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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Journal ArticleDOI
Precise and robust sideslip angle estimation based on INS/GNSS integration using invariant extended Kalman filter
TL;DR: In this paper , an innovative vehicle kinematic-based side-lip angle estimation method is proposed based on multi-sensor fusion, which fuses the information of inertial measurement unit, global navigation satellite system (GNSS), and onboard sensors to continuously estimate the attitude and velocity of the vehicle and thus obtain the sideslip angle.
Journal ArticleDOI
The Geometry of Navigation Problems
TL;DR: In this article , the invariant extended Kalman filter (IEKF) is applied to a large class of systems encompassing most problems involving a navigating vehicle encountered in practice and a methodology that systematically provides a group structure for the state space, including vectors of the body frame such as biases.
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Iterative Unbiased Conversion Measurement Kalman Filter with Interactive Multi-model Algorithm for Target Tracking
TL;DR: An interactive multi-model (IMM) based on iterative unbiased conversion measurement Kalman filter (IUCMKF) is proposed, which can attain a more accurate state of the target being tracked and the covariance estimation.
Book ChapterDOI
A reduced parallel transport equation on Lie Groups with a left-invariant metric
Nicolas Guigui,Xavier Pennec +1 more
TL;DR: In this article, the authors present a derivation of the parallel transport equation expressed in the Lie algebra of a Lie group endowed with a left-invariant metric, exemplified on the group of rigid body motions SE(3), using basic numerical integration schemes.
Journal ArticleDOI
Observer-based Controller for VTOL-UAVs Tracking using Direct Vision-Aided Inertial Navigation Measurements
TL;DR: In this article , an observer-based controller for a UAV is proposed to estimate the attitude, angular velocity, position, and linear velocity of the UAV in 6 degrees of freedom (DoF).
References
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Journal ArticleDOI
Kalman Filtering for Spacecraft Attitude Estimation
TL;DR: In this article, the authors present a review of the methods of Kalman filtering in attitude estimation and their development over the last two decades, focusing on three-axis gyros and attitude sensors.
Proceedings ArticleDOI
Complementary filter design on the special orthogonal group SO(3)
TL;DR: In this article, two different non-linear complementary filters are proposed: Direct complementary filter and Passive nonlinear complementary filter, which evolve explicity on the special orthogonal group SO(3) and can be expressed in quaternion form for easy implementation.
Journal ArticleDOI
Convergence analysis of the extended Kalman filter used as an observer for nonlinear deterministic discrete-time systems
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.
Journal ArticleDOI
Symmetry-Preserving Observers
TL;DR: Using the theory of invariant observers, i.e, symmetry-preserving observers, three non-linear observers are built for three examples of engineering interest: a non-holonomic car, a chemical reactor, and an inertial navigation system.