Position Error Bound for UWB Localization in Dense Cluttered Environments

Range-only localization techniques in dense cluttered environments typically lack accuracy due, notably, to partial and complete line-of-sight (LOS) blockage. Furthermore, the quality of the range measurements degrades with distance, and the geometric configuration of the beacons also affects the localization accuracy. In this paper we derive a fundamental limit of localization accuracy for an ultra-wide bandwidth (UWB) system operating in such environments, which we call the Position Error Bound (PEB). The impact of different ranging estimation errors due to beacons distance and biases on the best positioning accuracy is investigated. The statistical characterization of biases coming from measurement campaigns can easily be incorporated into this analysis. We show that the relative importance of information coming from different beacons varies depending on the propagation conditions, such as whether the beacon is LOS or non-line-of-sight (NLOS). We show in particular that NLOS beacons can significantly improve the localization accuracy compared to the case when they are not considered, especially in dense cluttered environments.