Real-time estimation of BDS/GPS high-rate satellite clock offsets using sequential least squares

Abstract

The real-time precise satellite clock product is one of key prerequisites for real-time Precise Point Positioning (PPP). The accuracy of the 24-hour predicted satellite clock product with 15 min sampling interval and an update of 6 h provided by the International GNSS Service (IGS) is only 3 ns, which could not meet the needs of all real-time PPP applications. The real-time estimation of high-rate satellite clock offsets is an efficient method for improving the accuracy. In this paper, the sequential least squares method to estimate real-time satellite clock offsets with high sample rate is proposed to improve the computational speed by applying an optimized sparse matrix operation to compute the normal equation and using special measures to take full advantage of modern computer power. The method is first applied to BeiDou Navigation Satellite System (BDS) and provides real-time estimation with a 1 s sample rate. The results show that the amount of time taken to process a single epoch is about 0.12 s using 28 stations. The Standard Deviation (STD) and Root Mean Square (RMS) of the real-time estimated BDS satellite clock offsets are 0.17 ns and 0.44 ns respectively when compared to German Research Center for Geosciences (GFZ) final clock products. The positioning performance of the real-time estimated satellite clock offsets is evaluated. The RMSs of the real-time BDS kinematic PPP in east, north, and vertical components are 7.6 cm, 6.4 cm and 19.6 cm respectively. The method is also applied to Global Positioning System (GPS) with a 10 s sample rate and the computational time of most epochs is less than 1.5 s with 75 stations. The STD and RMS of the real-time estimated GPS satellite clocks are 0.11 ns and 0.27 ns, respectively. The accuracies of 5.6 cm, 2.6 cm and 7.9 cm in east, north, and vertical components are achieved for the real-time GPS kinematic PPP.