A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter

Author(s)
Bonnabel, Silvere; Slotine, Jean-Jacques E.
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Abstract
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.
Date issued
2015-01
URI
http://hdl.handle.net/1721.1/97723
Department
Massachusetts Institute of Technology. Department of Mechanical Engineering; Massachusetts Institute of Technology. Nonlinear Systems Laboratory
Journal
IEEE Transactions on Automatic Control
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
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.
Version: Original manuscript
ISSN
0018-9286
1558-2523
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