A Multipath Error Reduction Method for BDS Using Tikhonov Regularization with Parameter Optimization

Abstract

Multipath error is an important factor restricting the relative positioning accuracy of the Beidou Navigation Satellite System (BDS). Because of the complexity of the reflection environment, the mathematical modeling of multipath errors is quite difficult. The sidereal filtering algorithm corrects multipath errors by using the feature of period repetition, which can greatly reduce its influence and improve the accuracy of positioning and attitude measurement. In view of the constellation heterogeneity of BDS, it is more complicated to apply sideral filtering. Based on the reconstructed single-difference residual of the carrier phase, the multipath repetition time of the Beidou satellite is estimated using the idea of segmentation. The Tikhonov regularization method and the classical wavelet method are used to extract the multipath of the single-difference residual of the carrier phase, and the “clean” sequence of the single-difference residual is obtained. The experimental results show that it is feasible to extract the multipath error correctly by Tikhonov regularization, and the multipath error is smoother than the original residual measurement. Furthermore, the estimation method of the regularization parameter is further optimized. After using the optimized Tikhonov regularization method with sidereal filtering, the mean RMS improvements of GEO, IGSO, and MEO satellites are 45.9%, 38.2%, and 37.5%, respectively. The positioning accuracy on E, N, and U components is improved by 24.8%, 26.3%, and 42.7%, respectively. The attitude resolution accuracy is improved by 22.9% in the yaw angle and 12.6% in the pitch angle. The proposed method can be an alternative BDS multipath error modeling and mitigation approach.