On the principles, assumptions and methods of geodetic very long baseline interferometry
F.J.J. Brouwer
Delft, 1985. 180 pages.
ISBN-13: 978 90 6132 232 0. ISBN-10: 90 6132 232 4. € 16.00
Summary
The accuracy of geodetic VLBI point positioning measurements is
assessed. The assessment is based on a software package developed for
the purpose which incorporates all possible computing models for
geodetic VLBI data analysis. Analysis of real and simulated data with
this package shows that an accuracy of 10 cm in point positioning has
been achieved with the ERIDOC and MERIT Short Campaign observing
campaigns. This analysis has also led to the formulation of criteria for
optimum design of a geodetic VLBI observing campaign, and to a general
approach for evaluating experiments designed to compare VLBI with other
geodetic techniques, because the ultimate accuracy of world-wide
geodetic measurements for geodynamics and positioning can only be
achieved by a combination of several techniques.
The DEGRIAS (DElft Geodetic Radio Interferometry Adjustment System)
software package and the background of its development are described in the
first three chapters of this publication. The package is the outcome of a
desire to incorporate geodetic VLBI into the system for the design and
computation of geodetic networks developed at the Delft Department of
Geodesy, commonly known as the Delft Approach. Chapters 2 and 3 provide
descriptions of the general and specific features of DEGRIAS respectively.
Under general features is included a sketch of all physical phenomena
relevant to VLBI observations, and the basic equations for the delay and
delay rate observables in the commonly used computing model, the kinematic
model. An analysis is given of the achieved level of precision of DEGRIAS in
modelling the phenomena that constitute the "real world" of geodetic VLBI.
The more detailed description in chapter 3 includes discussion of
linearisation of the equations for delay and delay rate and a discussion on
the rank deficiencies of the system of normal equations in the Least Squares
adjustment. Chapter 3 also presents the results of applying DEGRIAS to the
VLBI data of ERIDOC (European Radio Interferometry and DOppler Campaign) and
part of the MERIT (to Monitor Earth Rotation and Intercompare the Techniques
of observation and analysis) Short Campaign.
The experience gained with this data analysis led to the consideration in
chapter 4 of an optimized design for geodetic VLBI experiments. The
SCHED-module of DEGRIAS generates a schedule of observations starting from
visibility considerations for the sources and optimizing for slewing time.
The design of an observing session also has to be optimized with respect to
precision and reliability. The literature is mainly concerned with the
precision of geodetic VLBI, hence in this study, much attention has been
paid to its reliability. Simulation studies and analysis of real data has
uncovered estimates of magnitudes of errors that may be present in
individual observations, or in groups of observations, and which cannot be
detected by statistical testing. Based on studies performed on the network
designs for global networks from [Dermanis, 1977], for the MERIT Short
Campaign and for a possible European Geodynamics Network, the following
conclusions have been reached concerning the design of an experiment:
1. The reliability is generally poor due to the large difference between the
number of scheduled observations and the number of weighted observations in
the final Least Squares fit; small errors may therefore have a relatively
large impact on the final results for, for instance, station coordinates.
2. Low elevation observations (below about 10 degrees) should be excluded
from the VLBI schedule since the magnitude of the correction for
tropospheric refraction becomes less certain and since these observations
are of poor reliability.
3. For accurate measurements, the operation of a network with more than two
baselines (so that closed triangles can be formed) has the advantage of
improved likelihood of error detection and is therefore to be recommended.
4. Furthermore, it is concluded that much can be gained from a careful
design of the experiment with respect to precision and reliability, in
particular when the recommendation is followed to observe for 48 hours
instead of 24.
In chapter 5, the main computing models for geodetic VLBI are investigated.
As discussed in chapter 2, modelling of nutation in the kinematic model is a
troublesome aspect, together with refraction due to the wet component of the
troposphere and to the dry component at low elevations, and instrumental
effects. Ways of minimizing the risks of these errors have been sought by
considering alternative computing models. The model with the least number of
possible hypotheses for the description of the physical phenomena is the
geometric model. This model makes use only of
the simultaneity of measurements of several CO-observing baselines. The
idiosyncrasies of this model regarding precision and reliability are
discussed. On practical grounds, an intermediate model, called short-arc
computing model, is also presented, which models precession etc. only
during short intervals of time. Computing results with the three types of
models (geometric, short-arc, kinematic) are presented both for the European
Geodynamics Network and for the MERIT Short Campaign. It is concluded that
the geometric model - although very attractive from a theoretical point of
view - is hardly applicable in practice. The short-arc model, however, can
be considered as a promising alternative to the common kinematic one.
In Part II, a general approach is studied to combine and compare two sets of
3-dimensional Euclidean coordinates for a number of stations. The
differences in coordinates can, apart from their random character, be the
result of either a systematic bias between two applied measurement
techniques (intercomparison of techniques) or of a shift in position of one
or more of the stations (deformation analysis). It is concluded that any
comparison method should rest on a sound statistical basis. In chapter 6 an
approach to intercomparison, based on the similarity transformation, is
discussed which combines all the required qualities. The software developed
for this approach (called FUSION) is also described in this chapter. It has
been applied to analyse the differences between the Doppler and VLBI
coordinates determined in the ERIDOC campaign, which were comparable at the
0.5 metre level. FUSION has also been applied to the European Geodynamics
Network to establish what precision of measurement is required to detect
possible (tectonic) motions of stations in the Mediterranean area reliably.
Contents
Summary iii
Acknowledgements v
Part I. Geodetic VLBI
1. Introduction and scope 2
2. Standard computing model 13
3. 'DEGRIAS' software package 59
4. Design of VLBI experiment 90
5. Alternative computing models 114
Part II. Comparison of techniques
6. Network comparison 130
Part III. Concluding remarks
7. Conclusions & recommendations 148
Appendix 152