Bernese GPS Software Version 5.0 - Bernese GNSS Software

2. Fundamentals
where aROCK is the acceleration due to the Rock4 (Block I satellites) and Rock42 (Block
II satellites) models for the radiation pressure [Fliegel et al., 1992], and
where
aD = (aD0 + aDC · cos u + aDS · sin u) · eD = D(u) · eD
aY = (aY 0 + aY C · cos u + aY S · sin u) · eY = Y (u) · eY
aX = (aX0 + aXC · cos u + aXS · sin u) · eX = X(u) · eX
(2.10)
aD0, aDC, aDS, aY 0, aY C, aY S, aX0, aXC, and aXS are the nine parameters of the radiation
pressure model of the Bernese GPS Software Version 5.0 ,
eD is the unit vector satellite-to-sun,
eY = eD × r
is the unit vector along the spacecraft’s solar-panel axis assuming nominal
|eD × r|
satellite attitude (see Figure 2.2),
eX = eY × eD completes a right-handed orthogonal system of unit vectors,
D(u), Y (u), and X(u) are the total accelerations due to radiation pressure (on top of the
Rock4/42-models) in the directions eD, eY , and eX, and
u is the argument of latitude at time t for the satellite considered.
For GPS satellites the ROCK4/42 model, version T (including thermal re-radiation, also
called T10 and T20) is used at CODE. The a priori model is automatically scaled by
the factor r 2 0 /r2 , where r0 is the Astronomical Unit (AU), and r is the actual distance
between Sun and spacecraft. In order to compute the actual accelerations acting on the
satellite, ROCK models require the satellite mass. The satellite masses are given (together
with other satellite specific information like the antenna phase center eccentricity) in the
satellite information file (e.g., ${X}/GEN/SATELLIT.I05, see Section 22.4.5). Alternatively
to the ROCK4/42 model the model developed by [Springer et al., 1999] may be used as
a priori radiation pressure model (see Section 15). For GLONASS satellites no radiation
pressure model is available and, therefore, no a priori model is applied.
The acceleration due to the solar radiation pressure is switched off when the satellite is in
the Earth’s shadow and scaled according to the fraction of the solar disk not covered by the
Moon during lunar partial eclipses that regularly occur during New Moon.
In summary, in Version 5.0 of the Bernese GPS Software each satellite arc is characterized
by six osculating elements and by up to nine dynamical parameters as defined above. The
parameterization of the a priori orbits is defined in program ORBGEN (see Section 5.4.2).
2.2.2.4 Pseudo-Stochastic Orbit Parameterization
Whereas most users of the Bernese GPS Software only have to deal with the n = 6 + np ≤ 15
deterministic orbit parameters discussed in the previous section, the advanced user working
on orbit determination might also wish to parameterize the orbits additionally with
so-called pseudo-stochastic parameters, characterizing instantaneous velocity changes at
user-determined epochs in user-determined directions. The attribute stochastic is justified
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