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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
Parameterization of the Solar Radiation Pressure
model for GPS satellites
I. S. Gayazov
Institute of Applied Astronomy, St. Petersburg, Russia
The treatment of solar radiation pressure (SRP) effect until now is the main
problem in precise modeling of GPS satellite orbits. Especially it concerns periods
when satellites pass through the Earth shadow.
The standard SRP models based on design features of GPS satellites do not
provide the accuracy required today for the scientific applications. In spite of the
fact that the shape and reflecting properties of satellites practically do not vary,
and the shadow boundaries are determined accurately, the parameters of models
can not be adopted as constants. It is mainly due to changes in the orientation
regime of eclipsing satellites [1]. When the precise information on these changes is
not available the appropriate influence on orbit can be modeled only empirically.
This results in necessity of numerical experiments aimed to find the optimal
structure of SRP model in order to reduce orbit errors. The urgency of similar
experiments is stipulated also in relation with significant increase of interest to a
shared use of GPS and GLONASS satellites. At the same time, we have no reliable
radiation pressure model for GLONASS satellites in the scientific literature.
The problem posed above has been solved within the framework of activities
on creation of a software package GRAPE [2] for processing phase observations of
the global GPS network. While the basis of the dynamic model for this package
is the same as for LAGEOS­type satellites, the special investigation has been
carried out to improve the empirical SRP model for GPS satellites. For this
purpose the processing of the pseudo--observations (precise ephemeris produced
by International GPS Service) on the 240--day time span has been performed.
In general, finding of the best structure of empirical SRP model has not unam­
biguous solution. The solution depends on criteria under which the optimization
is carried out.
First, the search of the high accuracy model structure has been implemented
using the following two criteria:
-- minimum RMS of fitting to IGS precise orbits;
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-- accuracy of the recovered Earth rotation parameters, which have been used
in producing the precise orbits.
In the best complete model we obtained under these conditions the force com­
ponents along X; Y; Z axes of the satellite fixed coordinate system are presented
in the form
X = C
3
X
k=0
X 2k+1 sin[(2k + 1)(B + \DeltaB)] + X 2s sin 2(u \Gamma u 0 );
Z = C
2
X
k=0
Z 2k+1 cos[(2k + 1)(B + \DeltaB)] + Z 2c cos 2(u \Gamma u 0 );
Y = Y 0 + Y 2s sin 2(u \Gamma u 0 ) + Y 2c cos 2(u \Gamma u 0 );
where B --- sun­satellite­Earth angle; u; u 0
--- arguments of latitude of the satel­
lite and sun; X 2k+1 ; Z 2k+1 --- coefficients of standard T20 and T30 models as
given in IERS Conventions; C; \DeltaB; X 2s ; Z 2c ; Y 0 ; Y 2s ; Y 2c --- the empirical model
parameters.
In practice, however, all seven parameters of the empirical model cannot be
confidently determined from phase observations. Therefore we were interested to
obtain model of an optimum structure satisfying the following conditions:
-- the number of parameters which are determined from phase observations
should be as small as possible;
-- parameters, which are determined beforehand from pseudo--observations
and are fixed when processing the phase measurements, should be sufficiently
stationary.
From analysis of numerous evaluations under all the above mentioned cri­
teria four parameters have been selected for the empirical model of an optimal
structure: C; \DeltaB; Y 0 ; X 2s . Therewith, two of them \DeltaB; X 2s can be fixed without
noticeable deterioration of accuracy and only C; Y 0 can be determined directly
from phase observations. The results of calculations are presented in the paper.
References
1. Bar­Sever Y. E. A new model for GPS yaw attitude. Special Topics and New
Directions, Workshop Proc., Potsdam, 1995, 128--140.
2. Gayazov I. S., Keshin M. O, Fominov A. M. GRAPE software for GPS
data processing: first results of ERP determination. In: Proc. IGS Network
Workshop -- 2000, Oslo, 2000, extended abstracts.
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