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OCR for page 114
The Accuracy of Position Determinations by
lILBI Expected by the Year 2 0 0 0
Alan E. E. Rogers
MIT Haystack Observatory
Westford, Massachusetts 01886
INTRODUCTION
Very-Long-Baseline Interferometry (VLBI) was first used for geodetic
measurements in 1972 following the development of VLBI in the late 1960s
for the astronomical study of radio sources whose angular size is a few
millarcseconds or less and whose structure cannot be resolved with
conventional connected element interferometers. In geodetic VLBI the
relative arrival time (see Figure 1) of signals from distant quasars is
measured by recording digitized samples on magnetic tape for cross-
correlation at a central processor. A hydrogen maser frequency standard
provides a precise frequency reference for the receiver's local
oscillators as well as a time standard for the digitization and data
formatting as illustrated in Figure 2. A delay precision which greatly
exceeds the inverse recorded bandwidth is achieved by recording 14 2 MHz
bandwidth channels from S- and X-band in a fashion illustrated in Figure
3. The method, which is known as "bandwidth-synthesis", (Rogers, 1970)
allows a very wide bandwidth to be spanned with acceptable delay
sidelobes and ambiguity spacing provided enough channels are available
with minimum redundancy in spacings. The S- and X-band channels are
used to provide separate group delays whose appropriate linear
combination provides a delay almost free of the ionospheric path delay.
A complete description of the MKIII VLBI system has been given by Clark
et al., (1985~.
Present Level of Accuracy. For the past eight years geodetic
measurements made using the MKIII have achieved centimeter level
repeatability in the measurement of baseline length. A statistical
analysis of the repeatability of 100 baselines measured by the NASA
Crustal Dynamics Project has been made by Clark, (1987~. The length
repeatability from this analysis is approximately given by 5 mm plus 2 x
10-9 times the length and Table 1 lists the repeatability of some of the
more frequently measured baselines. The fractional term is mostly the
result of an r.m.s. error in the vertical of about 2 cm which maps into
length in an amount which is proportional to length. Table 2 gives a
list of the various error sources which will be discussed in more detail
later. The root sum square (RSS) is approximately in agreement with
present experience.
System Noise. The signal to noise ratio (SNR) is given by
SNR = LAF(2BT) i12/~2KT3)
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115
where A is the effective antenna area (or geometric mean for antennas of
different sizes), F is the radio source flux, 2BT is number of data bits
recorded in integration time T. T3 is the system temperature, K is
Boltzman's constant, and L is a digital processing loss factor of about
0.6. The standard deviation in the estimate of group delay is equal to
the inverse of the product of SNR and r.m.s. spanned bandwidth (measured
in radians/sec) and is equal to 80 ps (2.4 cm) at X-band for 10-meter
antennas of 50 percent efficiency and 60-K system temperatures observing
a 1 Jansky (10~26 Wm~2 Hz-~) radio source with 200 seconds of integration
at the normal 56 Mbit/s data recording rate of the MKIII. Improved
receivers using High Electron Mobility Transistors (HEMT) are expected
to reduce system temperature to 30 deg K and improvements in recorder
technology already support a 512 Mbit/s rate. While the system noise is
not a major error source, its contribution is important in experiments
with weak geometry such as very long baselines for which the mutual
visibility is poor or experiments with small mobile antennas.
,`; . ,
Instrumental Calibration. Drifts in the receiver and cable delays are
calibrated by injecting pulses (about 30 ps duration) into the receiver
at a 1 MHz rate. These pulses generate a low-intensity rail of signals
spaced 1 MHz apart which, when mixed to video, are made to appear as 10-
KHz tones in the upper sideband passbands by offsetting the local
oscillators. Extraction of the phases of these tones in the data
processing serves to calibrate the the phase delay of each 2-MHz-wide
passband. At present some systems are limited by the presence of
spurious signals from the digital electronics which corrupts the phases
of the calibration tones. This limit will be reduced to a negligible
level by better isolation of the I.F. electronics. The electrical
length of the cable which feeds the calibrator is electronically
measured to allow correction for changes due to temperature or flexure.
Other Instrumental Errors. Antenna flexure and changes in the axis
intersection with tower expansion are significant error sources in some
of the larger antennas used as base stations although these errors can
be accurately modelled. A more subtle instrumental error source exists
in present systems which is due to the variation of group delay in the
antenna feed with position angle. Since the calibration signals are
injected after the feed, these errors go uncorrected. These errors are
the result of frequency dependent polarization impurities in the present
feed and can be isolated by examining the "closure" of delays measured
on a triangle of baselines.
