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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
First results of GPS orbit determination with GRAPE
package using a square--root information filter
M. O. Keshin
Institute of Applied Astronomy, St. Petersburg, Russia
The zero--differenced carrier phase measurements contain the distance be­
tween the phase centres of receiver and transmitter antennas biased by unknown
integer number of cycles (phase ambiguities). The internal precision of such mea­
surements is at submillimetre level. Nevertheless one could attain the millimetre
precision provided that the various effects affecting the measurements are prop­
erly modelled (among these the most important ones are ionosphere and tropo­
sphere refraction, satellite and receiver clock errors, multipath). This allows us
to use such measurements for GPS satellite dynamics study as well as for high­
precision satellite orbit determination. In the case of GPS the problem of solar
radiation pressure modelling is of primary importance. Besides this, the correct
description of eclipse effects on satellite motion (solar panels orientation restoring
after the satellite quits the shadow zone) needs to be also considered.
The most useful estimation tool for processing zero--differenced measurements
is the Kalman filtering/smoothing algorithms, which allow to obtain sequentially
estimates of deterministic and stochastic parameters. Meanwhile, as it is noted
in [1], for the satellite dynamics study a more comprehensive approach would
be to apply the so--called information--related filtering algorithms (SRIF/SRIS)
constructed in terms of the square--root of the covariance matrix (information
matrix). Such algorithms are more stable to improper a priori knowledge of un­
known parameters and their covariances and less influenced by the round--off
errors in comparison with usual Kalman filtering approach.
The SRIF/SRIS algorithm was implemented in GRAPE package developed in
Institute of Applied Astronomy in accordance with the algorithm considered by
Biermann [2]. Following this monography, the state vector is divided into three
parts as follows:
ffl bias parameters (phase ambiguities),
ffl purely stochastic parameters (clock errors),
ffl dynamic parameters (initial satellites position vectors).
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To represent satellite dynamics one needs the matrices of partial derivatives
of satellite position vector for arbitrary epoch t with respect to its initial position
vector K e (t 0 ; t) and to parameters of radiation pressure models K p (t 0 ; t). In our
case these matrices are contained in conditional equations whereas a transition
matrix for these parameters is simply the identity matrix.
This paper presents the first results of GPS satellite orbit determination ob­
tained with GRAPE package on the base of the square--root filtering/smoothing
algorithm. The monthly series of phase measurements collected with about 20
permanent IGS stations were processed. The following criteria were used to se­
lect GPS stations:
ffl good Earth surface coverage,
ffl these stations must provide phase and P­code measurements at the both
frequencies.
The results of GPS satellite orbits determination are presented and some
aspects of realized methodology are discussed.
It should be noted that in this paper we restricted ourselves by estimation
of only initial satellite positions and velocities. Parameters of empirical solar
pressure model described in [3] were determined from pseudo--observations and
remained fixed. Their inclusion into the estimation scheme will be the next stage
of our investigation.
References
1. Chadwell C. D. Investigation of stochastic models to improve the Global
Positioning System satellite orbits. 1995, The Ohio State University Report
No. 429, Columbus, Ohio, USA.
2. Bierman G. J. Factorization methods for discrete sequential estimation. New
York: Academic Press, 1977.
3. 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 abstract.
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