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.

Accurate and reliable state estimation is becoming increasingly important as robots venture into the real world. Gaussian variational inference (GVI) is a promising alternative for nonlinear state estimation, which estimates a full probability density for the posterior instead of a point estimate as in maximum a posteriori (MAP)-based approaches. GVI works by optimizing for the parameters of a multivariate Gaussian (MVG) that best agree with the observed data. However, such an optimization procedure must ensure the parameter constraints of a MVG are satisfied; in particular, the inverse covariance matrix must be positive definite. In this work, we propose a tractable algorithm for performing state estimation using GVI that guarantees that the inverse covariance matrix remains positive definite and is well-conditioned throughout the optimization procedure. We evaluate our method extensively in both simulation and real-world experiments for range-only localization. Our results show GVI is consistent on this problem, while MAP is over-confident.

The combination of ultrawideband (UWB) radios and inertial measurement units (IMU) can provide accurate positioning in environments where the Global Positioning System (GPS) service is either unavailable or has unsatisfactory performance. The two sensors, IMU and UWB radio, are often not co-located on a moving system. The UWB radio is typically located at the extremities of the system to ensure reliable communication, whereas the IMUs are located closer to its center of gravity. Furthermore, without hardware or software synchronization, data from heterogeneous sensors can arrive at different time instants resulting in temporal offsets. If uncalibrated, these spatial and temporal offsets can degrade the positioning performance. In this paper, using observability and identifiability criteria, we derive the conditions required for successfully calibrating the spatial and the temporal offset parameters of a tightly-coupled UWB-IMU system. We also present an online method for jointly calibrating these offsets. The results show that our calibration approach results in improved positioning accuracy while simultaneously estimating (i) the spatial offset parameters to millimeter precision and (ii) the temporal offset parameter to millisecond precision.