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This paper presents the development and characterization of a system able to estimate the 2D relative position of nodes in a wireless network, based on the measurement of the distances between the nodes. To this end, this paper approaches the problem from two perspectives: implementation and theory. Combining a classical non-linear least square approach and a new convention on the arrangement of the nodes, a 2D relative positioning system was developed. Moreover, a numerical and theoretical study of the proposed system using the Cramér Rao Lower Bound (CRLB), proves that the estimator is efficient. The system uses Ultra Wide Band (UWB) ranging technology and the Bluetooth Low Energy protocol to acquire data. A Robot Operating System (ROS) library able to acquire BLE data from UWB devices was also developed. This library is open-source and available on github. The system was tested both in dynamic and static scenarios demonstrating the capability of estimating the relative position of a network comprised of 4 nodes with an update rate of 10 updates per second. The accuracy is in the order of 3 cm and 8 cm, in static and dynamic conditions respectively. A potential application of the developed system is for robot localization. In fact, autonomous robots, over the last years, have reached remarkable capabilities of localization both in indoor and outdoor scenarios using mainly GPS and vision. The developed relative localization system could address the limitations of these technologies and simplify robot cooperative tasks. The provided results and analysis show the feasibility of applying the proposed system for multi-robot cooperative localization and formation control scenarios.
Brunacci et al. (Sun,) studied this question.