Abstract

We have compared the VLBI and GPS terrestrial frames, realized using 3 years of time series observations (station positions and Earth orientation parameters), with colocation tie vectors for 24 sites. Our procedure was designed to ensure minimal internal distortion of the two space geodetic networks and takes advantage of the reduction in tie information needed with the time-series combination method by using the very strong contribution due to colocation of the daily pole of rotation. The results are discouraging in terms of the present tie status -- current differences are mostly at the 1 to 2 cm level -- and it is not possible without new information to further isolate problems at a finer level. Moreover, prospects for significant improvements in ITRF colocations are unlikely if past approaches continue to be followed. Consequently, alignment of the VLBI and GPS frames appears limited at the present level of 3 mm (0.5 ppb) in translation, scale, and Z rotation. We propose an alternative strategy for consideration by the IERS Working Group on co-locations, which requires at least two (preferably four) very well determined colocation sites.
Comparison strategy and results

With only 3 years of weekly GPS observations, a terrestrial reference frame can be realized with sub-mm internal precision at the midpoint epoch. A longer-term global solution of VLBI data attains a similar level. In order to relate independent frames in a multi-technique combination (such as ITRF) it is necessary to introduce tie vectors at a subset of colocation sites. The errors in these ties are usually much larger than the internal precisions of the space geodetic long-term frames and therefore significant internal distortions are nearly unavoidable, at least in the current context. It is very important to note that any systematic errors in the space geodetic frames must be considered as part of the colocation ties, not just the random measurement errors of the local surveys.

In order to try to make an undistorted comparison between VLBI-GPS differences and the corresponding local survey ties, we have developed a modified strategy. In the first step, 3 years (2001-2003) of weekly SINEX files from the IGS have been combined with VLBI session solutions from GSFC (deleting all small-network sessions) using the CATREF package developed at IGN. In the time series combination, the station position, velocity, polar motion, and polar motion rate parameters have been adjusted allowing for a 14-parameter Helmert transformation of the VLBI frame onto the GPS frame. Including the polar motion and polar motion rate parameters effectively acts as a daily colocation point which is free of any tie error, and therefore eliminates 4 degrees of freedom (rotations about X and Y, and their rates) in terms of the required tie information. We therefore used only two local site ties (together with the assumption of equal GPS and VLBI velocities at these two sites) in this combination, a very slightly over-determined system. The North Liberty (NLIB) and Hartebeesthoek (HRAO) sites were picked for the ties on account of geometrical considerations.

Demonstrating how powerful the polar motion frame colocation is, we found sigmas for the Helmert X and Y rotations of about 0.02 mas (0.6 mm) compared with sigmas of 4 to 5 mm for the other components -- see Appendix Table A1. We then compared the available local ties to those derived from our VLBI-GPS combination. The resulting site discrepancies for [VLBI - GPS]_space - [VLBI - GPS]_tie are given in Table A4, as the "Pre-fit Differences" for dX, dY, and dZ for the 24 sites with surveyed VLBI-GPS ties. The values themselves are not very meaningful since any errors in the NLIB or HRAO ties are redistributed into all the other site residuals and the non-rotational Helmert parameters are determined without redundancy. This step was only intended to produce a set of local discrepancies nearly free of any frame distortions. The "datum" for these discrepancy vectors is, however, ill- specified at this stage.

So a second Helmert transformation was then applied to the (space - tie) differences to minimize the datum defects. The results are shown in Appendix Table A4 as "Post-fit Differences" for dN, dE, and dH components. Of the 24 comparison sites, only the 13 where the GPS antenna is not covered with a radome were used in the Helmert transformation. We exclude all GPS sites with radomes since their use can affect the apparent GPS positions at the few-cm level. For instance, when the JPLA radome at KOKB was removed on 24 Sept 2002 the IGS coordinates shifted by about 27, 24, and 11 mm in the local N,E,H frame [Ferland, 2002]. An even larger vertical shift of about 50 mm was observed at HOFN when the TRIMBLE 24490-00 external radome was removed on 21 Sept 2001. UNAVCO and other groups have reported similar experiences [Braun et al., 1997]. A fundamental problem is that the IGS conventionally ignores the effect of any antenna radomes in its tables of phase center variations (PCVs); all antennas are treated as though radome-free even in those cases where the appropriate PCVs have been measured. This means that conventional surveys to the physical antenna reference point (ARP) will generally not correspond to the same reference point determined from global IGS solutions.

Appendix Table A3 shows that the 13 comparison sites, even though globally distributed, do not provide sufficiently uniform coverage to avoid high correlations among some of the Helmert parameters: Tx/Ry is -0.560, Ty/Rx is 0.535, Scale/Tz is -0.409.
Discussion of comparison residuals

The sites with GPS radomes in Table A4 show significantly larger vertical differences than the others. This is not simply due to excluding the radome sites from the Helmert transformation. Including them would change their mean and standard deviation vertical residuals insignificantly (from -12.7 and 34.6 mm to -11.1 and 32.7 mm, respectively). This is mostly because of the large tie discrepancies at SYOG, OHIG, FORT, and TIDB.

