Invariant filtering for wheeled vehicle localization with unknown wheel radius and unknown GNSS lever arm

TL;DR

This paper introduces an invariant extended Kalman filter for wheeled vehicle localization that effectively handles unknown wheel radius and GNSS lever arm, enhancing robustness and applicability in challenging conditions.

Contribution

It adapts invariant Kalman filtering to a new problem setting with unknown parameters, extending its application scope for vehicle localization.

Findings

The invariant filter performs well in simulations.

The approach yields autonomous error equations.

It handles unknown wheel radius and GNSS lever arm effectively.

Abstract

We consider the problem of observer design for a nonholonomic car (more generally a wheeled robot) equipped with wheel speeds with unknown wheel radius, and whose position is measured via a GNSS antenna placed at an unknown position in the car. In a tutorial and unified exposition, we recall the recent theory of two-frame systems within the field of invariant Kalman filtering. We then show how to adapt it geometrically to address the considered problem, although it seems at first sight out of its scope. This yields an invariant extended Kalman filter having autonomous error equations, and state-independent Jacobians, which is shown to work remarkably well in simulations. The proposed novel construction thus extends the application scope of invariant filtering.