Relative clock estimation method between two LEO satellites
with a double-difference solution constraint
Junhong Liu, Defeng Gu
n
, Bing Ju, Yuwang Lai, Dongyun Yi
Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha 410073, China
article info
Article history:
Received 26 June 2014
Received in revised form
9 December 2014
Accepted 23 December 2014
Available online 31 December 2014
Keywords:
Relative clock
Low earth orbit (LEO)
Global positioning system (GPS)
Double-difference (DD) solution
Single-difference (SD) observations
abstract
A method of estimating the relative clocks between two spaceborne global positioning
system (GPS) receivers based on the single-difference (SD) observations is investigated in
this paper. Especially, the advantages of introducing a double-difference (DD) solution
constraint, including the orbits and ambiguities, are discussed with the simulated data
and the real data of Gravity Recovery And Climate Experiment (GRACE) satellites. The
theoretical accuracy analysis shows that the accuracy of the relative clocks is improved
and the edge effects are eliminated with a DD solution constraint. The simulations
indicate a potential accuracy improvement of at least 30% of the relative clocks with the
constraint. Furthermore, one month's real data is processed and the overlapping data arcs
are used to validate the accuracy of the relative clock solutions. The average overlapping
root mean square (RMS) of the relative clock solutions is approximate 99 ps and 31 ps
without and with the DD solution constraint, respectively. Moreover, the jumps of the day
boundaries are weakened evidently by adding the DD solution constraint. This paper
demonstrates that the accuracy and stability of the estimated relative clocks between two
low earth orbit (LEO) satellites from SD observations are improved obviously with the DD
solution constraint.
& 2014 IAA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
The twin GRACE satellites were launched into a near
polar orbit on March 17, 2002. Their initial orbit altitudes
are about 500 km and the distance between them is kept
about 200 km [1]. Each satellite carries a codeless dual-
frequency GPS receiver, a K/Ka band ranging instrument
(KBR) [2], an ultra-stable oscillator (USO), an acceler-
ometer and two star trackers [1]. The GRACE mission
measurements are excellent on the recovery of the earth
gravity [3,4]. The time of both KBR and GPS receivers is
provided by the USO. To cancel the long term USO error,
the accuracy of the relative clocks between the two space-
crafts must be better than 150 ps [5].
GPS code measurements are widely used in time transfer
since 1980 [6]. In addition, the carrier phase is also investi-
gated to solve the relative clocks between two GPS receivers
because its precision is much higher than that of the code
measurements [7,8]. With t he highly precise GPS products
[9], the relative clock solution methods could be categorized
into tw o types depending on different obser v ations: zero-
difference (ZD) method and single-difference (SD) method
[10]. ZD method employs the undifferentiated observations
to obtain the relative clocks by using the differences of these
two independent solutions [11]. The performance of ZD
method depends on the accuracy of the single receive r's
absolute clock solution, which can be refined by the precise
point positioning (PPP) [12–14], especially for fixing SD
ambiguities between GPS satellites [1 5].Comparedwiththe
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/actaastro
Acta Astronautica
http://dx.doi.org/10.1016/j.actaastro.2014.12.014
0094-5765/& 2014 IAA. Published by Elsevier Ltd. All rights reserved.
n
Corresponding author.
E-mail address: gudefeng_nudt@163.com (D. Gu).
Acta Astronautica 109 (2015) 34–41