Bernese GPS Software Version 5.0 - Bernese GNSS Software

2. Fundamentals
2.2 GNSS Satellite Orbits
Precise GNSS orbits are a prerequisite for all applications of the GNSS where high accuracy
is required. Today highest precision GPS and GLONASS orbits are available through the
IGS and its Analysis Centers. In the first section (motivation) we study the impact of orbit
errors on the estimated station coordinates. We also include indications of precision for
the currently available orbit products (broadcast orbits, IGS orbits, CODE orbits). In the
following Sections 2.2.2 and 2.2.3 we present some of the basic concepts underlying the
orbit part of the Bernese GPS Software Version 5.0 , the keywords being Keplerian orbit,
osculating elements, orbit parameterization, and numerical integration.
The steps needed to make precise orbit information, e.g., obtained from the IGS, available
for GPS data processing with the Bernese GPS Software and to introduce broadcast information
are presented in Chapter 5. In Chapter 15 details concerning the estimation of orbit
parameters are given.
2.2.1 Motivation
Prior to 1992, the orbit quality was considered as one of the primary accuracy limiting
factors in the applications of the GPS for geodesy and geodynamics. Since the IGS started
its operations on June 21, 1992, this statement is no longer true. Orbits of an unprecedented
accuracy are available today for all active GPS satellites with a delay of less than 12 days
after the observations. Since January 1, 1996, so-called IGS preliminary orbits were made
available only 36 hours after the observation; since June 30 (beginning of GPS week 860)
this preliminary orbit is called IGS Rapid Orbit and is ready to be used only 17 hours after
the observations. The IGS Final Orbit is made available 13 days after the observations.
A near real-time IGS product, the IGS Ultra Rapid Orbit, is generated since March 2000.
These near real-time orbits are delivered since April 19, 2004, four times a day at 3 UT,
9 UT, 15 UT, and 21 UT with an average delay of only 6 hours. The first 24 hours in
the files are based on the more than 200 IGS stations delivering hourly data, the following
24 hours are extrapolated and may be used for real-time applications. All orbit products
generated at the CODE Analysis Center for the IGS also contain precise GLONASS orbits
as of June 8, 2003 (GPS week 1222) obtained in a combined analysis.
What is the impact of this development? In order to answer this question we study the effect
of unmodeled orbit errors on the estimated station coordinates. There is a crude, but handy
rule of thumb which was derived by [Bauerˇsíma, 1983], giving the error ∆x in a component
of a baseline of length l as a function of an orbit error of size ∆X:
∆x(m) ≈ l
· ∆X(m) ≈
d
l(km)
25 ′ · ∆X(m) (2.6)
000(km)
where d ≈ 25 ′ 000 km is the approximate distance between the satellite system and the
survey area. For sessions of about 1–2 hours (and shorter) Eqn. (2.6) gives satisfactory
results [Beutler, 1992]. For permanent site occupations the formulae given by [Zielinski,
1988], which were derived using statistical methods and are more optimistic by a factor of
4–10, seem to be more appropriate.
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