Page 89 - 卫星导航2021年第1-2合期

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

Table 4 Receiver orbits elements
Orbit type Elements
Perigee altitude Apogee altitude Inclination (°) Argument Mean anomaly (°) RAAN (°)
(km) (km) of Perigee (°)
SSTO 192.8 68,016.8 16.301 192.719 0 309.684
GEO at 125° 35,681.3 35,740.6 0.1186 90.847 78.2409 83.169
GEO at 0° 35,788.1 35,788.1 0.111 0 123.352 89.859
GEO at 240° 35,788.1 35,788.1 0.111 0 3.352 89.859

No. k available navigation satellite position param- coordinate system used in each GNSS, the coordinate of
eter and the pseudorange calculated according to the navigation satellite from diferent system must be con-
ephemerides at that moment. Because of the diferent verted to the same coordinate system before calcula-
tion (Jing et al. 2014). After transforming both sides of
the Eq. (4) and seeking the expected value, we can get
2
the expression E[dξdξ ] = Hσ where H =[QQ ]
T
T −1
R
Table 5 Scenario and dξ is the vector of position error and clock error,
√
Scenario Constellation composition PDOP = trace{H 3×3 } . Without considering the
receiver clockerror, the 3D position estimation error can
1 BDS express as σ p = PDOPσ R , the σ R is the pseudorange error,
2 GPS + Galileo + GLONASS including satellite position errors, clock ofset errors,
3 GPS + Galileo + GLONASS + BDS signal propagation errors, and instrumentation errors,
MEO (only MEO satellites)
4 GPS + Galileo + GLONASS + BDS which can be approximately regarded as a function of

Table 6 Synthetic results
Scenario and orbit Parameters
% of time position C/N dB·Hz Positioning error (m)
0
solvable
Min Max Median Min Max Median
Scenario 1
SSTO 28.4 23.68 50.11 39.35 1.41 1051.29 33.34
GEO at 0° 71.4 28.76 49.2 40.86 33.98 1030.13 88.96
GEO at 125° 8.7 28.76 48.16 36.11 45.95 1045.10 131.56
GEO at 240° 72.0 28.76 48.16 43.60 36.99 1088.78 98.69
Scenario 2
SSTO 19.7 20.02 49.14 39.06 1.05 921.49 27.07
GEO at 0° 18.5 21.70 47.76 48.16 52.19 805.47 103.30
GEO at 125° 20.7 21.70 47.76 40.90 50.96 855.79 125.03
GEO at 240° 23.6 21.64 47.76 40.98 43.13 854.95 103.53
Scenario 3
SSTO 37.8 20.02 49.61 38.30 0.93 1260.10 58.49
GEO at 0° 55.4 21.70 48.16 38.71 37.47 1089.27 82.25
GEO at 125° 52.9 21.70 48.16 40.77 34.47 1373.59 83.85
GEO at 240° 57.6 21.64 48.16 40.78 30.73 1283.32 78.85
Scenario 4
SSTO 50.0 20.02 50.11 39.12 0.92 888.13 63.95
GEO at 0° 97.0 21.70 49.21 40.87 27.58 199.98 51.83
GEO at 125° 52.9 21.70 48.16 40.77 34.47 1373.59 83.85
GEO at 240° 97.2 21.64 48.16 42.44 26.78 715.43 57.99