Atmospheric Limits. As can be seen from the table, the atmosphere is
thought to be the largest error source. There are two distinctly
different methods currently employed to correct for the atmospheric path
delays. The first method is largely one of 'self-atmospheric
calibration'' in which the unmodelled "wet" atmospheric zenith delay
after correction of the data for the delay through the 'I cry" troposphere
is derived by least square analysis every few hours or for each
observation using a Kalman filter. In this method it is important to
include observations at low elevations to separate the atmospheric delay
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116
signature from the signature of a station height as illustrated in
Figure 4. In the second method the atmospheric delay for both dry and
wet components is calibrated by barometric pressure and water vapor
radiometry (WVR), respectively. The first or self-calibration method is
limited by errors in the dry atmospheric "mapping function" (Davis et
al., 1985), or elevation dependence which depends on the atmospheric
lapse rate and height of the troposphere as well as the pressure and
temperature at ground level. The second or direct calibration method is
also limited by a knowledge of the mapping function although not so
severely since low angle observations are not required and can be
avoided. In addition, the direct calibration is limited by the accuracy
of the ground pressure measurement needed to derive the dry atmosphere
zenith path and any breakdown in the assumption of hydrostatic
equilibrium used to derive the path length from ground pressure.
Further, the derivation of the wet delay from the WVR measurements
(Resch, 1984) is subject to errors due to the departure of the
atmosphere from the model assumed for the estimate of the "retrieval"
coefficients. Better site dependent algorithms for the conversion of
WVR data to wet path delay are now being developed. However, because
there may be a bias in the WVR determined wet delay or a bias in the dry
delay which results from barometer calibration errors or other unknown
cause, the direct method is usually combined with the estimation of a
bias for each experiment. At the present state of the art, the two
methods are producing almost the same level of accuracy or marginally
better results with the second method and the latest generation of WVRs
capable of measuring the wet delay to better than 1 cm as inferred from
the repeatability of results. Both methods assume azimuthal symmetry
for the dry delay and hence, are equally limited by the presence of
horizontal gradients. Perhaps the real promise for future improvements
will come with an understanding of the biases between WAR determined
path delays and the wet path delay solutions using VLBI data which may
well be errors in the model for the dry delay. In addition, the
incorporation of a horizontal gradient and mapping function parameters
in the self-calibration may improve results if there is enough
"geometric strength" in the data to allow for the estimation of
additional parameters which are highly correlated with existing
parameters.
The Very Long Baseline Array (VLBA). The National Radio Astronomy
Observatory (NRAO) under contract to the National Science Foundation
(NSF) is building an array of ten new 25-meter antennas to form a
network of stations dedicated to VLBI. The antennas which span the
United States, with antenna in Hawaii and another in the Virgin Islands
(see Table 3), will be equipped with the new generation of VLBI
electronics and recorders (which support a data rate up to 512 Mbit/s).
The VLBA will be used for both astronomy and geophysics. Geodetic VLBI
methods will be used to determine the station locations, earth rotation,
polar motion, earth tides, tectonic plate motion, ocean loading, other
geophysical parameters needed to provide the highest accuracy astrometry
which might, for example, be used to search for perturbations which
might indicate the presence of planets in orbit around nearby stars.
The ten VLBA antennas combined with an effective aperture of 79 meters
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117
or a single VLBA antenna using 256 Mbit/s recording could operate with
an ultracompact transportable VLBI system using an antenna as small as
one meter and reducing the cost of making high accuracy geodetic ties to
remote locations.
SUMMARY
At the present time atmospheric calibration is the dominant error
source and will probably remain as the ultimate limit. Instrumental
errors and errors due to source structure are likely to be reduced to a
negligible level in the next decade. It is likely that the fractional
accuracy of baseline length measurements will improve to 1 x 10-9 or
perhaps 5 x 10-~°.
ACKNOWLEDGEMENT
Geodetic VLBI research at the Haystack Observatory is supported by
the National Aeronautics and Space Administration under Contract
NAS-5-29120. Haystack Observatory has designed and prototyped data
acquisition and recording systems for the NRAO VLBA under Contract
AUI-216.
OCR for page 118
118
REFERENCES
Clark, T. A., et al.
Interferometer
438-449, 1985.
Clark, T. A.
