Along with the rapid development of advanced driving assistance systems for intelligent vehicles, essential functions such as forward collision warning and collaborative cruise control need to detect the relative positions of surrounding vehicles. This paper proposes a relative planar localization system based on the ultra-wideband (UWB) ranging technology. Three UWB modules are installed on the top of each vehicle. Because of the limited space on the vehicle roof compared with the ranging error, the traditional triangulation method leads to significant positioning errors. Therefore, an optimal localization algorithm combining homotopy and the Levenberg–Marquardt method is first proposed to enhance the precision. The triangular side lengths and directed area are introduced as constraints. Secondly, a UWB sensor error self-correction method is presented to further improve the ranging accuracy. Finally, we carry out simulations and experiments to show that the presented algorithm in this paper significantly improves the relative position and orientation precision of both the pure UWB localization system and the fusion system integrated with dead reckoning.
