Many indoor mobile robotic applications require knowledge of the exact robot location within the work environment, for completing typical tasks. However, the accuracies of the existing indoor location-tracking systems are quite unsatisfactory. Therefore, this paper introduces a high-accuracy 3D indoor positioning approach that uses a weighted nonlinear leastsquares (WNLS) method. The method is tested with a set of indoor wireless sensor networks (WSNs) that employ ultra-wideband (UWB) sensors. The P440 UWB ranging and communication modules (RCMs) are utilized in this study, and both the NLS and WNLS methods are investigated. The results indicate that the WNLS method provides better positional accuracy than the NLS method, in 3D indoor positioning for a WSN employing uniform UWB sensors. Furthermore, the WNLS method can attain the reliability and robustness of the NLS method, irrespective of the configuration of WSNs. The WNLS method can be expected to improve the overall performance of 3D indoor positioning with UWB technologies. From our research, it can be concluded that WNLS can achieve more accurate positioning than NLS for a system that uses heterogeneous sensors for positioning, as long as the ranging errors between the sensors can be estimated.