In response to the issue of decreased positioning accuracy in indoor Ultra-Wideband (UWB) localization due to non-line-of-sight (NLOS) interference, an adaptive Kalman filtering method based on robust estimation principles is proposed. This method combines weighted least squares estimation for distance measurements to derive positioning coordinates. In a line-of-sight scenario, distance measurements are conducted. The acquired data is utilized to compute the innovation vector and covariance. Based on this information, threshold criteria are established to identify measurement outliers resulting from non-line-of-sight (NLOS) conditions. Subsequently, the Sage-Husa filter is employed to estimate the system noise covariance. Weighted least squares estimation is applied to process distance measurements, resulting in the optimal estimation of tag coordinates. Verify the feasibility and effectiveness of the algorithm through MATLAB simulation and carry out distance measurement and positioning tests in indoor environments. Simulation and experimental results demonstrate that the adaptive Kalman filtering method based on robust estimation principles, combined with weighted least squares, effectively identifies NLOS errors and tracks sudden state changes during the localization process, the error in the x-direction is about 1 cm and in the y-direction is about 2 cm, thereby enhancing the accuracy of indoor UWB positioning.