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

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 guara...

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Bibliographic Details
Main Authors: Bonnabel, Silvere (Author), Slotine, Jean-Jacques E. (Contributor)
Other Authors: Massachusetts Institute of Technology. Department of Mechanical Engineering (Contributor), Massachusetts Institute of Technology. Nonlinear Systems Laboratory (Contributor)
Format: Article
Language:English
Published: Institute of Electrical and Electronics Engineers (IEEE), 2015-07-13T14:42:08Z.
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Summary: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.

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