http://hdl.handle.net/1721.1/81471 https://orcid.org/0000-0002-0505-1400 https://orcid.org/0000-0002-2225-7275 |
| _version_ | 1826190212387045376 |
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| author | Karaman, Sertac Frazzoli, Emilio Chaudhari, Pratik Anil |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Karaman, Sertac Frazzoli, Emilio Chaudhari, Pratik Anil |
| author_sort | Karaman, Sertac |
| collection | MIT |
| description | In this paper, the filtering problem for a large class of continuous-time, continuous-state stochastic dynamical systems is considered. Inspired by recent advances in asymptotically-optimal sampling-based motion planning algorithms, such as the PRM* and the RRT*, an incremental sampling-based algorithm is proposed. Using incremental sampling, this approach constructs a sequence of Markov chain approximations, and solves the filtering problem, in an incremental manner, on these discrete approximations. It is shown that the trajectories of the Markov chain approximations converge in distribution to the trajectories of the original stochastic system; moreover, the optimal filter calculated on these Markov chains converges to the optimal continuous-time nonlinear filter. The convergence results are verified in a number of simulation examples. |
| first_indexed | 2024-09-23T08:36:47Z |
| format | Article |
| id | mit-1721.1/81471 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:36:47Z |
| publishDate | 2013 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/814712022-09-30T09:56:09Z Sampling-based algorithm for filtering using Markov chain approximations Karaman, Sertac Frazzoli, Emilio Chaudhari, Pratik Anil Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Chaudhari, Pratik Anil Karaman, Sertac Frazzoli, Emilio In this paper, the filtering problem for a large class of continuous-time, continuous-state stochastic dynamical systems is considered. Inspired by recent advances in asymptotically-optimal sampling-based motion planning algorithms, such as the PRM* and the RRT*, an incremental sampling-based algorithm is proposed. Using incremental sampling, this approach constructs a sequence of Markov chain approximations, and solves the filtering problem, in an incremental manner, on these discrete approximations. It is shown that the trajectories of the Markov chain approximations converge in distribution to the trajectories of the original stochastic system; moreover, the optimal filter calculated on these Markov chains converges to the optimal continuous-time nonlinear filter. The convergence results are verified in a number of simulation examples. United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-11-1-0046) 2013-10-23T12:09:43Z 2013-10-23T12:09:43Z 2012-12 Article http://purl.org/eprint/type/ConferencePaper 978-1-4673-2066-5 978-1-4673-2065-8 978-1-4673-2063-4 978-1-4673-2064-1 http://hdl.handle.net/1721.1/81471 Chaudhari, Pratik, Sertac Karaman, and Emilio Frazzoli. “Sampling-based algorithm for filtering using Markov chain approximations.” In 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 5972-5978. Institute of Electrical and Electronics Engineers, 2012. https://orcid.org/0000-0002-0505-1400 https://orcid.org/0000-0002-2225-7275 en_US http://dx.doi.org/10.1109/CDC.2012.6426014 Proceedings of the 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) MIT web domain |
| spellingShingle | Karaman, Sertac Frazzoli, Emilio Chaudhari, Pratik Anil Sampling-based algorithm for filtering using Markov chain approximations |
| title | Sampling-based algorithm for filtering using Markov chain approximations |
| title_full | Sampling-based algorithm for filtering using Markov chain approximations |
| title_fullStr | Sampling-based algorithm for filtering using Markov chain approximations |
| title_full_unstemmed | Sampling-based algorithm for filtering using Markov chain approximations |
| title_short | Sampling-based algorithm for filtering using Markov chain approximations |
| title_sort | sampling based algorithm for filtering using markov chain approximations |
| url | http://hdl.handle.net/1721.1/81471 https://orcid.org/0000-0002-0505-1400 https://orcid.org/0000-0002-2225-7275 |
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