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.

The majority of commercial and open-source autopilot software for uncrewed aerial vehicles rely on the tried and tested extended Kalman filter (EKF) to provide the state estimation solution for the inertial navigation system (INS). While modern implementations achieve remarkable robustness, it is often due to the careful implementation of exception code for a multitude of corner cases along with significant skilled tuning effort. In this paper, we use the data wealth of the ArduPilot community to identify and highlight the most common real-world challenges in INS state estimation, including sensor self-calibration, robustness in static conditions, global navigation satellite system (GNSS) outliers and shifts, and robustness to faulty inertial measurement units (IMUs). We propose a novel equivariant filter (EqF) formulation for the INS solution that exploits a Semi-Direct-Bias symmetry group for multi-sensor fusion with self-calibration capabilities and incorporates equivariant velocity-type measurements. We augment the filter with a simple innovation-covariance inflation strategy that seamlessly handles GNSS outliers and shifts without requiring coding of a whole set of exception cases. We use real-world data from the Ardupilot community to demonstrate the performance of the proposed filter on known cases where existing filters fail without careful exception handling or case-specific tuning and benchmark against the ArduPilot’s EKF3, the most sophisticated EKF implementation currently available.

Event-based cameras are popular for tracking fast-moving objects due to their high temporal resolution, low latency, and high dynamic range. In this article, we propose a novel algorithm for tracking event blobs using raw eventsasynchronouslyin real time. We introduce the concept of anevent blobas a spatio-temporal likelihood of event occurrence where the conditional spatial likelihood is blob-like. Many real-world objects, such as car headlights or any quickly moving foreground objects, generate event blob data. The proposed algorithm uses a nearest neighbor classifier with a dynamic threshold criteria for data association coupled with an extended Kalman filter to track the event blob state. Our algorithm achieves highly accurate blob tracking, velocity estimation, and shape estimation even under challenging lighting conditions and high-speed motions ($>$11 000 pixels/s). The microsecond time resolution achieved means that the filter output can be used to derive secondary information, such as time-to-contact or range estimation, that will enable applications to real-world problems, such as collision avoidance, in autonomous driving.

Visual-inertial odometry (VIO) is the problem of estimating a robot's trajectory by combining information from an inertial measurement unit (IMU) and a camera and is of great interest to the robotics community. This article develops a novel Lie group symmetry for the VIO problem and applies the recently proposed equivariant filter. The proposed symmetry is compatible with the invariance of the VIO reference frame, leading to improved filter consistency. The bias-free IMU dynamics are group-affine, ensuring that filter linearization errors depend only on the bias estimation error and measurement noise. Furthermore, visual measurements are equivariant with respect to the symmetry, enabling the application of the higher order equivariant output approximation to reduce the approximation error in the filter update equation. As a result, the equivariant filter based on this Lie group is a consistent estimator for VIO with lower linearization error in the propagation of state dynamics and a higher order equivariant output approximation than standard formulations. Experimental results on the popularEuRoCandUZH FPVdatasets demonstrate that the proposed system outperforms other state-of-the-art VIO algorithms in terms of both speed and accuracy.

Visual Inertial Odometry (VIO) is of great interest due the ubiquity of devices equipped with both a monocular camera and Inertial Measurement Unit (IMU). Methods based on the extended Kalman Filter remain popular in VIO due to their low memory requirements, CPU usage, and processing time when compared to optimisation-based methods. In this paper, we analyse the VIO problem from a geometric perspective and propose a novel formulation on a smooth quotient manifold where the equivalence relationship is the well-known invariance of VIO to choice of reference frame. We propose a novel Lie group that acts transitively on this manifold and is compatible with the visual measurements. This structure allows for the application of Equivariant Filter (EqF) design leading to a novel filter for the VIO problem. Combined with a very simple vision processing front-end, the proposed filter demonstrates state-of-the-art performance on the EuRoC dataset compared to other EKF-based VIO algorithms.