In order to establish the position of the center of mass of the Earth in the
International Celestial Reference Frame, observations of the Global Positioning
Satellite (GPS) constellation using the IVS network are important. With a good
frame-tie between the coordinates of the IVS telescopes and nearby GPS
receivers, plus a common local oscillator reference signal, it should be
possible to observe and record simultaneously signals from the astrometric
calibration sources and the GPS satellites. The standard IVS solution would
give the atmospheric delay and clock offsets to use in analysis of the GPS
data. Correlation of the GPS signals would then give accurate orbital
parameters of the satellites {\bf in the ICRF reference frame}, i.e. relative
to the positions of the astrometric sources. This is particularly needed to
determine motion of the center of mass of the earth along the rotation axis.Comment: 5 pages, 2 figures, Conference Proceedings - International Very Long
  Baseline Service General Meeting 201

Dickey, John M.

English

arXiv

In order to establish the position of the center of mass of the Earth in the International Celestial Reference Frame, observations of the Global Positioning Satellite (GPS) constellation using the IVS network are important. With a good frame-tie between the coordinates of the IVS telescopes and nearby GPS receivers, plus a common local oscillator reference signal, it should be possible to observe and record simultaneously signals from the astrometric calibration sources and the GPS satellites. The standard IVS solution would give the atmospheric delay and clock offsets to use in analysis of the GPS data. Correlation of the GPS signals would then give accurate orbital parameters of the satellites in the ICRF reference frame, i.e., relative to the positions of the astrometric sources. This is particularly needed to determine motion of the center of mass of the earth along the rotation axis

Dickey, J. M.