The residuals of the non-radome sites are smaller in the verticals but similar to the other sites in the horizontal components. It is possible that somewhat smaller residuals exist using an alternate subset of comparison sites, but we have not found any other set that improves the overall situation for the non-radome sites. The 3D residuals for those sites range from about 6 to 25 mm, most between 1 and 2 cm. This comparison should represent a near-optimal, undistorted view of the current status of local ties between VLBI and GPS networks. It is conceivable that the actual situation might be worse. For instance, if any globally systematic height bias exists in either or both techniques, then that bias would be absorded into the Helmert scale parameter and not be seen in the site residuals.

If this comparison is indeed representative of the current state-of-the-art, which we believe it is, and if there are no neglected systematic biases absorbed into the Helmert parameters at a significant level, then our results imply that the alignment of the VLBI and GPS frames is limited to an overall accuracy of slightly more than 3 mm (see Table A2 sigmas). However, the actual X and Y rotations in a multi-technique time series combination will be much better determined (sub-mm) due to the polar motion colocation.
Conclusions

• Based on these results we conclude that:
• Current VLBI-GPS colocation connection differences are mostly at the 1 to 2 cm level (3D).
• The local tie differences are probably the combined effects of systematic errors in the GPS, VLBI, and local survey measurements plus random errors in the surveys; random GPS and VLBI errors are probably negligible.
• It is generally not possible, without additional information presently unavailable, to further isolate the contributors to the local colocation differences. (The ties for OHIG and SYOG could be in error but the small number of VLBI sessions involving these stations makes these results unreliable.)
• The current situation has improved only marginally over the past two decades, except to correct blunders and to increase the number of colocations with GPS. There is no prospect of significant improvements by continuing to follow the established approach.
• Therefore, alignment of the VLBI and GPS frames appears limited at the 3 mm (0.5 ppb) level in translation, scale, and Z rotation.

Recommendations

Even overlooking possible globally systematic frame biases, to perform a better alignment of the VLBI and GPS frames to the 1 mm level overall, a major improvement in the local ties is required, at least by a factor of 3 in accuracy and/or an increase in the number and distribution of colocation sites. Considering the history of this effort, such a large general improvement seems unlikely. Instead we suggest a more focussed approach that may yield greater benefits.

• Ignore GPS sites with radomes -- While methods may be adopted to handle these stations better in the future, this will take some time and the established IGS frame will not be useful for frame ties at these sites for some years. Until that time, performing local surveys to these GPS stations is a futile effort.
• Always use the IGS data in the local surveys -- Local tie surveys usually do not use data from the IGS GPS receiver. This makes it impossible to check for local tie closure to the GPS phase reference point to guard against biases (especially in the local height). The IGS data should be used, together with simultaneous GPS data from nearby control markers, and the reduction of that data should follow the same conventions adopted by the IGS Analysis Centers.
• VLBI deformations must be checked -- Local tie surveys involving VLBI antennas should include sufficient measurements to determine the non- ideal variations of the antenna due to gravity and construction defects. It is particularly important to check for the level of gravitational sag of the feed/subreflector structure and useful also to monitor flexure of the primary reflector [Rogers et al., 1978; Carter et al., 1980].
• Minimum of two well-determined colocation sites required -- At a minimum, it is essential to have at least two colocation sites with local ties (including all components) confidently and reliably measured to <2 mm in each component. The error budgets must consider all systematic and random contributions. Only in this way is it possible to try to better isolate tie errors at the other colocation sites through a global comparison like the one described here.
• Tetrahedral colocation network better for redundancy -- Rather than try to accomplish all these rather ambitious goals at all colocation sites, it may be more cost-effective and feasible to identify a geometrically robust subnet of 3 or 4 sites where these types of comprehensive surveys can be made. We suggest a tetrahedral array. For example, the network of HRAO, HOB2, MKEA, and WTZR, all with measured local ties confidently determined to <2 mm in each component (including all systematic and random effects) would permit the VLBI and GPS frames to be aligned to better than 1 mm globally.
• Then try to build further network redundancy -- When the tetrahedral array has been accomplished, then it would be advisable to expand in order to increase robustness and long-term stability.
• Other techniques can be linked to GPS similarly -- The approach suggested here can be applied likewise with colocations between GPS and the other techniques, SLR and DORIS. Multiple colocations among several techniques, such as at HRAO and WTZR, are ideal.

References

Braun, J., B. Stephens, O. Ruud and C. Meertens, The effect of antenna covers on GPS baseline solutions, University NAVSTAR Consortium report, Development & Testing - The Effect of Antenna Covers On GPS Baseline Solutions | UNAVCO Facility , 17 June 1997.

Carter, W.E., A.E.E. Rogers, C.C. Counselman, and I.I. Shapiro, Comparison of geodetic and radio interferometric measurements of the Haystack-Westford base line vector, J. Geophys. Res., 85(B5), 2685-2687, 1980.

Ferland, R., RF KOKB coordinates discontinuity, IGS Mail 4151, 08 November 2002.

