For the problems of Non-Line-of-Sight (NLOS) observation errors and inaccurate predictive dynamics model in wireless ultra-wideband (UWB) positioning systems, an improved strong tracking cubature Kalman filter (ISTCKF) positioning algorithm is proposed in this paper. The main idea of the algorithm is as follows. First, the observations are reconstructed based on the weighted positioning results obtained from the predictive dynamics model and the least squares algorithm. Second, the difference in statistical properties between the observation noise and the NLOS errors is utilized to identify the NLOS observations by the corresponding judgment statistics obtained from the operation between the original observations and the reconstructed observations. The main positioning error of the UWB positioning system at the current moment is then judged by the NLOS identification results, and the corresponding fading factors are calculated according to the judgment results. Finally, the corresponding ISTCKF is constructed based on the fading factors to mitigate the main positioning error and obtain accurate positioning result in the UWB positioning system. In this paper, the reconstructed observations mitigate the observation noise in the original observation, and then the ISTCKF mitigates the main errors in the UWB positioning system. The experimental results show that the ISTCKF algorithm reduces the positioning error by 55.2%, 32.3% and 28.9% compared with STCKF, ACKF and RSTCKF, respectively. The proposed ISTCKF algorithm significantly improves the positioning accuracy and stability of the UWB system.