NASA Technical Reports Server

J. M. Dickey: How and Why to Do VLBI on GPS, IVS 2010 General Meeting Proceedings, p.65–69
http://ivscc.gsfc.nasa.gov/publications/gm2010/dickey.pdf
How and Why to Do VLBI on GPS
J. M. Dickey
University of Tasmania
e-mail: john.dickey@utas.edu.au
Abstract
In order to establish the position of the center of mass of the Earth in the International Celestial
Reference Frame, observations of the Global Positioning Satellite (GPS) constellation using the IVS
network are important. With a good frame-tie between the coordinates of the IVS telescopes and
nearby GPS receivers, plus a common local oscillator reference signal, it should be possible to observe
and record simultaneously signals from the astrometric calibration sources and the GPS satellites. The
standard IVS solution would give the atmospheric delay and clock offsets to use in analysis of the
GPS data. Correlation of the GPS signals would then give accurate orbital parameters of the satellites
in the ICRF reference frame, i.e., relative to the positions of the astrometric sources. This is
particularly needed to determine motion of the center of mass of the earth along the rotation axis.
1. Background
Methods of observing the Global Positioning System (GPS) satellites with the International
Very Long Baseline Interferometry Service for Geodesy and Astrometry (IVS) telescopes have been
discussed for more than a decade (Hase 1999 [9], Petrachenko et al. 2004 [12]). The motivation is
to measure the orbits of the GPS spacecraft in near-real-time with high precision directly in the
reference frame defined by the extragalactic radio sources, i.e., the International Celestial Refer-
ence Frame (ICRF, Ma 2008 [11], Boboltz et al. 2010 [5]). The challenge of extending the ICRF to
the International Terrestrial Reference Frame (ITRF) involves combining data from other sources
such as Satellite Laser Ranging (SLR), the Gravity Recovery and Climate Experiment (GRACE),
the Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) systems, and
measurements using GPS receivers themselves (e.g., Argus et al. 2010 [2], Tregoning et al. 2009
[14]).
A particularly important issue is the motion of the Earth’s center of mass (CE). A discrepancy
between the ITRF2000 and ITRF2005 suggests that the mass distribution of the Earth is changing
in such a way that the CE is moving northward at a rate of 1.8 mm yr−1 (Altamimi et al. 2007
[1], Tregoning and Watson 2009 [15]). If this motion were real it would raise problems with other
precision measurements such as sea level rise and glacial isostatic adjustment (e.g., Beckley et al.
2007 [4]). The problem is the reference frames themselves. While SLR, GRACE, and DORIS
are ultra-sensitive to the Earth’s gravitational field, the IVS solutions for the Earth Orientation
Parameters (EOPs) are sensitive only to the rotation of the Earth’s surface. The frame-tie between
the ICRF and the satellite orbits (measured in the ITRF) introduces uncertainty in the CE position
at the level of millimeters. This frame-tie could be simplified by correlating the GPS signals along
with those from the ICRF-defining quasars as part of the IVS operation.
The CE position could be a sensitive measure of the global average of glacial melting, given
the asymmetry of the latitudinal distribution of land and sea between the Northern and Southern
Hemispheres. Melting of sea ice has no impact on the CE, but melting of ice caps such as those in
IVS 2010 General Meeting Proceedings 65
https://ntrs.nasa.gov/search.jsp?R=20110011853 2019-08-29T18:35:18+00:00Z
J. M. Dickey: VLBI on GPS
Greenland and Antarctica leads to a redistribution of the mass as the melt water adjusts to follow
an equipotential. This glacial melting contributes to sea level rise, and so it has been studied
quantitatively (Bahr et al. 2007 [3] and references therein); the mass of ice whose melting gives a
rise in the mean sea level of 1 mm is mi = 3.3 · 10
14 kg (Dyurgerov and Meier 2005 [7] figure 5 ff).
Comparing this to the total Earth mass gives a prediction for the motion of the CE along the axis
of rotation of z˙:
z˙ = − R⊕
(
f mi
2 M⊕
) (
s˙
mm yr−1
)
≃ −0.4 mm yr−1
where R⊕ and M⊕ are the Earth radius and mass, and f is a dimensionless number between -1 and
+1 given by the mass-weighted mean of the sine of the latitude where the ice melts. Assuming that
f ∼ 1 gives the value of -0.4 mm yr−1 above, with the minus indicating southward motion because
most glacial melting is (for now) in the Northern Hemisphere. More accurate measurement of the
motion of the CE would be a valuable addition to our knowledge of the effects of global warming
(Dickey et al. 2002 [6]). This could be accomplished by determining the orbital parameters of the
GPS satellites directly from measurements coupled with routine IVS observations. Combining the
two would circumvent the need for a series of techniques, each based on a different observable, to
establish the CE together with the ITRF itself. The main advantage of combining IVS and GPS
satellite orbit measurement is not improved precision in the measurements, although that might
be possible, but rather the direct measurement of satellite orbits relative to the ICRF calibrators.
2. IVS Techniques
The simplest approach (method 1) to measuring GPS signals with the IVS array is to use
the radio telescopes themselves to record the GPS signals, and then to correlate these signals to
determine the delay on each baseline and hence the position of each satellite as a function of time.
The radio telescope beams are narrow, so that the satellites are observed one at a time, and their
approximate positions must be tracked using an ephemeris. The main disadvantage of this method
is that the GPS signals are in the 1500-1600 MHz and 1200-1300 MHz ranges, which are well below
the S-band (2100-2400 MHz) frequencies of the IVS receivers. Thus new, wideband receivers would
have to be built for all the network telescopes, in order to accommodate observations of both GPS
and the standard IVS calibration sources together.
A more ambitious but ultimately simpler method (method 2, illustrated in Figure 1) is to
use a standard, geodetic-quality GPS antenna and receiver near each IVS telescope, using local
oscillators locked to the same station clock for the GPS and IVS receivers and simultaneously
recording the receiver outputs on separate channels on the same media. A precise frame-tie or
