Calibration-Free Network Localization Using Non-line-of-sight Ultra-wideband Measurements

We present a method for calibration-free, infrastructure-free localization in sensor networks. Our strategy is to estimate node positions and noise distributions of all links in the network simultaneously -- a strategy that has not been attempted thus far. In particular, we account for biased, NLOS range measurements from UWB devices that lead to multi-modal noise distributions, for which few solutions exist to date. Our approach circumvents cumbersome a-priori calibration, allows for rapid deployment in unknown environments, and facilitates adaptation to changing conditions. Our first contribution is a generalization of the classical multidimensional scaling algorithm to account for measurements that have multi-modal error distributions. Our second contribution is an online approach that iterates between node localization and noise parameter estimation. We validate our method in 3-dimensional networks, (i) through simulation to test the sensitivity of the algorithm on its design parameters, and (ii) through physical experimentation in a NLOS environment. Our setup uses UWB devices that provide time-of-flight measurements, which can lead to positively biased distance measurements in NLOS conditions. We show that our algorithm converges to accurate position estimates, even when initial position estimates are very uncertain, initial error models are unknown, and a significant proportion of the network links are in NLOS.