Satellite Geodesy and Navigation Present and Futureexphy.uni-duesseldorf.de/Opt_clocks_workshop/Talks_Workshop... · Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program,

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


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


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


(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


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


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


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)


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.


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


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


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


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)


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!)


Atmosphere sounding using GPS

Profiles of the atmosphere temperature and specific humidity derived from radio-occultation technique.


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)


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!)


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.


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)


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.


Master clock in the Molniya type orbit?

Highly eccentric orbit. Clock stays over two positions for several hours.


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


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.

Documents

Satellite Geodesy and Navigation Present and Futureexphy.uni-duesseldorf.de/Opt_clocks_workshop/Talks_Workshop... · Workshop on an Optical Clock Mission in ESA's Cosmic Vision Program,