Precise Orbit Determination of Global Navigation Satellite System of ...

Chapter 8 Geostationary Orbit Determination And Prediction During Satellite Maneuvers
Clearly from Eq.(8-57), the acceleration is in the earth-fixed system, which cannot be directly compared with the
acceleration from the dynamic model. The coordinate system conversion should be made before. The
transformation can de done as follows.
Assuming [ N ] is the nutation transformation matrix, [ P ] the precession matrix, [ C ] the polar motion matrix
and [ G ] the sidereal time transformation matrix, then transformations from the earth-fixed coordinate system to
inertial coordinate system are
ϖ ϖ
ri = [ N][ P][ C][ G] re
(8-58)
ϖ& ϖ ϖ
r = [ N][ P][ C] Gr ] & + [ Gr & ]
(8-59)
{ }
{ }
i e e
ϖ& ϖ ϖ
r [ N][ P][ C] [ Gr ] & [ Gr & ] &
i = e +2 e
(8-60)
where
ϖ ϖ
ri, re
ϖϖ
r& , &
i re
ϖϖ
r& , r&
position vectors of satellite in the inertial and the earth-fixed systems, respectively
velocity vectors of satellite in the inertial and the earth-fixed systems, respectively
i e acceleration vectors of satellite in the inertial and the earth-fixed systems, respectively
Normally ϖ r &and [ G & ] are very small, therefore the product of [ & ϖ
] & can be neglected.
According to the method described above, using simulation data, the results of orbit prediction during satellite
maneuvers are shown in Figure 8-13 and Figure 8-14.
For the maneuver operated at the acceleration of Eq.(8-53), the orbit prediction during satellite maneuver is
drawn as in Figure 8-13; for the maneuver acceleration of Eq.(8-54), the orbit prediction is drawn in Figure 8-14.
In the orbit prediction, it is assumed that 50% of maneuver acceleration is modeled by nominal maneuver force
model, Eq.(8-55) and Eq.(8-56); 20% of maneuver acceleration were corrected by Eq.(8-57), which was updated
at the rate of about 60 minutes for Figure 8-13 and 10-15 minutes for Figure 8-14 by kinematic orbit
determination results, the remaining 30% were unmodeled maneuver force errors that were not corrected during
orbit prediction.
110
Gr e
Figure 8-13 Orbit Prediction during Satellite Maneuver