Ultra-wideband (UWB) has gained increasing interest for providing real-time positioning to robots in GPS-denied environments. For a robot to act on this information, it also requires its heading. This is, however, not provided by UWB. To overcome this, either multiple tags are used to create a local reference frame connected to the robot or a single tag is combined with ego-motion estimation from odometry or Inertial Measurement Unit (IMU) measurements. Both odometry and the IMU suffer from drift, and it is common to use a magnetometer to correct the drift on the heading; however, magnetometers tend to become unreliable in typical GPS-denied environments. To overcome this, a lightweight particle filter was designed to run in real time. The particle filter corrects the ego-motion heading and location drift using the UWB measurements over a moving horizon time frame. The algorithm was evaluated offline using data sets collected from a ground robot that contains line-of-sight (LOS) and non-line-of-sight conditions. An RMSE of 13 cm and 0.12 (rad) was achieved with four anchors in the LOS condition. It is also shown that it can be used to provide the robot with real-time position and heading information for the robot to act on it in LOS conditions, and it is shown to be robust in both experimental conditions.

Real-time relative pose (RP) estimation is a cornerstone for effective multi-agent collaboration. When conventional global positioning infrastructure such as GPS is unavailable, the use of Ultra-Wideband (UWB) technology on each agent provides a practical means to measure inter-agent range. Due to UWB's precise range measurements and robust communication capabilities, external hardware installations are not needed. However, when only a single UWB device per agent is used, the relative pose between the agents can be unobservable, resulting in a complex solution space with multiple possible RPs. This paper proposes a novel method based on an Unscented Particle Filter (UPF) that fuses single UWB ranges with visual-inertial odometry (VIO). The proposed decentralized method solves the multi-modal solution in 3D (4-DoF) for the RP when it is unobservable. Moreover, a pseudo-state is introduced to correct the rotational drift of the agents. Through simulations and experiments involving two robots, the proposed solution was shown to be competitive and less computationally expensive than state-of-the-art algorithms. Additionally, the proposed solution provides all possible relative poses from the first measurement. The code and link to the video are available https://github.com/y2d2/UPF_RPE .