Position Error Bound and Localization Accuracy Outage in Dense Cluttered Environments

For most outdoor applications, systems such as Global Positioning System (GPS) provide users with accurate location estimates. However, similar range-only localization techniques in dense cluttered environments typically lack accuracy and reliability due, notably, to dense multipath, line-of-sight (LOS) blockage and excess propagation delays through materials. In particular, range measurements between a receiver and a transmitter are often positively biased. Furthermore, the quality of the range measurement degrades with distance, and the geometric configuration of the beacons also affects the localization accuracy. The Position Error Bound (PEB) is a practical measure of the localization accuracy of such system at a single location. The PEB quantifies the impact of different ranging estimation errors due to beacons distance and biases on the best positioning accuracy. In most practical systems, however, localization must be provided throughout an area, not only at a single point. We introduce the concept of localization accuracy outage, which extends the PEB to multiple locations, so that it quantifies the localization accuracy throughout an area. We illustrate this through several numerical examples, and show that, just as with the single location case, the information from NLOS beacons can be valuable in scenarios with multiple locations, especially in dense cluttered environments.