Satellite Geodesy and Navigation Present and Future Drazen Svehla Institute of Astronomical and Physical Geodesy Technical 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
Ground Phase Clocks (Colorado Springs USNO) (2.9 10-16 /day) 7 mm Stability of GPS receiver and H-maser Root 200 s Only phase clocks estimated. Troposphere (TZD), station coord., EOPs, etc., fixed to IGS white noise drift 1/ f 200 s Clear white noise up to 200 s and frequency drift with 1/f
spirit leveling Relativistic Geodesy on the Ground ACES MW-link B B geoid C D A B ellipsoid 50 m E B C E C = C + gdn + gdn +... gap... + gdn H E = B A gdn A B D random walk effect 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
CHAMP & GRACE Gravity Field Models Error degree variances for CHAMP and GRACE gravity fields Degree Standard Deviations in Geoid Heights [m] CHAMP Mean Fields 10 20 30 40 50 60 10-1 10-1 10-2 10-2 10-3 10-3 10-4 10-4 10 20 30 40 50 60 Degree 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 Degree Degree Standard Deviations in Geoid Heights [m] GRACE Combined Mean Fields 1cm 0.1m 2 /s 2 1cm 0.1m 2 /s 2 50 100 150 10-1 10-1 10-2 10-2 10-3 10-3 (Gruber 2005) 10-4 10-4 GGM2C error calibrated EIGEN-CG03C error calibrated GGM2C minus EIGEN-CG03C GRACE prediction 10-5 10-5 50 100 150 2 m 1 cm / 400km 0.1 / 400km 2 s
spherical harmonics degree/order =100 Comparison with GPS-levelling geoid heights Latitude 0 10 20 30 39.9999 70 70 60 60 1 m f/f=1 10-16 Latitude 0 10 20 30 39.9999 70 70 60 60 50 50 50 50 EGM96 (Gruber 2005) 40 40 0 10 20 30 39.9999 Longitude -1.29-1.09-0.89-0.69-0.49-0.29-0.09 0.11 0.31 0.51 0.71 40 40 0 10 20 30 39.9999 Longitude -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 60 230 240 250 260 270 280 290 300 60 60 50 50 50 50 Latitude 40 40 Latitude 40 40 30 30 30 30 20 20 230 240 250 260 270 280 290 300 Longitude 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 1.05-0.95-0.75-0.55-0.35-0.15 0.05 0.25 0.45 0.65 0.85 1.05
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 10-17 RMS [m] 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. (Gruber 2005)
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
Relativistic Geodesy in Space Doppler: f f r r f f 0 0 = = V r 2GM 2 c r + v 2 r / 2 + Φ 0 2 c 1 1 1 a r 1 + 2GM rr Nv rr Nv r j / c / c / a + 2V j 1 1 rr Nv rr Nv r j / c / c 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 /c 2 e sine
Improved Relativistic GPS Clock Corrections constant periodic additional constant and periodic correction due to variable semi-major axis and J 2 Relativistic model accurate to 15ps periodic constant GPS Satellite Phase Clocks Phase clocks for GPS (PRN 14) STD=0.120 ns Value computed without correction estimated 6h signal 6h periodic correct. excellent agreement with real data 0 24
Relativistic Geodesy in Space Assumption: GPS satellite in the Molniya type orbit (orbit eccentricity increased) a da = GM c e 2 dt 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 altimetry 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 Jason-1 GPS reflectometry CHAMP radar altimetry 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? thermal noise 360 B σ = n (1 PLL 2 c / n + π 1 2Tc / 0 n 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 θ 2 / dt 2 B n = 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.
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)
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 link Sun Earth 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 L1 (Earth-Sun) International Cometary Explorer Genesis WIND The 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 Observatory The ESA Planck Surveyor The ESA Gaia probe The NASA Terrestrial Planet Finder mission The 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.