Equivariant Filter (EqF)

Abstract

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.

20 pages, 3 figures, published in IEEE TAC

References in corpus (8)

• Quaternion kinematics for the error-state Kalman filter
• Symmetry-preserving Observers
• Non-linear Symmetry-preserving Observer on Lie Groups
• An EKF-SLAM algorithm with consistency properties
• Observers for invariant systems on Lie groups with biased input measurements and homogeneous outputs
• Observer Design for Nonlinear Systems with Equivariance
• Constructive Observer Design for Visual Simultaneous Localisation and Mapping
• Nonlinear Attitude Filtering: A Comparison Study

Cited by in corpus (8)

• EqVIO: An Equivariant Filter for Visual Inertial Odometry
• InGVIO: A Consistent Invariant Filter for Fast and High-Accuracy GNSS-Visual-Inertial Odometry
• T-ESKF: Transformed Error-State Kalman Filter for Consistent Visual-Inertial Navigation
• Equivariant IMU Preintegration with Biases: a Galilean Group Approach
• A Symmetry-Preserving Reduced-Order Observer
• On the Existence of Linear Observed Systems on Manifolds with Connection
• Equivariant Filter Design for Range-only SLAM
• Equivariant Filter for Relative Attitude and Target's Angular Velocity Estimation