Low-rank Tensor Integration for Gaussian Filtering of Continuous Time Nonlinear Systems
Integration-based Gaussian filters such as un-scented, cubature, and Gauss-Hermite filters are effective ways to assimilate data and models within nonlinear systems. Traditionally, these filters have only been applicable for systems with a handful of states due to stability and scalability issues. I...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Electrical and Electronics Engineers (IEEE)
2021
|
| Online Access: | https://hdl.handle.net/1721.1/137861.2 |
| _version_ | 1811075031711612928 |
|---|---|
| author | Gorodetsky, Alex Arkady Karaman, Sertac Marzouk, Youssef M |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Gorodetsky, Alex Arkady Karaman, Sertac Marzouk, Youssef M |
| author_sort | Gorodetsky, Alex Arkady |
| collection | MIT |
| description | Integration-based Gaussian filters such as un-scented, cubature, and Gauss-Hermite filters are effective ways to assimilate data and models within nonlinear systems. Traditionally, these filters have only been applicable for systems with a handful of states due to stability and scalability issues. In this paper, we present a new integration method for scaling quadrature-based filters to higher dimensions. Our approach begins by decomposing the dynamics and observation models into separated, low-rank tensor formats. Once in low-rank tensor format, adaptive integration techniques may be used to efficiently propagate the mean and covariance of the distribution of the system state with computational complexity that is polynomial in dimension and rank. Simulation results are shown on nonlinear chaotic systems with 20 state variables. |
| first_indexed | 2024-09-23T09:59:22Z |
| format | Article |
| id | mit-1721.1/137861.2 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:59:22Z |
| publishDate | 2021 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/137861.22021-12-20T14:19:48Z Low-rank Tensor Integration for Gaussian Filtering of Continuous Time Nonlinear Systems Gorodetsky, Alex Arkady Karaman, Sertac Marzouk, Youssef M Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Integration-based Gaussian filters such as un-scented, cubature, and Gauss-Hermite filters are effective ways to assimilate data and models within nonlinear systems. Traditionally, these filters have only been applicable for systems with a handful of states due to stability and scalability issues. In this paper, we present a new integration method for scaling quadrature-based filters to higher dimensions. Our approach begins by decomposing the dynamics and observation models into separated, low-rank tensor formats. Once in low-rank tensor format, adaptive integration techniques may be used to efficiently propagate the mean and covariance of the distribution of the system state with computational complexity that is polynomial in dimension and rank. Simulation results are shown on nonlinear chaotic systems with 20 state variables. 2021-12-20T14:19:47Z 2021-11-09T13:34:04Z 2021-12-20T14:19:47Z 2017-12 2019-10-28T18:14:56Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/137861.2 Gorodetsky, Alex A., Karaman, Sertac and Marzouk, Youssef M. 2017. "Low-rank tensor integration for Gaussian filtering of continuous time nonlinear systems." en 10.1109/CDC.2017.8264064 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/octet-stream Institute of Electrical and Electronics Engineers (IEEE) Other repository |
| spellingShingle | Gorodetsky, Alex Arkady Karaman, Sertac Marzouk, Youssef M Low-rank Tensor Integration for Gaussian Filtering of Continuous Time Nonlinear Systems |
| title | Low-rank Tensor Integration for Gaussian Filtering of Continuous Time Nonlinear Systems |
| title_full | Low-rank Tensor Integration for Gaussian Filtering of Continuous Time Nonlinear Systems |
| title_fullStr | Low-rank Tensor Integration for Gaussian Filtering of Continuous Time Nonlinear Systems |
| title_full_unstemmed | Low-rank Tensor Integration for Gaussian Filtering of Continuous Time Nonlinear Systems |
| title_short | Low-rank Tensor Integration for Gaussian Filtering of Continuous Time Nonlinear Systems |
| title_sort | low rank tensor integration for gaussian filtering of continuous time nonlinear systems |
| url | https://hdl.handle.net/1721.1/137861.2 |
| work_keys_str_mv | AT gorodetskyalexarkady lowranktensorintegrationforgaussianfilteringofcontinuoustimenonlinearsystems AT karamansertac lowranktensorintegrationforgaussianfilteringofcontinuoustimenonlinearsystems AT marzoukyoussefm lowranktensorintegrationforgaussianfilteringofcontinuoustimenonlinearsystems |