survey of the relative positions of the two antennas is also needed. The GPS antennas are nearly
omni-directional and so they receive the signals from all satellites that are above the horizon.
Correlating the outputs from the GPS receivers should give multiple delay peaks on each baseline,
one for each spacecraft. With three or more baselines the positions of all the satellites can be fixed,
and their orbital parameters determined from the position vs. time over an extended observation.
Note that it is the carrier signal that gives the correlation peak and hence provides the relative
delay on each baseline; there is no need to decode the information carried in the modulation of
the carrier as for normal GPS operation.
The main advantage of the second method is that the radio telescopes simultaneously carry
out normal IVS observing, so that the correlation and position solutions from the ICRF sources
66 IVS 2010 General Meeting Proceedings
J. M. Dickey: VLBI on GPS
Figure 1. An illustration of the second method for combining observations of the GPS signals with the IVS
calibrators. The advantages of recording signals from two antennas simultaneously at each station outweigh
the difficulties of measuring the offset between the two, both in position and in the LO/RF round-trip delay.
provide clock offsets, EOPs, and atmospheric delays at all times during the observation. These
results can be extended to the frequency of the GPS to predict values for the propagation delay
through the neutral and ionized components of the atmosphere. Determination of the clock offsets
effectively puts the GPS satellite positions in the reference frame of the astronomical sources. This
accomplishes the frame-tie that allows the CE to be directly measured in the ICRF with a
single technique. Other satellite measurement techniques could still improve the precision of the
measured CE position, but the fundamental reference frame of the measurement would become the
ICRF rather than the ITRF. This avoids problems with the registration (offset) of one reference
frame relative to the other.
3. Applications
Evidence of the need for better long-term monitoring of the GPS orbital elements in the
ICRF frame comes from comparison of time series of terrestrial reference positions using GPS
and GRACE. Figure 2 from Tregoning and Watson (2009 [15]) shows the time series and resulting
power spectrum of a reference point near Darwin, NT. There is strong vertical motion with an
annual period resulting from seasonal groundwater variation. Unfortunately, determination of this
variation, and hence of the groundwater supply in the region, is confused by another effect with a
similar period, the synodic period of the GPS constellation or draconitic period, 351.4 days. The
GRACE and GPS positions agree well except for periods between 0.5 and 1.5 years in the vertical
direction as seen in Figure 2. This problem could be alleviated by independent measurement of the
IVS 2010 General Meeting Proceedings 67
J. M. Dickey: VLBI on GPS
Figure 2. An illustration of the current problem with GPS orbital elements. At the draconitic period of
the GPS satellites, i.e. the synodic period of the constellation as a whole, there is a significant discrepancy
between position measurements using GRACE and those using GPS. The figures are taken from Tregoning
and Watson (2009) [15], who studied time series of positions for a geodetic reference site near Darwin, NT.
GPS satellite positions in the ICRF, that could be provided by the extension of the IVS technique
described here.
4. Conclusions
The modest proposal of this contribution is that IVS operations in the future should include
recording of one or more bands in the 1.5 GHz range collected from a GPS receiver near the main
radio astronomy antenna. The GPS receiver should have its local oscillator phase-locked to the
station clock. As a preliminary experiment, three antennas could be equipped in this way for test
observations. As an ultimate goal, the GPS signal from each satellite could be decoded to predict
the delay expected on each baseline, to save time in the correlation step. Two very important
steps toward the operation described here are the pioneering studies by Tornatore and Haas (2010
[13]) and Kwak et al. (2010 [10]) described in this volume.
68 IVS 2010 General Meeting Proceedings
J. M. Dickey: VLBI on GPS
5. Acknowledgements
I am grateful to Paul Tregoning, Christopher Watson, Richard Coleman, and Jim Lovell for
suggesting and explaining this topic to me.
References
[1] Altamimi, Z., Sillard, P., and Boucher, C., 2002b, J. Geophys. Res., 107(B10), 2214,
doi:10.1029/2001JB000561.
[2] Argus, D.F., Gordon, R.G., Heflin, M.B., Ma, C., et al. 2010, Geophys. Journal International 180,
913-960.
[3] Bahr, D.B., Dyurgerov, M., Meier, M.F., 2009 Geophysical Research Letters, 36, CiteID L03501.
[4] Beckley B. D., F. G. Lemoine, S. B. Luthcke, R. D. Ray, N. P. Zelensky, 2007, Geophys. Res. Lett.,
34, L14608, doi:10.1029/2007GL030002.
[5] Boboltz, D.A., Gaume, R.A., Fey, A.L., Ma, C., Gordon, D., IERS/IVS Working Group on ICRF2,
2010, AAS Meeting 215 no. 469.06, BAAS 41, 512.
[6] Dickey, J.O., Marcus, S.L., de Viron, O., and Fukumori, I., 2002 American Geophysical Union abstract
U72A-0013.
[7] Dyurgerov, M.B. and Meier, M.F., 2005, Glaciers and the Changing Earth System: A 2004 Snapshot,
INSTAAR, Occasional Paper No. 58, (University of Colorado at Boulder: Boulder), ISSN 0069-6145.
[8] Fey, A.L., Ma, C., Arias, E.F., Charlot, P., Feissel-Vernier, M., et al., 2004, A.J. 127, 3587.
[9] Hase, H., 1999, Proceedings of the 13th Working Meeting on European VLBI for Geodesy and Astrom-
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[10] Kwak, Y., Kondo, T., Gotoh, T., Amagai, J., Takiguchi, H., et al., 2010, Proceedings of the Sixth
General Meeting of the IVS, in press (this volume).
[11] Ma, C. 2008, Proceedings of IAU Symposium 248, p. 337.
[12] Petrachenko, W. et al. 2004, IVS 2004 General Meeting Proceedings, ed. N.R. Vandenberg and K.D.
Bavar, NASA/CP-2004-212255, 2004.
[13] Tornatore, V. and Haas, R., 2010, Proceedings of the Sixth General Meeting of the IVS, in press (this
volume).
[14] Tregoning, P., Ramillien, G., McQueen, H., and Zwartz, D., 2009, J. Geophys. Res., 114, B06406,
doi:10.1029/2008JB006161.
[15] Tregoning, P. and Watson, C.S., 2009, J. Geophys. Res.,, Vol. 114, No. B9, B09403,
doi:10.1029/2009JB006344.
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