Drazen Svehla_Vision.pdf - Quantum Optics and Relativity

Satellite Geodesy and Navigation
Present and Future
Drazen Svehla
Institute of Astronomical and Physical Geodesy
Technical University of Munich, Germany
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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� Clocks for navigation
Content
� Relativistic geodesy on the ground
� Planetary relativistic geodesy
� Clocks for GPS radio-occultation and GPS altimetry
� Can clock improve the GPS receiver performance?
� Master clock in the Molniya type orbit
� Pioneer anomaly – two master clocks in the planetary mission
� Master clocks in Lagrange points: Planetary Navigation System
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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GPS Satellite Clocks
• GPS satellite clock variations can easily reach several nanoseconds!
• For the real time GPS applications we need a possibility to predict clock variation with an
accuracy below 1 cm for a period of 1 hour (

(Colorado Springs – USNO)
Root
drift 1/ f
Ground Phase Clocks
≈ 200 s
≈ 200 s
white noise
Only phase clocks estimated.
Troposphere (TZD), station coord., EOPs,
etc., fixed to IGS
Clear white noise up to 200 s
and frequency drift with 1/f
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
(2.9×10 -16 /day)
≈ 7 mm
Stability of GPS
receiver and
H-maser
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A
E A
B
B
Relativistic Geodesy on the Ground
B’
B’’
geoid
ellipsoid
B C E
... ...
C = C + gdn + gdn + gap + gdn
∫
H = gdn
spirit leveling
∫ ∫ ∫
A B D
random walk effect
50 m
ACES
MW-link
C D
B
B′
Ellipsoid: Geometry measured with GPS
HGeoid:
Gravity measured with gravimetry (clocks)
ACES to help in the:
→ realization of the World height system
→ combination of space/ground gravimetry
Clocks can be used to determine in situ geopotential numbers globaly
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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E

Degree Standard Deviations in Geoid Heights [m]
10 -1
10 -2
10 -3
10 -4
10
10
20
20
CHAMP & GRACE Gravity Field Models
CHAMP Mean Fields
30
1cm ≈ 0.1m 2 /s 2
30
Degree
Error degree variances
for CHAMP and GRACE gravity fields
40
40
50
EIGEN-3P error un-calibrated
TUM2S error un-calibrated
EIGEN-3P minus TUM2S
EIGEN-3P minus ITG-CHAMP01S
TUM2S minus ITG-CHAMP01S
CHAMP prediction
2
m
1 cm /1000km → 0.1 /1000km
2
s
50
60
60
10 -1
10 -2
10 -3
10 -4
Degree
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Degree Standard Deviations in Geoid Heights [m]
10 -1
10 -2
10 -3
10 -4
10 -5
GRACE Combined Mean Fields
50
1cm ≈ 0.1m 2 /s 2
50
100
100
150
(Gruber 2005)
GGM2C error calibrated
EIGEN-CG03C error calibrated
GGM2C minus EIGEN-CG03C
GRACE prediction
150
2
m
1 cm / 400km → 0.1 / 400km
2
s
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10 -1
10 -2
10 -3
10 -4
10 -5

spherical
harmonics
degree/order
=100
EGM96
(Gruber 2005)
Latitude
Comparison with GPS-levelling geoid heights
Latitude
0
0
10
10
20
20
Longitude
30
30
39.9999
70 70
60 60
50 50
40 40
39.9999
-1.29 -1.09 -0.89 -0.69 -0.49 -0.29 -0.09 0.11 0.31 0.51 0.71
230 240 250 260 270 280 290 300
60 60
50 50
40 40
30 30
20 20
230 240 250 260 270 280 290 300
Longitude
-0.95 -0.75 -0.55 -0.35 -0.15 0.05 0.25 0.45 0.65 0.85 1.05
1 m ≈ ∆f/f=1·10 -16
20
Longitude
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Latitude
Latitude
0
0
10
10
20
30
30
39.9999
70 70
60 60
50 50
40 40
39.9999
-1.29 -1.09 -0.89 -0.69 -0.49 -0.29 -0.09 0.11 0.31 0.51 0.71
GRACE
EIGEN-CG03C
230 240 250 260 270 280 290 300
60 60
50 50
40 40
30 30
20
230 240 250 260 270 280 290
20
300
Longitude
-0.95 -0.75 -0.55 -0.35 -0.15 0.05 0.25 0.45 0.65 0.85 1.05
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GPS-
Levelling
Data Set
Comparison with GPS-Levelling Geoid Heights
• Model up to d/o 60
• Omission error from d/o 61 to d/o 720 estimated from GPM98 model
(Wenzel)
• GRACE models: GGM02S, GGM02C, EIGEN-GRACE02S, EIGEN-CG03C,
Monthly models for 2004-03.
