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Shi et al. Satell Navig             (2021) 2:5                                           Page 6 of 13












              6 m)                                              6 m)
               Y ECI  (×10                                Number of visible satellites  Y ECI  (×10        Number of visible satellites










                             X  (×10 m)                                          X  (×10 m)
                                                                                       6
                                   6
                              ECI                                                 ECI
                                 a                                                  b




               6 m)                                             6 m)
               Y ECI  (×10                                Number of visible satellites  Y ECI  (×10        Number of visible satellites










                             X ECI  (×10 m)                                      X ECI  (×10 m)
                                                                                       6
                                   6
                                 c                                                  d
              Fig. 4  The number of visible satellites of the spacecraft in SSTO orbit under diferent combinations: a BDS; b GPS + Galileo + GLONASS; c
              GPS + Galileo + GLONASS + BDS (only MEO satellites); d GPS + Galileo + GLONASS + BDS




            the C/N 0 (Capuano et  al.  2016). According to the data   only consider the ephemeris error, satellites clock error
            from the Chang’E-5 T lunar returning program, when the   and receiver noise (  E N  ). According to the statistical value
            spacecraft height is 10,000–60,000  km, σ R is 5.7–8.1  m   of SISRE for each GNSS and the E N  of 0.5 m in Table 3.
            (single-diferencing C/A code) (Fan et  al.  2015). Under   (Montenbruck et al. 2018; Sadman and Hossam-E-Haider
            certain conditions(non-fltered), a lower position error   2019; Xi et al. 2019), the following formula is used to cal-
            needs a lower PDOP value which is  dependent on  the   culate the position accuracy σ:
            geometrical relationship between the navigation satellites
            and the receiver, and the number of available satellites.   σ = PDOP × (SISRE +E N )          (5)
                                                                                   t
            As the height of the spacecraft increases, the 3D posi-
            tion error will inevitably rise with the ascent of PDOP.   For simplicity, the SISRE t  is weighted according to the
            To compare the position error under diferent GNSSs   proportion of satellites in each system at time t.
            combinations, the Signal-in-Space Ranging Error (SISRE)
            and PDOP are used together to evaluate position accu-  Doppler shift
            racy.  Te  pseudorange  error  is  from  various  sources  in   It is obvious that the Doppler shift should be considered
            space segment, propagation segment and user segment   in the design of receiver (Lorga et al. 2010). After esti-
            (Acharya 2014; Parkinson 1995). In the current study, we   mating the coordinates and velocities of the navigation
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