With the rapid development of the Internet of Things (IoT), the positioning accuracy requirement of the IoT is increasing, especially for those applications without Global Navigation Satellite System (GNSS) signals. Ultra-Wideband (UWB) is treated as a high-accuracy positioning method that can be utilized in GNSS-blocked environments. However, UWB’s performance is still limited when it is applied in practical applications due to errors such as Non-Line-of-Sight (NLOS) errors, multipath errors, and systematic errors in UWB range values. To constrain the impacts of these mentioned errors on UWB positioning accuracy, this work proposes a novel UWB positioning model by introducing a UWB ranging offset calibration algorithm and a moving average filter into a robust extended Kalman filter. In such a UWB positioning model, the ranging offset calibration algorithm is employed to limit the infuence of UWB systematic errors, and the prior residual-based IGG-III weighting model is used to restrain the impacts of NLOS and multipath errors. The moving average filter is to further decrease the impact of the measuring noise on UWB positioning parameter estimation. To investigate the effectiveness of this proposed method, three sets of UWB experiments are arranged in three classic user environments. The experimental results show that (1) after applying the UWB ranging offset calibration algorithm, UWB positioning accuracies in classic environments, namely indoor condition, outdoor condition, and transition area are increased by 50.3%, 20.2%, and 46.9%, respectively; (2) the moving average filter can effectively improve the smoothness of UWB positioning results in terms of standard deviation; (3) the prior residual-based robust theory brings about 49.4% and 25.2% positioning improvements to horizontal and vertical components under poor measurement quality conditions, but such improvements are rather slight when there are good-quality measurements; and (4) after applying the ranging offset calibration algorithm and moving average filter to the robust EKF together, the elevation accuracy of UWB positioning is increased by 67.1%, 22.2%, and 50.5%, respectively, in the three classic user environments.