Equivariant Filter Design for Range-Only SLAM

Range-only Simultaneous Localisation and Mapping (RO-SLAM) is of interest due to its practical applications in ultra-wideband (UWB) and Bluetooth Low Energy (BLE) localisation in terrestrial and aerial applications and acoustic beacon localisation in submarine applications. In this work, we consider a mobile robot equipped with an inertial measurement unit (IMU) and a range sensor that measures distances to a collection of fixed landmarks. We derive an equivariant filter (EqF) for the RO-SLAM problem based on a symmetry Lie group that is compatible with the range measurements. The proposed filter does not require bootstrapping or initialisation of landmark positions, and demonstrates robustness to the noprior situation. The filter is demonstrated on a real-world dataset, and it is shown to significantly outperform a state-of-the-art EKF alternative in terms of both accuracy and robustness.