modeling earth radiation pressure and its impact on gps orbits and ground tracking stations
Post on 02-Feb-2016
28 Views
Preview:
DESCRIPTION
TRANSCRIPT
Institute for Astronomical and Physical Geodesy 1
Newcastle, 30.06.2010
Modeling Earth radiation pressure
and its impact on
GPS orbits and ground tracking stations
Carlos Rodriguez-Solano
Urs Hugentobler
Peter Steigenberger
Tim Springer
Bernese GPS Software NAPEOS Software
Institute for Astronomical and Physical Geodesy 2
Newcastle, 30.06.2010
1 Motivation
● GPS – SLR orbit anomaly: 4 – 5 cm
● SLR residuals for GPS satellites (mean subtracted) in a Sun-fixed reference frame show a peculiar pattern:
Urschl et al. (2008)l
Angle satellite – Earth – Sun:
.coscoscos 0 u
Institute for Astronomical and Physical Geodesy 3
Newcastle, 30.06.2010
1 Motivation
● More recently …
● SLR range residuals based on reprocessed ESOC orbit series 1995.0 – 2009.0
● SLR and GPS agree very well!
● Only a small bias (~1.8 cm) and eclipse season (attitude) effects remain
Institute for Astronomical and Physical Geodesy 4
Newcastle, 30.06.2010
1 Motivation
● Orbit-related frequencies on geodetic time series GPS draconitic year
● Station coordinates
(> 200 IGS sites).
Also computed by:
Ray et al. (2009)
● Geocenter position.
Also pointed out by:
Hugentobler et al. (2006)
● 9 years of tracking data: 2000.0 – 2009.0
13.65 ± 0.02 daysPenna et al. (2007):13.66 days
Institute for Astronomical and Physical Geodesy 5
Newcastle, 30.06.2010
2 Earth Radiation Model
● Computation of Irradiance [W/m2] at satellite position, assuming:
– Earth scattering properties approximated as a Lambertian sphere
– emitted and reflected radiation infrared and visible radiation
● Types of models:
1) Analytical: Constant albedo, Earth as point source only radial acceleration:
2) Numerical: Constant albedo, finite Earth radius
3) Latitude-dependent reflectivity and emissivity
4) Latitude-, longitude- and time-dependent reflectivity and emissivity from NASA CERES project
r
hR
EAhE
E
sunEAERM ˆ
4
1sincos
3
2,
22
AE = πRE2, RE = 6378 km, ESUN = 1367 W/m2, h = satellite altitude, α = albedo (≈ 0.3)
Institute for Astronomical and Physical Geodesy 6
Newcastle, 30.06.2010
● CERES (Clouds and Earth's Radiant Energy System)
NASA EOS project
Reflectivity
Emissivity
● CERES data, monthly averages, July 2007
http://science.larc.nasa.gov/ceres/
2 Earth Radiation Model
Institute for Astronomical and Physical Geodesy 7
Newcastle, 30.06.2010
Min.
Diff.:
Max.
Diff.:
-3.2% +3.7%
-6.7% +10.8%
-7.4% +14.0%
E4: CERES data(August 2007)
E3: Latitude dependency
E2: Numerical, constant albedo
E1: Analytical, constant albedo
2 Earth Radiation Model
Institute for Astronomical and Physical Geodesy 8
Newcastle, 30.06.2010
3 GPS Satellite Model
● Box-wing model
● Three main satellite surfaces:1) +Z side, pointing always to the Earth2) Front-side of solar panels, pointing always to the Sun3) Back-side of solar panels
● Main dependency on angle ψ satellite – Earth – Sun
Institute for Astronomical and Physical Geodesy 9
Newcastle, 30.06.2010
4 Acceleration on the Satellites
● Earth radiation and satellite models of increasing complexityfor PRN06 and β0 = 20.2°
Along track acceleration [m/s2]
Cross track acceleration [m/s2]Radial acceleration [m/s2]
Institute for Astronomical and Physical Geodesy 10
Newcastle, 30.06.2010
● Key factors can be already identified:- No large differences between Earth radiation models
- Analytical box-wing model with block specific optical properties and with antenna thrust
● Most important factor box-wing (solar panels change drastically w.r.t. the Earth over one revolution)
● Magnitude of acceleration compared to solar radiation pressure is just 1-2 %
● But if the change of acceleration (minimum to maximum) is compared the effect is up to 20% of the solar radiation pressure
Solar radiation pressure solar panels are fixed, bus changes orientationEarth radiation pressure bus is fixed, solar panels change orientation
● Comparable to Y-bias effect (1x10-9 m/s2)
4 Acceleration on the Satellites
Institute for Astronomical and Physical Geodesy 11
Newcastle, 30.06.2010
● Implementation of a priori acceleration in the Bernese GPS Software
● Computation of GPS orbits as done by CODE for one year (2007) of tracking data
● Orbit differences = perturbed orbit (with albedo) – reference orbit (without albedo)
● Simplest model
● Earth radiation:
- Analytical
● GPS satellite:
- Cannon-ball
PRN05
PRN06
5 Impact on the Orbits
