The Invariant Extended Kalman Filter as a Stable Observer
Axel Barrau,Silvere Bonnabel +1 more
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In this article, the authors analyzed the convergence aspects of the invariant extended Kalman filter (IEKF) when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations.Abstract:
We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie groups is that the estimation error is autonomous. In this paper we first generalize this result by characterizing the (much broader) class of systems for which this property holds. For those systems, the Lie logarithm of the error turns out to obey a linear differential equation. Then, we leverage this “log-linear” property of the error evolution, to prove for those systems the local stability of the IEKF around any trajectory, under the standard conditions of the linear case. One mobile robotics example and one inertial navigation example illustrate the interest of the approach. Simulations evidence the fact that the EKF is capable of diverging in some challenging situations, where the IEKF with identical tuning keeps converging.read more
Citations
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References
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TL;DR: Convergence analysis of the extended Kalman filter (EKF), when used as an observer for nonlinear deterministic discrete-time systems, is presented and it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified EKF significantly.
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