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05/28/02 AGU Spring 2002 1
Assessing the Compatibilityof Microwave Geodetic
SystemsProf. Thomas Herring
Room 54-611; [email protected]
http://bowie.mit.edu/~tah
05/28/02 AGU Spring 2002 2
Overview
• Examine the compatibility of VLBI and GPSsystems by comparing clock and atmosphericdelay estimates from the two systems
• Data Analyzed:– End of the CONT96 VLBI experiments– Common stations: Fairbanks, Wettzell, Kokee,
Nyales20. No GPS at NRAO station.– Additional 20 global stations used in GPS analysis
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VLBI and GPS Network
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Analysis Technique
• VLBI: CALC+SOLVK Kalman filter– Clock process noise consistent with 10-14 Alan
standard deviation at 1000 seconds; Quadraticterms removed apriori.
– Atmospheric process noise: Derived from delay-ratevariance: Typical random walk values 10mm/sqrt(hr); variations of factor of three about thisvalue
– Constant zenith delay based on station height andzero water vapor
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Analysis Technique
• GPS: GAMIT program– Clocks estimated epoch-by-epoch relative to
Fairbanks/Gilcreek clock– Phase clocks aligned with clocks from pseudo-
range estimates– Atmospheric delay estimated with piece-wise linear
function with nodes every 2-hours. Stochasticnoise 20 mm/sqrt(hr)
– Constant apriori zenith delay.
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Some effects that might be expected:Clock effects
• GPS is controlled by 10.23 MHz oscillators• On the Earth’s surface these oscillators are set to
10.23x(1-4.4647x10-10) MHz (39,000 ns/day ratedifference)
• This offset accounts for the change in potential andaverage velocity once the satellite is launched.
• The first GPS satellites had a switch to turn this effecton. They were launched with “Newtonian” clocks
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Corrections terms
• Propagation path curvature due to Earth’s potential (a fewcentimeters)
• Clock effects due to changing potential
• For e=0.02 effect is 47 ns (14 m)
†
Dt =2GM
c3 ln Rr + Rs + rRr + Rs - r
Ê
Ë Á
ˆ
¯ ˜
†
Dt =- GM
c2 e a sin E
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Relativistic Effects (SA off)
-50
-25
0
25
50
0 4 8 12 16 20 24
PRN 03 Detrended; e=0.02Clock - trend (ns)GR Effect (ns)
Cloc
k er
ror (
ns)
Time (hrs)
50 ns=15m
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Comparisons
• Atmospheric delays:– Easiest comparison because apriori zenith delay
chosen as constant and the same apriori used forVLBI and GPS
• Clocks:– Clocks are more difficult to compare because:
• No absolute standard for either system (show clocksrelative to Fairbanks/Gilcreek)
• VLBI has different quadratic removed each day. Clocksrelative to ensemble
• GPS also referred to Fairbanks. Only linear trend removedeach day.
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Fairbanks Atmospheric delays
-0.100
-0.050
0.000
0.050
0.100
0.150
260 265 270 275 280
Fairb
anks
Atm
osph
ere
(m)
1996 Day of year
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Wettzell Atmosphere
0.000
0.050
0.100
0.150
0.200
0.250
260 265 270 275 280
Wet
tzel
l Atm
osph
ere
(m)
1996 Day of year
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Zoom of Wettzell (Sep 19-20)
0.040
0.060
0.080
0.100
0.120
0.140
0.160
0.180
263 264 264 264 265 266 266
Wet
tzel
l Atm
osph
ere
(m)
1996 Day of year
GPS Day boundaries
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Zoom Wettzell (Sept 30-Oct 2)
0.040
0.060
0.080
0.100
0.120
0.140
0.160
0.180
274 275 276 277 278 279
Wet
tzel
l Atm
osph
ere
(m)
1996 Day of year
GPS Day boundaries
Notice ~2cmdeviations
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KOKEE Atmosphere
0.050
0.100
0.150
0.200
0.250
0.300
260 265 270 275 280
Koke
e At
mos
pher
e (m
)
1996 Day of year
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NyAlison Atmosphere
0.000
0.050
0.100
0.150
0.200
0.250
260 265 270 275 280
NyAl
ison
atm
osph
ere
(m)
1996 Day of Year
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Zoom of NyAlison (Sep 30-Oct 2)
0.000
0.020
0.040
0.060
0.080
0.100
274 275 276 277 278 279 280
NyAl
ison
atm
osph
ere
(m)
1996 Day of Year
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Clock comparisons
• Clock comparison are “complicated” by theremoval of trends from VLBI results (can becorrected but currently time-consuming).
• Absolute offsets can not be comparedbecause of VLBI group delay ambiguities; theGPS alignment of phase and range; unknowndelays in VLBI and GPS electronics
• Examine difference of Wettzell and Fairbanksclocks
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Wettzell-Fairbanks comparison
-0.60
-0.40
-0.20
0.00
0.20
0.40
264 266 268 270 272 274 276 278
Cloc
k of
fset
(m)
1996 Day of year
Green GPS; Brown VLBI
"Quadratic" in VLBI probably due to apriori quadratic in VLBI analysis
Linear trends removed each GPS day;Linear and quadratic (apriori) from VLBI each day
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Wettzell-Fairbanks with VLBI quadraticremoved
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
274 275 276 277 278 279
Wet
tzell-F
airba
nks c
lock (
m)
1996 Day of year
Likely phase connectionproblem in GPS
Zoom next figure
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Zoom area for Wettzell
-0.10
-0.05
0.00
0.05
0.10
278 278 278 279 279 279
Wet
tzell-F
airba
nks c
lock (
m)
1996 Day of year
Not clear why difference in behavior;GPS shows atmospheric delay fluctuation
not seen in VLBI estimates (separation problem?)
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Conclusions• Initial study of comparison between VLBI and GPS
clock parameters and atmospheric delay estimates.• Initial results indicate that clocks are comparable
quality (no smoothing in GPS)• Next steps:
– Accounting for clock rates and accelerations applied to VLBI– More consistency in mapping functions and gradients– Effects of model changes in GPS (antenna phase centers) on
clock comparisons– Time dependent process for GPS atmospheres (validation
using VLBI data)• Possible use of GPS atmospheres and clocks in the
analysis of VLBI?