• Editing criteria: 3*sigma
0.5 m ≈∆f/f=5·10 RMS [m]
-17
Num.
Points
EGM96 TUM2S
(CHAMP)
EIGEN-
3P
GRACE
Models
USA 5139 0.400 0.441 0.401 0.400
Canada 1564 0.477 0.515 0.474 0.467
Europe 177 0.372 0.298 0.250 0.237
Germany 660 0.255 0.173 0.124 0.155
Australia 195 0.495 0.524 0.500 0.469
Japan 828 0.512 0.482 0.476 0.491
* GPS-Levelling Data for Australia, Japan and Germany provided by AUSLIG, Japanese Geographical
Survey Institute and BKG respectively. Contributions are gratefully acknowledged.
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
(Gruber 2005)
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Planetary Relativistic Geodesy
Too high requirements for the clock stability over short time inerval
Gravity Frequency Shift measurements
between space & ground clocks
Gravity Frequency Shift measurements
between space clocks
relative clock stability over short time
(e.g. 10 -18 /10 min) is essential !!!
GRACE concept (intersatellite laser link) is much more accurate
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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Doppler:
Standard IGS
corrections:
f
f
r
r
Relativistic Geodesy in Space
−
−
f
f
0
0
=
=
−V
r
r
+ v
2
r
/ 2 + Φ
2
c
rr
2GM
⎛ 1 1 ⎞1
− Nvr
2 ⎜ − ⎟ rr
c ⎝ a r ⎠1
− Nv
0
+ 2GM
/ a + 2V
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
j
/ c
/ c
constant periodic
Correction in the GPS
satellite clock
frequency:
38.575008 µs/day
nominal semi-major
axis ≈26 561km
j
rr
1−
Nvr
rr
1−
Nv
j
/ c
/ c
Eccentricity correction:
-2(a·GM) 0.5 /c 2 ·e·sinE
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Improved Relativistic GPS Clock Corrections
constant periodic
GPS Satellite Phase Clocks
Phase clocks for GPS (PRN 14) STD=0.120 ns
additional constant and periodic
correction due to
variable semi-major axis and J 2
Relativistic model accurate to ≈15ps
periodic constant
estimated 6h signal
6h periodic correct.
0 24
Value computed without
correction
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
excellent
agreement with
real data
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Relativistic Geodesy in Space
Assumption: GPS satellite in
the Molniya type orbit
(orbit eccentricity increased)
How accurately we could estimate e.g. semi-major axis of the Earth?
GPS altitude: a=26 550 km e=0.7 + clock (10 -16 /day) → RMS(a)=9 m
+ clock (10 -18 /day) → RMS(a)=0.09 m
GM
ISS altitude: a=6770 km e=0.7 + clock (10 -16 /day) → RMS(a)=4 m
+ clock (10 -18 /day) → RMS(a)=0.04 m (today ±0.10 m)
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
da
=
a
c
e
2
dt
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Clocks for GPS radio-occultation
• improving performances of the GPS tracking (weak signal, cycle-slips)
• use of the zero-difference approach → no need for the “slave” GPS satellite to
remove receiver clock parameter
•clocks of high stability over short periods (< 5 min are essential!)
