# Equivariant Filter (EqF)

arXiv: https://arxiv.org/abs/2010.14666 · HTML: https://mlsanity.com/paper/2010.14666/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2020.

## Built on by (most cited first, 1 of 1)

- [Equivariant Filter for High Performance Image Tracking using an Event Camera](https://mlsanity.com/paper/2607.09103/) (2026)

## Abstract (arXiv)

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.