Rogers, A.E.E., C.A. Knight, H.F. Hinteregger, A.R. Whitney, C.C. Counselman, I.I. Shapiro, S.A. Gourevitch, and T.A. Clark, Geodesy by radio interferometry: Determination of a 1.24-km base line vector with ~5-mm repeatability, J. Geophys. Res., 83, 325-334, 1978.
Appendix

Table A1 contains the Helmert parameters and formal errors from the CATREF joint combination of 3 years of VLBI and GPS data together with local ties at 24 colocation sites. Inclusion of the polar motion and polar motion rate parameters allows the rotations about X and Y to be very precisely determined compared to the other components. Only two local ties (NLIB and HRAO) were used to eliminate singularities in the Helmert transformations so the transformation values themselves are not necessarily very meaningful. The rate parameters are not shown since only 3 years of data were used.

Table A1. Step 1 Helmert parameters at epoch 2002 7 1

Value Sigma
Rot. about X 0.136 mas 0.018
Rot. about Y -0.106 mas 0.021
Rot. about Z 0.073 mas 0.162
X translation 0.12 cm 0.40
Y translation 0.70 cm 0.42
Z translation 0.21 cm 0.36
Scale Change -1.31 ppb 0.65

Table A2 contains the Helmert parameters and formal errors that minimize the colocation discrepancies resulting from the CATREF VLBI-GPS combination using the 13 colocation sites listed in Table A4.

Table A2. Step 2 Helmert parameters at epoch 2002 7 1

Value Sigma
Rot. about X -0.1033 mas 0.1188
Rot. about Y -0.0251 mas 0.1176
Rot. about Z -0.0131 mas 0.1116
X translation 0.417 cm 0.3229
Y translation -1.001 cm 0.2904
Z translation -0.006 cm 0.3074
Scale Change 0.3960 ppb 0.4963

Table A3. Helmert parameter correlations corresponding to Table A2

Rx Ry Rz Tx Ty Tz S
Rx 1.000 0.106 0.213-0.140 0.535 0.290-0.007
Ry 0.106 1.000-0.159-0.560 0.125 0.246 0.017
Rz 0.213-0.159 1.000-0.264-0.234 0.005 0.036
Tx -0.140-0.560-0.264 1.000-0.002-0.096-0.162
Ty 0.535 0.125-0.234-0.002 1.000 0.145 0.058
Tz 0.290 0.246 0.005-0.096 0.145 1.000-0.409
S -0.007 0.017 0.036-0.162 0.058-0.409 1.000

Table A4. Local Residuals: [VLBI - GPS]_space - [VLBI - GPS]_tie

Pre-fit Differences Post-fit Differences
IGS (mm) (mm)
Site dX dY dZ dN dE dH Tie markers
====================================================================
Included in Helmert transformation:
ALGO 4.0 -17.0 10.0 -1.2 -1.3 9.4 40104M002->S001
CRO1 8.0 -7.0 5.0 1.9 4.9 -2.0 43201M001->S001
HOB2 2.0 -22.0 8.0 5.1 10.0 -11.4 50116M004->S002
HRAO 0.0 0.0 0.0 1.3 12.5 -1.7 30302M004->S001
MADR 8.0 -9.0 9.0 3.5 -0.4 6.2 13407S012->S010
MATE 17.0 -11.0 -1.0 -8.3 -6.5 6.0 12734M008->S005
MEDI 12.0 -16.0 1.0 -3.9 -9.5 2.8 12711M003->S001
MKEA -8.0 -8.0 3.0 -1.2 -5.4 8.1 40477M001->S001
PIE1 -11.0 1.0 -11.0 -8.6 -16.5 -13.4 40456M001->S001
WES2 17.0 -11.0 11.0 1.5 12.0 8.6 40440S020->S003
WTZR 10.0 -2.0 2.0 -4.3 4.3 3.9 14201M010->S004
YEBE -3.0 -2.0 2.0 5.6 5.9 -7.0 13420M001->S001
YELL -4.0 -1.0 -20.0 -7.5 -9.2 -22.4 40127M003->M004

Not included in Helmert transformation (with GPS radomes):

FAIR R -9.0 -11.0 7.0 -8.6 -3.3 8.8 40408M001->S002
FORT R 24.0 -23.0 2.0 1.1 2.7 20.9 41602M001->S001
GODE R 8.0 -7.0 2.0 -0.4 4.7 -2.8 40451M123->M125
KOKB R -6.0 -8.0 5.0 1.0 -3.8 7.6 40424M004->S007
MDO1 R -4.0 -20.0 5.0 -4.5 -4.4 10.1 40442M012->S017
NLIB R 0.0 0.0 0.0 3.5 -3.6 -9.9 40465M001->S001
NYA1 R 3.0 3.0 -5.0 -2.5 9.8 -7.1 10317M003->S003
OHIG R -27.0 16.0 55.0 -12.9 -11.5 -69.0 66008M001->S001
ONSA R 6.0 -3.0 6.0 0.4 3.9 4.3 10402M004->S002
SYOG R -34.0 -16.0 80.0 -0.9 22.6 -89.2 66006S002->S004
TIDB R 8.0 -14.0 12.0 9.0 0.4 -13.9 50103M108->S010
====================================================================

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