Obstructed GNSS positioning assisted by opportunistic LEO Doppler leveraging real-time PPP with state space representation

The Global Navigation Satellite System (GNSS) signals may be unexpectedly blocked in complicated environments with severe obscuration or GNSS interference. The Doppler signal of low-earth-orbit (LEO) satellites can be utilized as a signal of opportunity (SoOP) to aid the GNSS system. Firstly, we proposed a fusion mathematical model for precise point positioning (PPP) using Doppler of LEO and pseudorange and carrier phase of GNSS to improve the positioning performance in the case of insufficient GNSS satellites. Subsequently, we derived the worst-case influence of the orbit error of LEO and expounded state space representation (SSR) of GNSS satellite orbit. Meanwhile, the other two ephemerides, including the broadcast ephemeris and ultra-fast precise ephemeris, are also attempted to make the LEO-assisted GNSS fusion system flexibly selective under different real-time scenario conditions. Furthermore, we derived the Cramer-Rao lower bound (CRLB) of the LEO-assisted GNSS system and analyzed its usability and convergence. Finally, two field experiments were conducted to verify the performance of the LEO-assisted GNSS fusion system with different ephemerides by using our self-developed LEO-assisted GNSS positioning receiver under insufficient GNSS satellites. The experimental results show that the positioning performance of PPP with SSR corrections is better than the other two ephemerides. Meanwhile, the LEO-assisted GNSS system works better than the stand-alone GNSS system in insufficient GNSS. Furthermore, the effect of LEO satellites on positioning accuracy increases as the number of GNSS satellites decreases and the ephemeris accuracy increases.