2020/10/27 by Pieter van Goor, van Goor, Pieter, Tarek Hamel +3 · 1 citation
Engineering · Computer Science · #Inertial Sensor and Navigation #Target Tracking and Data Fusion in Sensor Networks #Adaptive Control of Nonlinear Systems
paper · pdf · doi:10.48550/arxiv.2010.14666
The kinematics of many systems encountered in robotics, mechatronics, and avionics are naturally posed on homogeneous spaces; that is, their state lies in a smooth manifold equipped with a transitive Lie group symmetry. This paper proposes a novel filter, the Equivariant Filter (EqF), by posing the observer state on the symmetry group, linearising global error dynamics derived from the equivariance of the system, and applying extended Kalman filter design principles. We show that equivariance of the system output can be exploited to reduce linearisation error and improve filter performance. Simulation experiments of an example application show that the EqF significantly outperforms the extended Kalman filter and that the reduced linearisation error leads to a clear improvement in performance.