Improved Kalman Filtering Algorithm Based on Levenberg–Marquart Algorithm in Ultra-Wideband Indoor Positioning

Abstract

To improve the current indoor positioning algorithms, which have insufficient positioning accuracy, an ultra-wideband (UWB) positioning algorithm based on the Levenberg–Marquardt algorithm with improved Kalman filtering is proposed. An alternative double-sided two-way ranging (ADS-TWR) algorithm is used to obtain the distance from the UWB tag to each base station and calculate the initial position of the tag by the least squares method. The Levenberg–Marquardt algorithm is used to correct the covariance matrix of the Kalman filter, and the improved Kalman filtering algorithm is used to filter the initial position to obtain the final position of the tag. The feasibility and effectiveness of the algorithm are verified by MATLAB simulation. Finally, the UWB positioning system is constructed, and the improved Kalman filter algorithm is experimentally verified in LOS and NLOS environments. The average X-axis and the Y-axis positioning errors in the LOS environment are 6.9 mm and 5.4 mm, respectively, with a root mean square error of 10.8 mm. The average positioning errors for the X-axis and Y-axis in the NLOS environment are 20.8 mm and 18.0 mm, respectively, while the root mean square error is 28.9 mm. The experimental results show that the improved algorithm has high accuracy and good stability. At the same time, it can effectively improve the convergence speed of the Kalman filter.