A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter
The contraction properties of the extended Kalman filter, viewed as a deterministic observer for nonlinear systems, are analyzed. The approach relies on the study of an auxiliary “virtual” dynamical system. Some conditions under which exponential convergence of the state error can be guaranteed are...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Institute of Electrical and Electronics Engineers (IEEE)
2015
|
| Online Access: | http://hdl.handle.net/1721.1/97723 https://orcid.org/0000-0002-7161-7812 |
| _version_ | 1826200448955056128 |
|---|---|
| author | Bonnabel, Silvere Slotine, Jean-Jacques E. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Bonnabel, Silvere Slotine, Jean-Jacques E. |
| author_sort | Bonnabel, Silvere |
| collection | MIT |
| description | The contraction properties of the extended Kalman filter, viewed as a deterministic observer for nonlinear systems, are analyzed. The approach relies on the study of an auxiliary “virtual” dynamical system. Some conditions under which exponential convergence of the state error can be guaranteed are derived. Moreover, contraction provides a simple formalism to study some robustness properties of the filter, especially with respect to measurement errors, as illustrated by a simplified inertial navigation example. This technical note sheds another light on the theoretical properties of this popular observer. |
| first_indexed | 2024-09-23T11:36:38Z |
| format | Article |
| id | mit-1721.1/97723 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:36:38Z |
| publishDate | 2015 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/977232022-10-01T04:46:21Z A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter Bonnabel, Silvere Slotine, Jean-Jacques E. Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Nonlinear Systems Laboratory Slotine, Jean-Jacques E. The contraction properties of the extended Kalman filter, viewed as a deterministic observer for nonlinear systems, are analyzed. The approach relies on the study of an auxiliary “virtual” dynamical system. Some conditions under which exponential convergence of the state error can be guaranteed are derived. Moreover, contraction provides a simple formalism to study some robustness properties of the filter, especially with respect to measurement errors, as illustrated by a simplified inertial navigation example. This technical note sheds another light on the theoretical properties of this popular observer. 2015-07-13T14:42:08Z 2015-07-13T14:42:08Z 2015-01 2014-03 Article http://purl.org/eprint/type/JournalArticle 0018-9286 1558-2523 http://hdl.handle.net/1721.1/97723 Bonnabel, Silvere, and Jean-Jacques Slotine. “A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter.” IEEE Trans. Automat. Contr. 60, no. 2 (February 2015): 565–569. https://orcid.org/0000-0002-7161-7812 en_US http://dx.doi.org/10.1109/TAC.2014.2336991 IEEE Transactions on Automatic Control 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 | Bonnabel, Silvere Slotine, Jean-Jacques E. A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter |
| title | A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter |
| title_full | A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter |
| title_fullStr | A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter |
| title_full_unstemmed | A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter |
| title_short | A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter |
| title_sort | contraction theory based analysis of the stability of the deterministic extended kalman filter |
| url | http://hdl.handle.net/1721.1/97723 https://orcid.org/0000-0002-7161-7812 |
| work_keys_str_mv | AT bonnabelsilvere acontractiontheorybasedanalysisofthestabilityofthedeterministicextendedkalmanfilter AT slotinejeanjacquese acontractiontheorybasedanalysisofthestabilityofthedeterministicextendedkalmanfilter AT bonnabelsilvere contractiontheorybasedanalysisofthestabilityofthedeterministicextendedkalmanfilter AT slotinejeanjacquese contractiontheorybasedanalysisofthestabilityofthedeterministicextendedkalmanfilter |