  Ultra-wideband (UWB) time difference of arrival(TDOA)-based localization has
emerged as a low-cost and scalable indoor positioning solution. However, in
cluttered environments, the performance of UWB TDOA-based localization
deteriorates due to the biased and non-Gaussian noise distributions induced by
obstacles. In this work, we present a bi-level optimization-based joint
localization and noise model learning algorithm to address this problem. In
particular, we use a Gaussian mixture model (GMM) to approximate the
measurement noise distribution. We explicitly incorporate the estimated state's
uncertainty into the GMM noise model learning, referred to as uncertainty-aware
GMM, to improve both noise modeling and localization performance. We first
evaluate the GMM noise model learning and localization performance in numerous
simulation scenarios. We then demonstrate the effectiveness of our algorithm in
extensive real-world experiments using two different cluttered environments. We
show that our algorithm provides accurate position estimates with low-cost UWB
sensors, no prior knowledge about the obstacles in the space, and a significant
amount of UWB radios occluded.
