Near Real-Time Precise Orbit Determiation of Low Earth Orbit Satellites Using an Optimal GPS Triple-Differencing Technique
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Date
2006-11
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Ohio State University. Division of Geodetic Science
Abstract
During the last decade, numerous Low Earth Orbit (LEO) satellites, including
TOPEX/POSEIDON, CHAMP and GRACE, have been launched for scientific purposes
at altitudes ranging from 400 km to 1300 km. Because of highly complex dynamics of
their orbits, coming from the Earth gravity field and the atmospheric drag, accurate and
fast LEO orbit determination has been a great research challenge, especially for the
lowest altitudes. To support GPS meteorology that requires an accurate orbit in near realtime,
efficient LEO orbit determination methods were developed using the tripledifferenced
GPS phase observations, as presented in this dissertation. These methods
include the kinematic, dynamic, and reduced-dynamic approach based on the wave
algorithm.
To test the developed algorithms, 24 hours of CHAMP data on February 15, 2003,
which amounts to 15 revolutions, were used for each method. The EIGEN2 geopotential
model was used with degree and order up to 120. Precise IGS orbits are used for the GPS
satellites, and 43 IGS ground tracking stations were chosen using the algorithm
developed in this study, based on the network optimization theory. The estimated orbit
solutions were compared with the published Rapid Science Orbit (RSO) and the
consistency testing was performed for the dynamic solution. In addition to the
comparison with other orbit solutions, the SLR residuals were also computed as an
independent validation of the methods presented here.
The kinematic orbit solution depends on the satellite geometry and data quality. The
absolute kinematic positioning solution, with an RMS error of ±26 meters in 3D, was
used as an initial approximation for the kinematic orbit determination. Because of the
inaccuracy of the initial approximated orbit, there is a bias up to a few hundred epochs in
the kinematic solution. This bias is effectively removed with the backward filter by fixing
the last epoch from the forward filter solution. After the forward and backward filtering,
the kinematic approach shows accuracy better than ±20 cm in 3D RMS for a half day arc
compared to the reference RSO.
The dynamic approach requires careful modeling of the atmospheric drag force
which is the most dominant nonconservative force at LEO’s altitude. In addition, the
empirical force modeling, which is similar to the stochastic process noise in the reduceddynamic
approach, absorbs most of the remaining unmodeled forces. The two frequencies
of the empirical forces, that is, once- and twice-per-revolution, are modeled in this study.
Also after a thorough testing of the most suitable size of the arc length for the
atmospheric drag parameters, the scaling factors for the drag force are estimated every
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hour. With this careful modeling, the dynamic solution shows an agreement within ±8 cm
in position and ±0.12 mm/s in velocity of RSO. The computation time of the dynamic
solution for the 24-hour arc is 2.5 hours on a 3 GHz PC platform.
The wave algorithm, as implemented in this study, for the LEO precise orbit
determination (POD) represents a new approach to the reduced-dynamic technique. This
approach shows a better fit to RSO for each tested segment. However, there is slightly
larger bias in its solution, thus, the overall RMS of fit is comparable to the dynamic orbit
solution. This follows from the fact that the concept of the reduced-dynamic approach is
already incorporated in the dynamic orbit determination in the form of the empirical force
modeling. Therefore, there is no room for further improvement by the process noise
modeling to take care of the unmodeled forces. A simplified force model is considered for
future study in conjunction with the wave filter approach.
The CHAMP orbit is successfully estimated in this study to support, for example,
the GPS meteorology, using a new method that is accurate as well as fast and efficient.
The applied wave algorithm shows the possibility of further improvement in the RMS of
fit as long as the bias is modeled appropriately. The hypothesis testing indicates that the
estimated dynamic solution of this study is consistent with the published RSO, thus,
further accuracy improvement cannot be expected without other types of measurements,
while its easy and time-effective implementation represents the major improvement, as
compared to the existing solutions. Also, the SLR residual test shows that the CHAMP
orbit solution estimated in this study is comparable to solutions determined by other
analysis centers, such as JPL and GFZ.
Description
This report was prepared by Tae-Suk Bae under the supervision of Professor Dorota A. Grejner-Brzezinska, Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University. This report was originally submitted to the Graduate School of The Ohio State University in partial fulfillment of the requirements for the Ph.D. degree.
This research was supported by the grants from NASA (NASA NIP Project, OSURF #740809).
This research was supported by the grants from NASA (NASA NIP Project, OSURF #740809).