Bernese GPS Software Version 5.0 - Bernese GNSS Software

2.2.2.3 Deterministic Orbit Parameterization
2.2 GNSS Satellite Orbits
The force model used within the Bernese GPS Software Version 5.0 includes the Earth’s
potential up to a selectable degree and order, the gravitational attractions of Sun and
Moon as well as of the planets Jupiter, Venus, and Mars, the elastic Earth tidal corrections
according to IERS 1996 conventions [McCarthy, 1996], pole tide, ocean tides, and general
relativistic corrections (see Section 5.4). Solar radiation pressure is applied according to the
model described in this section, including satellites specific empirical force terms.
When determining or characterizing the orbit of a satellite, we first have to specify six
parameters defining the position and the velocity vectors at the initial epoch t0 of the arc.
One might use the Cartesian components of the vectors r0 = r(t0) and v0 = v(t0) for that
purpose. In the Bernese GPS Software, we use the osculating elements of the initial epoch
t0 to define the initial conditions: a0 = a(t0), e0 = e(t0), i0 = i(t0), Ω0 = Ω(t0), ω0 = ω(t0),
and u00 = u0(t0).
Each orbit (or, to be even more precise, each arc) is a solution of the equations of motion
(2.8). Many parameters have to be known to solve these equations of motion: Most
of the force field constituents of Table 2.9 are characterized by many parameters (think of
the parameters necessary for the Earth’s gravity potential). So, in principle, each orbit is
characterized by six osculating elements and by the set of all model parameters. Most of
these dynamical parameters are known with sufficient accuracy from other analyses (SLR
in particular) and it is neither necessary nor possible (in most cases) to improve or solve
for these parameters in GNSS analyses. Of course, each orbit determination center has to
tell what orbit models it actually uses and what numerical values are adopted for the parameters.
Within the IGS this is done through so-called Analysis Center Questionnaires.
The questionnaire for the CODE Analysis Center is accessible at ftp://ftp.igs.org/pub/
center/analysis/code.acn or at ftp://ftp.unibe.ch/aiub/CODE/CODE.ACN.
As mentioned previously the parameters p0,p1,... given explicitly in Eqn. (2.8) are those
dynamical parameters which – in general – have to be estimated for each arc and each
satellite individually in order to obtain a reliable orbital fit. If we assume that there are
np such dynamical parameters, we may state that the orbit or arc is parameterized by
n = 6 + np parameters. If these parameters are known and if one and the same model is
used for the known part of the force field, everybody should be able to reconstruct one and
the same trajectory r(t) of the satellite using numerical integration starting from time t0
(see Section 2.2.3). In this sense our n = 6+np orbit parameters uniquely specify a satellite
orbit.
What are the dynamical parameters used in the Bernese GPS Software Version 5.0 ? Let us
first state that formally we attribute these parameters to radiation pressure (but we have
to admit that other effects may be absorbed by them, as well).
According to [Beutler et al., 1994] we write the radiation pressure model (the CODE extended
radiation pressure model) in the following way:
arpr = aROCK + aD + aY + aX
(2.9)
Bernese GPS Software Version 5.0 Page 31