Model of distance and bandwidth dependency of TOA-based UWB ranging error

In this paper, a statistical model for the range error provided by TOA estimation using UWB signals is given. To this purpose, a large set of UWB channel measurements covering the bandwidth between 3.1 and 10.6 GHz has been collected and processed. By analyzing the measurement results, the range error has been modeled as a Gaussian random variable for LOS and as a combination of a Gaussian and an exponential random variable for NLOS propagation. The distance and bandwidth dependency of both the mean and the standard deviation of the range error has been investigated, and an insight in the different phenomena which affect the estimation accuracy, is provided. It is shown that both the signal bandwidth and the distance between the transmitter and the receiver, significantly affect the range error characterization. From the proposed model, the estimation accuracy achieved by TOA-based UWB ranging on the global set of measurements has been derived and compared with the data. For LOS, using the full bandwidth, the range error is at centimeter level; it increases in NLOS due to the additional delay introduced by the propagation through dielectric materials and to the more dense multipath.