Authors :Jian Wang Tianhe Xu Wenfeng Nie Guochang Xu

Abstract：The real-time kinematic (RTK) positioning with the multi-baseline solution (MBS) can provide high accuracy and availability for emerging applications. When the multi-systems and multi-frequencies observations for multiple stations are adopted, a heavy computational burden can arise to degrade the performance of RTK positioning. In this paper, a simplified multi-baseline solution (SMBS) algorithm based on the equivalence principle is proposed to improve the computational efficiency. Firstly, the classical equivalent observation equations (COE) are introduced and the variance–covariance (VC) matrix for SD observations is presented. Then, the simplified equivalent observation equations (SOE) can be obtained throughthe formuladerivationof transformation matrix. Secondly, the sequential Kalman filter (SKF) with multiple groups is used instead of the classical Kalman filter (CKF) to improve filtering efficiency. Finally, the performance of the proposed algorithm is comprehensively evaluated and analyzed by the static and kinematic experiments. The results demonstrate that the SMBS algorithm adopting SOE and SKF strategies can significantly accelerate the processing procedure of RTK positioning and reduce the processing time for a single epoch. The SOE strategy has an average efficiency improvement by approximately 74.7% for static, and 60.6% for the kinematic experiment, and the improvement of the SKF strategy is 49.6% and 58.0%. Moreover, the SMBS algorithm can provide a higher positioning accuracy and availability than the single-baseline solution (SBS) model. Especially for multiple reference stations, the state parameters of the rover station can be compressed to enhance the geometric strength of the positioning model, which can provide a smaller PDOP and ADOP values and improve the performance of ambiguity resolution (AR).