iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Satellite Geodesy and Navigation Satellite Geodesy and Navigation Present and FuturePresent and Future
Drazen Svehla
Institute of Astronomical and Physical GeodesyTechnical University of Munich, Germany
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Content
Clocks for navigation
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
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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 (<10-14 / 3600s or <33ps/3600s) → ACES M-maser
• GALILEO satellites to use H-maser
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
(Colorado Springs – USNO)
Only phase clocks estimated. Troposphere (TZD), station coord., EOPs, etc., fixed to IGS
Ground Phase Clocks
(2.9×10-16/day)
≈ 7 mm
Stability of GPS receiver and
H-maser
≈ 200 s
drift 1/ f
Root
white noise
≈ 200 s
Clear white noise up to 200 s
and frequency drift with 1/f
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Relativistic Geodesy on the Ground
geoid
ellipsoidB’’
B’
B
A
C D
E
... ...B C E
E AA B D
B
BB
C C gdn gdn gap gdn
H gdn
H′
= + + + +
=
∫ ∫ ∫
∫Ellipsoid: Geometry measured with GPSGeoid: Gravity measured with gravimetry (clocks)
Clocks can be used to determine in situ geopotential numbers globaly
random walk effect
ACESMW-link
spirit leveling
50 m
ACES to help in the:→ realization of the World height system → combination of space/ground gravimetry
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
CHAMP & GRACE Gravity Field Models
Error degree variances for CHAMP and GRACE gravity fields
Degree
Deg
ree
Sta
ndar
dD
evia
tions
inG
eoid
Hei
ghts
[m]
10
10
20
20
30
30
40
40
50
50
60
60
10-4 10-4
10-3 10-3
10-2 10-2
10-1 10-1
EIGEN-3P error un-calibratedTUM2S error un-calibratedEIGEN-3P minus TUM2SEIGEN-3P minus ITG-CHAMP01STUM2S minus ITG-CHAMP01SCHAMP prediction
Degree
Deg
ree
Sta
ndar
dD
evia
tions
inG
eoid
Hei
ghts
[m]
50
50
100
100
150
150
10-5 10-5
10-4 10-4
10-3 10-3
10-2 10-2
10-1 10-1
GGM2C error calibratedEIGEN-CG03C error calibratedGGM2C minus EIGEN-CG03CGRACE prediction
CHAMP Mean Fields GRACE Combined Mean Fields
(Gruber 2005)
2
21 /1000 0.1 /1000mcm km kms
→2
21 / 400 0.1 / 400mcm km kms
→
1cm ≈ 0.1m2/s2
1cm ≈ 0.1m2/s2
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Comparison with GPS-levelling geoid heights
GRACEEIGEN-CG03C
spherical harmonicsdegree/order=100
EGM96Longitude
Latit
ude
0
0
10
10
20
20
30
30
39.9999
39.9999
40 40
50 50
60 60
70 70
-1.29 -1.09 -0.89 -0.69 -0.49 -0.29 -0.09 0.11 0.31 0.51 0.71
Longitude
Latit
ude
0
0
10
10
20
20
30
30
39.9999
39.9999
40 40
50 50
60 60
70 70
-1.29 -1.09 -0.89 -0.69 -0.49 -0.29 -0.09 0.11 0.31 0.51 0.71
Longitude
Latit
ude
230
230
240
240
250
250
260
260
270
270
280
280
290
290
300
300
20 20
30 30
40 40
50 50
60 60
-0.95 -0.75 -0.55 -0.35 -0.15 0.05 0.25 0.45 0.65 0.85 1.05
Longitude
Latit
ude
230
230
240
240
250
250
260
260
270
270
280
280
290
290
300
300
20 20
30 30
40 40
50 50
60 60
-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
(Gruber 2005)
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Comparison with GPS-Levelling Geoid Heights
GPS-LevellingData Set
Num.Points
EGM96 TUM2S(CHAMP)
EIGEN-3P
GRACE Models
USA 5139 0.400 0.441 0.401 0.400Canada 1564 0.477 0.515 0.474 0.467Europe 177 0.372 0.298 0.250 0.237Germany 660 0.255 0.173 0.124 0.155Australia 195 0.495 0.524 0.500 0.469Japan 828 0.512 0.482 0.476 0.491
• 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
RMS [m]0.5 m ≈ ∆f/f=5·10-17
(Gruber 2005)
* GPS-Levelling Data for Australia, Japan and Germany provided by AUSLIG, Japanese Geographical Survey Institute and BKG respectively. Contributions are gratefully acknowledged.
