Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows
© 1991-2012 IEEE. In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold learning technique, with a linear Kalman filte...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Institute of Electrical and Electronics Engineers (IEEE)
2021
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| Online Access: | https://hdl.handle.net/1721.1/135213 |
| _version_ | 1811070242617556992 |
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| author | Shnitzer, Tal Talmon, Ronen Slotine, Jean-Jacques |
| author2 | Massachusetts Institute of Technology. Nonlinear Systems Laboratory |
| author_facet | Massachusetts Institute of Technology. Nonlinear Systems Laboratory Shnitzer, Tal Talmon, Ronen Slotine, Jean-Jacques |
| author_sort | Shnitzer, Tal |
| collection | MIT |
| description | © 1991-2012 IEEE. In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold learning technique, with a linear Kalman filter and with concepts from Koopman operator theory. More concretely, using diffusion maps, we construct data-driven virtual state coordinates, which linearize the system model. Based on these coordinates, we devise a data-driven framework for state estimation using the Kalman filter. We demonstrate the strengths of our method with respect to both parametric and non-parametric algorithms in three tracking problems. In particular, applying the approach to actual recordings of hippocampal neural activity in rodents directly yields a representation of the position of the animals. We show that the proposed method outperforms competing non-parametric algorithms in the examined stochastic problem formulations. Additionally, we obtain results comparable to classical parametric algorithms, which, in contrast to our method, are equipped with model knowledge. |
| first_indexed | 2024-09-23T08:33:23Z |
| format | Article |
| id | mit-1721.1/135213 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:33:23Z |
| publishDate | 2021 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1352132023-09-26T19:58:13Z Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows Shnitzer, Tal Talmon, Ronen Slotine, Jean-Jacques Massachusetts Institute of Technology. Nonlinear Systems Laboratory Massachusetts Institute of Technology. Department of Mechanical Engineering © 1991-2012 IEEE. In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold learning technique, with a linear Kalman filter and with concepts from Koopman operator theory. More concretely, using diffusion maps, we construct data-driven virtual state coordinates, which linearize the system model. Based on these coordinates, we devise a data-driven framework for state estimation using the Kalman filter. We demonstrate the strengths of our method with respect to both parametric and non-parametric algorithms in three tracking problems. In particular, applying the approach to actual recordings of hippocampal neural activity in rodents directly yields a representation of the position of the animals. We show that the proposed method outperforms competing non-parametric algorithms in the examined stochastic problem formulations. Additionally, we obtain results comparable to classical parametric algorithms, which, in contrast to our method, are equipped with model knowledge. 2021-10-27T20:22:30Z 2021-10-27T20:22:30Z 2020 2020-08-07T15:48:59Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135213 en 10.1109/TSP.2020.2987750 IEEE Transactions on Signal Processing Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Shnitzer, Tal Talmon, Ronen Slotine, Jean-Jacques Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows |
| title | Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows |
| title_full | Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows |
| title_fullStr | Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows |
| title_full_unstemmed | Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows |
| title_short | Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows |
| title_sort | diffusion maps kalman filter for a class of systems with gradient flows |
| url | https://hdl.handle.net/1721.1/135213 |
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