Multi-robot systems must have the ability to accurately estimate relative states between robots in order to perform collaborative tasks, possibly with no external aiding. Three-dimensional relative pose estimation using range measurements oftentimes suffers from a finite number of non-unique solutions, or ambiguities. This paper: 1) identifies and accurately estimates all possible ambiguities in 2D; 2) treats them as components of a Gaussian mixture model; and 3) presents a computationally-efficient estimator, in the form of a Gaussian-sum filter (GSF), to realize range-based relative pose estimation in an infrastructure-free, 3D, setup. This estimator is evaluated in simulation and experiment and is shown to avoid divergence to local minima induced by the ambiguous poses. Furthermore, the proposed GSF outperforms an extended Kalman filter, demonstrates similar performance to the computationally-demanding particle filter, and is shown to be consistent.

This dataset contains multiple trajectories of a custom sensor rig inside a motion capture (mocap) arena. Attached to the sensor rig are a stereo camera, providing image streams and inertial measurement unit (IMU) data, and one or two ultra-wideband (UWB) tags, providing distance measurements to up to 8 fixed and known UWB anchors. Also fixed in the mocap arena are 55 Apriltag [2] landmarks of known position, which are detected online by the stereo camera. A depiction of the experimental setup can be found in Figure 1. A compact version of the dataset can be found on Github and is the recommended starting point for using the dataset. It contains all pre-processed csv files of the data, as well as some convenience functions for reading the data. If required, the full dataset can be found on Google Drive. In addition to the aforementioned csv files, the full dataset also includes the raw bag files and many analysis plots, making it easier to choose which part of the dataset to use for the given application. Both the Github repository and drive are structured as follows: data//: folder containing all data of the run of name (see Section 3 for an overview of the different runs).