Meeting,
, Precision Geodesy the MKIII Very-Long-Baseline
System, IEEE Trans
Presented at NASA's
October 1987.
.
Geosci. Remote
Sens., GE-23,
Crustal Dynamics Project Users
Davis, J. L., et al., Geodesy by Radio Interferometry: Effects of
Atmospheric Modeling Errors on Estimates of Baseline Length, Radio
Sci. Vol. 20, pp. 1593-1607, 1985.
Resch, G. M., Water Vapor Radiometry in Geodetic Application in Geodetic
Refraction, edited by F. K. Brunner, Springer-Verlag, New York,
1984.
Rogers, A. E. E., Very-Long-Baseline Interferometry with Large Bandwidth
for Phase-Delay Measurements,
1970.
Radio Sci., Vol. 5,
PP
1239-1248,
OCR for page 119
119
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OCR for page 120
120
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OCR for page 121
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1 1
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S-BAND
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FUNCTION
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Figure 3. SIX Frequencies Recorded for "Bandwidth Synthesis"
-
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122
ATMOSPHERIC DELAY
~SIGNATURE~ TAUZENITH=2.27 METERS
c
J
hJ
GEOMETRICAL DELAY ~SIGNATURE-
OF HEIGHT DFFSET CF 2.27 METERS
0 ELEVATION ANGLE S0
Figure 4. Atmospheric Delay Signature
Demonstrated \/L B ~ Baseline Repeat~ility
RMS Repeambility
.
I3aselinc Lcngth Lcngth Tr:lnsvcrsc
. kn1 nln, 111111
Mojavc - OVRO 245 ~6
Moja~c - hionu nlcn t Pc;, k 27 1 9 8
Mojavc - Vandcnbcrg | 351 l l l | 12
Onsale ~ WcttzcIt 920 S
OVRO - Ft. Davis IS08 9 8
~.
Mojavc - \Vcstrord 3904 8
Haystack - Onsala S600 IS
.
Present Levelof Accuracy
5mm plus 2 x 10-. times tl's length
Table 1. Demonstrated VLBI Baseline Repeatability
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123
ERROR SOURCES
.
Instrumentation:
Instr. noise(SNR~ 70)
Antenna hexure
ERROR EST.
~ 5,nm
<5 mm ~ vertical
- ~
i
Lower system temperatures and
Aver according rates frill improve |
-
~mpors~t for large as~tennas -
can be motelled
can be modelled
Antenna tower e~cp~ion
Spurious sign^/cal errors
Polarization impurity
Cloci; instability
Ionosphere
Source structure
_ _
~ a mm
_ ..
_ ~ 5 trim
_
_ e: 2 ~
_
I_ be
_ ~ ~ =:~-~V
2 Am
a: 1 mm
(1 x 10_14 ~r 10 [L Ia ~
. - ~
= 2 Am
can be corsected
VLBA will make better mans
Atmosphere:
dry troposphere
lOmm in vertical
needs better pressure calibration
(hydrostatic equib. errors?)
estimate additional prompters
(improved WAR al~onmthms)
·~e ~ ch 1:-=~ Lite:
may be tegrated by
weal zeometn
. ~,
mapping function
(or wet troposphere)
hon20ntal gradients
RSS
~lOr~:nvati~
2 mm
20m~n ~ vertical
8mm tra~s~rerse
,
Table 2. Error Sources for Geodetic VLBI
LOCATION N LAI1TUDE A L:OtIGI~uE ELEVATION CONS
~ deg,~in, sec ~ Din. sec ~ (~;NSL1
Pie Town, NM 34 18 03.61 108 07 07.242371 First VLll in B7
Kitt Peak, AZ 31 S7 22.39 111 36 42.26 1916 antenna complete
Lo' Altos ,NK 3S 66 30.33 106 14 42.01 1967 co~lotc in 88
tI. Liberty, ~41 46 17.03 91 34 26. IS 241 complete in 88
Brewster, HA 48 07 S2.80 119 60 SS.34 2SS complete in 89
Fort Davis ,SX 30.63 103.94 161S complete in 89
St. Crolx, VI 1?.7S 66.60 IS bcts`6 acquired
Acne Velley,CA 3?.23 118.28 123S being acquired
t2~ Lee, HI 19. SA lSS.61 3200 negotiating alte
.Horehe ss e ~ne~,otlatlng s 1 ee
Table 3. VLBA Site Locations and Status Nov 87
Representative terms from entire chapter:
atmospheric delay