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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Atmosphere sounding using GPS
Profiles of the atmosphere temperature and specific humidity derived from radio-occultation technique.
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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GPS
reflectometry
Clocks for GPS altimetry
CHAMP
Jason-1 nadir observations at Dec. 26,
2004 between 02:15 and 02:40 UTC
predicted GPS reflection events
as seen by a fictious GPS
receiver onboard Jason-1
GPS precise orbit
determination
radar
altimetry
Jason-1
GPS altimetry is not limited to nadir
observations (e.g. JASON-1)
Slide taken from (Helm et al 2006)
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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Clocks for GPS reflectometry (altimetry)
TEC map 200/2002 and ISS Orbit
52°
-52°
•determination of the ocean heights, wind speed (scatterometry) and tsunami detection
•Extreme Earth’s events (tsunami, hurricanes) are taking place in the equator region.
•reflected signal could be tracked in open-loop mode without the need of the direct signal
(zero-difference approach)
• improving performances of the GPS tracking (weak signal, cycle-slips)
•clocks of high stability over short periods (< 5 min are essential!)
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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σ
PLL
Can clock improve GPS receiver performance?
360
=
2π
thermal noise
Bn c / n
0
( 1
1
+
2Tc
/ n
B n = carrier loop bandwidth
0
)
oscillator phase noise
σ ( τ ) f
144
dynamic stress error
(signal line of sight
acceleration)
dR
= 0.
2809
A L
θ A2
= e2
2
B
B
n
n
•Tracking thresholds and GPS measurements errors are closely related, because the
receiver loses lock when the measurement errors exceed a certain boundary.
•Narrowing the loop bandwidth decreases the thermal noise and oscillator phase noise,
however dynamic stress error is increased, but signal dynamics can be predicted.
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
θ
2
/ dt
2
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Can clock improve GPS receiver performance?
Kinematic POD GRACE-A
GRACE GPS Baseline
with FIXED ambiguities
RMS= 2.8 mm
Time in hours
(Status 2003-2004)
Compared to CHAMP results are by at least
factor of 2 better (ultra-stable clock)
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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Pioneer Anomaly – clocks in the
planetary mission?
Pioneer 10 & 11 discovered the “gravity” anomaly in the solar system.
Several groups try to resolve the problem.
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
link
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Master clock in the
Molniya type orbit?
Highly eccentric orbit. Clock stays over two positions for several hours.
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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Master clocks in Lagrange Points
Planetary Navigation System
link
Sun
L1 (Earth-Sun)
International Cometary Explorer
Genesis
WIND
The Solar and Heliospheric Observatory (SOHO)
The Advanced Composition Explorer (ACE)
LISA Pathfinder
Earth
L2 (Earth-Sun)
Wilkinson Microwave Anisotropy Probe (WMAP)
James Webb Space Telescope (JWST)
The ESA Herschel Space Observatory
The ESA Planck Surveyor
The ESA Gaia probe
The NASA Terrestrial Planet Finder mission
The ESA Darwin mission
5 stable Lagrange points in
the two-body system
(Earth-Moon or Earth-Sun)
By just one clocks in e.g. L1 or
L2 the max. Earth baseline of
some 12 000 km can be
extended up to 1 500 000 km
for Earth-Sun system or
300 000 km for Earth-Moon
system
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
L2 (Earth-Moon)
TDRS
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Conclusions
1. The main applications of clocks in geodesy is precise navigation and timing.
2. Relativistic geodesy on the ground is a very promising method to bridge the gap
between geometrical navigation and gravity field determination in establishing
homogeneous World height system.
3. For relativistic planetary geodesy a highly stable clocks over a short period of
time would be essential. The GRACE concept is much more accurate.
4. ACES + GPS radio-occultation + GPS altimetry are new applications
5. Clocks can improve GPS receiver performance
6. Master clock in the Molniya type orbit
7. Two clocks in the PIONEER 10&11 orbit?
8. Planetary Navigation System is proposed based on clocks in the Lagrange
points. This could cover geodesy part of the mission.
Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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