Institute for Astronomical and Physical Geodesy 12
Newcastle, 30.06.2010
● Implementation of apriori acceleration in the Bernese GPS Software
● Computation of GPS orbits as done by CODE for one year (2007) of tracking data
● Orbit differences = perturbed orbit (with albedo) – reference orbit (without albedo)
● Most complex model
● Earth radiation:
- CERES data
● GPS satellite:
- Num. Box-Wing
- Block specific
- Antenna thrust
PRN05
PRN06
5 Impact on the Orbits
Institute for Astronomical and Physical Geodesy 13
Newcastle, 30.06.2010
● Orbit differences = perturbed orbit (with albedo) – reference orbit (without albedo)
● Comparable with SLR – GPS residuals in a Sun-fixed reference frame (β0 and ∆u)
5 Impact on the Orbits
Urschl et al. (2008)
Institute for Astronomical and Physical Geodesy 14
Newcastle, 30.06.2010
● SLR validation: SLR measurements – GPS orbits
● SLR-GPS orbit anomaly mean reduction of 16 mm - 1.1 cm albedo (TUM, ESA) - 0.5 cm antenna thrust (TUM)
5 Impact on the Orbits
● TUM:
● ESA:
Institute for Astronomical and Physical Geodesy 15
Newcastle, 30.06.2010
6 Impact on the Ground Stations
Institute for Astronomical and Physical Geodesy 16
Newcastle, 30.06.2010
6 Impact on the Ground Stations
● Change of spectra for the North coordinates, > 200 IGS sites and 9 years of tracking data
● Main reduction on the sixth peak
● Where the other peaks come from? Solar radiation pressure?
● Why this pattern on the North stations residuals?
Institute for Astronomical and Physical Geodesy 17
Newcastle, 30.06.2010
● Orbit residuals (NORTH) as a function of latitude and DOY
● Mainly effect of cross-track component orientation of solar panel
● Almost direct effect of the orbits (cross-track) on the ground stations positions
● Systematic “deformation” of the Earth
6 Impact on the Ground Stations …and Orbits
Institute for Astronomical and Physical Geodesy 18
Newcastle, 30.06.2010
7 Impact on the LOD
● Change of Length of Day (LOD) due to Earth radiation pressure around 10 µs
● Effect on other geodetic parametersimportance of orbit modeling
Institute for Astronomical and Physical Geodesy 19
Newcastle, 30.06.2010
● Earth radiation pressure has a non-negligible effect on GPS orbits (1x10-9 m/s2) comparable to Y-bias on ground stations (mainly North) at the submillimeter level
● Albedo causes a mean reduction of the orbit radius of about 1 cm
● The largest impact in periodic variations is caused by the solar panels Use of a box-wing satellite model is a must
● Different Earth radiation models as well as satellite model details have a small impact on the orbits
● Albedo can partially explain the peculiar pattern observed in SLR residuals ● Recommendation for an adequate but simple modelling:
Earth radiation model with CERES data (or alternatively the analytical model for constant albedo) Analytical box-wing model with block specific optical properties and with antenna thrust
8 Conclusions
Institute for Astronomical and Physical Geodesy 20
Newcastle, 30.06.2010
9 References
Fliegel H, Gallini T, Swift E (1992) Global Positioning System Radiation Force Model for Geodetic Applications. Journal of Geophysical Research 97(B1): 559-568
Fliegel H, Gallini T (1996) Solar Force Modelling of Block IIR Global Positioning System satellites. Journal of Spacecraft and Rockets 33(6): 863-866
Hugentobler U, van der Marel, Springer T (2006) Identification and mitigation of GNSS errors. Position Paper, IGS 2006 Workshop Proceedings
Knocke PC, Ries JC, Tapley BD (1988) Earth radiation pressure effects on satellites. Proceedings of AIAA/AAS Astrodynamics Conference: 577-587
Press W, Teukolsky S, Vetterling W, Flannery B (1992) Numerical Recipes in Fortran 77, 2nd edn. Cambridge University Press
Ray J, Altamimi Z, Collilieux X, van Dam T (2008) Anomalous harmonics in the spectra of GPS position estimates. GPS Solutions 12: 55-64
Rodriguez-Solano CJ, Hugentobler U, Steigenberger P (2010) Impact of Albedo Radiation on GPS Satellites. IAG Symposium – Geodesy for Planet Earth, accepted
Urschl C, Beutler G, Gurtner W, Hugentobler U, Schaer S (2008) Calibrating GNSS orbits with SLR tracking data. Proceedings of the 15th International Workshop on Laser
Ranging: 23-26
Ziebart M, Sibthorpe A, Cross P (2007) Cracking the GPS – SLR Orbit Anomaly. Proceedings of ION-GNSS-2007: 2033-2038
Institute for Astronomical and Physical Geodesy 21
Newcastle, 30.06.2010
1 Motivation
● Consistent bias of 4 – 5 cm
The GPS – SLR Orbit Anomaly.
