Impact of Signal-in-Space Error on LEO PNT Augmented PPP Convergence

This paper addresses the LEO PNT that augments the GNSS PPP convergence and analyzes the impact of the Signal-InSpace Error (SISE) of the LEO satellites on the PPP convergence time (CT). Existing papers reported that the GNSS PPP CT was significantly reduced to a few minutes level by using the navigation satellite constellation in the LEO. Following this background, in this paper, we assumed global LEO satellite constellations that were the Walker 30/3/1, 60/6/1, 120/12/1, 240/24/1, and 480/48/1, all with inclination of 55? and altitude of 975km, and the LEO-augmented GPS PPP CT at a receiver located in Japan (36N, 140E) was evaluated. The SISE of the LEO satellites were varied such as 2cm, 10cm, 20cm, 30cm, and 40cm, all of them are 1-sigma values, and their impact on the PPP CT was scrutinized. We focused on the CT less than three minutes and we call it the three-minute CT in this paper, and the CT was defined by the time of the first epoch such that after this epoch, the PPP filter reached the horizontal accuracy of less than 10 centimeters and continuously kept that accuracy for 5 minutes. According to our simulation results, we found that the 30-satellite constellation did not achieve the three-minute CT for all of the SISE cases and for the 60-satellite constellation, only when the SISE was 2cm, the three-minute CT was observed. For the 120-satellite constellation, the SISE cases of 30cm and 40cm did not result in the three-minute CT, indicating that the SISE level of 20cm will become necessary to achieve such a rapid PPP convergence. The 240-satellite constellation showed the three-minute CT for all of the SISE cases except for the SISE of 40cm. On the other hand, the 480-satellite constellations showed the three-minute CT for all of the SISE cases. If we target the CT within one minute, the 120-satellite, 240-satellite, and 480-satellite constellation all achieved such a ultra rapid convergence when the SISE was 2cm. Moreover, the 480-satellite constellation with SISE of 10cm also showed the CT less than one minute. By taking into account the achievable SISE by the onboard GNSS navigation called the PPP in Space method (onboard PPP) and the practical consideration, we found that for achieving the three-minute CT with high probability, the 240-satellite constellation is the most feasible choice among the constellations considered in this paper. For the one-minute CT, we found that the 480-satellite constellation with SISE level of 10cm becomes necessary.