CATOA: Cooperative Calibration of Timestamp Measurements for Distributed Multi-Robot Localization

Ultra-wideband (UWB) is a popular technology for robotic localization in global positioning system (GPS)-challenged and vision-obstructed scenarios. In UWB localization systems, distance information is extracted from ToA and ToD timestamp measurements. However, these measurements are easily influenced by hardware limitations and complex propagation environments, making an effective calibration method crucial for achieving high-accuracy ranging. This paper proposes a cooperative timestamp calibration method, which effectively mitigates ranging errors with scalability, adaptability, and flexibility. Our approach reduces the calibration complexity from O(N<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>) to O(N) for networks within N nodes and allows for distributed implementation to lower communication costs. The enabler is developing a new timestamp measurement model that can rectify all timestamps across different devices in a unified manner, coupled with the introduction of cooperative model training techniques that accommodate both feasible and infeasible scenarios for precisely labeling node positions. Real-world experimental results show that our method reduces the ranging error from 38.02 cm to 8.17 cm within a fully labeled 4-node network and from 16.77 cm to 9.61 cm in an 8-node network without labeling.