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Planetary Relativistic GeodesyToo 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
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Relativistic Geodesy in Space
cvNcvN
racGMff
cvNcvN
cVaGMvV
ff
j
rr
j
rjrrr
/1/1112
/1/12/22/
20
20
2
0
rrrr
rrrrr
−−
⎟⎠⎞
⎜⎝⎛ −=−
−−++Φ++−
=−Doppler:
constant periodic
Standard IGS corrections:
Correction in the GPS satellite clock
frequency: 38.575008 µs/day
nominal semi-major axis ≈26 561km
Eccentricity correction:
-2(a·GM)0.5/c2·e·sinE
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Improved Relativistic GPS Clock Correctionsconstant periodic
periodic constant
additional constant and periodic correction due to
variable semi-major axis and J2
Relativistic model accurate to ≈15ps
6h periodic correct.estimated 6h signal
Phase clocks for GPS (PRN 14) STD=0.120 ns
0 24
GPS Satellite Phase Clocks
excellent agreement with
real data
Value computed without correction
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Relativistic Geodesy in Space
Assumption: GPS satellite in the Molniya type orbit
(orbit eccentricity increased)
dtec
GMada
2
=
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
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)
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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!)
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Atmosphere sounding using GPS
Profiles of the atmosphere temperature and specific humidity derived from radio-occultation technique.
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Clocks for GPS altimetryJason-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
Jason-1
CHAMP
radar altimetry
GPS reflectometry
GPS precise orbit determination
GPS altimetry is not limited to nadir observations (e.g. JASON-1)
Slide taken from (Helm et al 2006)
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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!)
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Can clock improve GPS receiver performance?
oscillator phase noisedynamic stress error(signal line of sight
acceleration)
n
LAA B
f)(1442τσθ = 2
22
2/2809.0n
e BdtdR
=θ
thermal noise
)/2
11(/2
360
00 nTcncBn
PLL +=π
σ
Bn = carrier loop bandwidth
•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.
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
GRACE GPS Baseline with FIXED ambiguities
RMS= 2.8 mm
Time in hours(Status 2003-2004)
Kinematic POD GRACE-ACan clock improve GPS receiver performance?
Compared to CHAMP results are by at least factor of 2 better (ultra-stable clock)
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Pioneer Anomaly – clocks in the planetary mission?
link
Pioneer 10 & 11 discovered the “gravity” anomaly in the solar system. Several groups try to resolve the problem.
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Master clock in the Molniya type orbit?
Highly eccentric orbit. Clock stays over two positions for several hours.
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
Master clocks in Lagrange Points Planetary Navigation System
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
Earth
Sun
link
L1 (Earth-Sun)International Cometary ExplorerGenesisWINDThe Solar and Heliospheric Observatory (SOHO)The Advanced Composition Explorer (ACE)LISA Pathfinder
L2 (Earth-Sun)Wilkinson Microwave Anisotropy Probe (WMAP) James Webb Space Telescope (JWST) The ESA Herschel Space ObservatoryThe ESA Planck SurveyorThe ESA Gaia probe The NASA Terrestrial Planet Finder missionThe ESA Darwin mission
L2 (Earth-Moon)TDRS
iapgWorkshop on an Optical Clock Mission in ESA's Cosmic Vision Program, Düsseldorf, March 8 - 9, 2007
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.