Ziebart et al. (2007)
Institute for Astronomical and Physical Geodesy 22
Newcastle, 30.06.2010
1 Motivation
Power Spectrum Estimation Using the FFT
Use of Discrete FFT instead of Lomb-Scargle periodogram
Why?
Data has the same time spacing (1 day) but problem with data missing
FFT still appropiate if data is missing and e.g. set to zero
Lomb-Scargle periodogram robust if time spacing is not the same, e.g. in astronomical measurements
As expected results are very similar using both methods
but Power Spectrum using FFT is much faster and simpler
Press et al. (1992)
Institute for Astronomical and Physical Geodesy 23
Newcastle, 30.06.2010
1 Motivation
Institute for Astronomical and Physical Geodesy 24
Newcastle, 30.06.2010
1 Motivation
● Period:
27.6 +/- 0.1 days
Institute for Astronomical and Physical Geodesy 25
Newcastle, 30.06.2010
only reflection
only emission
● Comparison of analytical and numerical models for constant albedo:
- Different albedos of the Earth
2 Earth Radiation Model
Institute for Astronomical and Physical Geodesy 26
Newcastle, 30.06.2010
● Comparison of analytical and numerical models for constant albedo:
- Different satellite altitudes
2 Earth Radiation Model
Institute for Astronomical and Physical Geodesy 27
Newcastle, 30.06.2010
E3 – E4
E2 – E4
E1 – E4
2 Earth Radiation Model
Institute for Astronomical and Physical Geodesy 28
Newcastle, 30.06.2010
● General radiation pressure model from Fliegel et al. (1992,1996)
● Analytical model assuming Earth radiation to be purely radial Acceleration acting on the satellites
Satellite Bus
Solar Panels
,13
21
c
E
M
Af r
2coscos1
3
21cos
c
E
M
Af r
.2sinsin13
2cos
c
E
M
Af r
A: area of satellite surface ψ: angle satellite – Earth – Sun
M: mass of satellite μ: specularity, 0 diffuse to 1 specular
E: Earth‘s irradiance ν: reflectivity, 0 black to 1 white
c: velocity of light in vacuum
3 GPS Satellite Model
Institute for Astronomical and Physical Geodesy 29
Newcastle, 30.06.2010
● Simpler model: cannon-ball model (no solar panels) average over ψ
● More sophisticated model: Numerical box-wing model considering the full disc of the Earth (not purely radial radiation)
● In total three GPS satellite models:- S1: cannon-ball- S2: analytical box-wing - S3: numerical box-wing
● Additionally consideration of:- B: block specific dimensions and optical properties- A: thrust due to navigation antennas
● Many possibilities: 4 Earth radiation models
3 GPS satellite models
2 extras (turn on/off)
4 Acceleration on the Satellites
Institute for Astronomical and Physical Geodesy 30
Newcastle, 30.06.2010
4 Acceleration on the Satellites
● Earth radiation and satellite models of increasing complexityfor PRN06 and β0 = 20.2°
Along track acceleration [m/s2]
Cross track acceleration [m/s2]Radial acceleration [m/s2]
Institute for Astronomical and Physical Geodesy 31
Newcastle, 30.06.2010
● Earth Radiation Models: E1: analytical, constant albedo E2: numerical, constant albedo E3: numerical, latitude dependent albedo E4: numerical, CERES data
● Other options: B: block specific dimensions and optical properties A: thrust due to navigation antennas R: a priori solar radiation pressure (ROCK) model
● GPS Satellite Models: S1: cannon-ball S2: analytical box-wing S3: numerical box-wing
4 Acceleration on the Satellites
Institute for Astronomical and Physical Geodesy 32
Newcastle, 30.06.2010
● Acceleration over one year in a sun-fixed coordinate system, E1-S1 and E1-S2
Cannon-ball: radial acceleration
Box-wing: radial acceleration
Minimum at dark side of the Earth
Maximum at dark side of the Earth
Caused by infrared radiation acting on solar panels
4 Acceleration on the Satellites
Institute for Astronomical and Physical Geodesy 33
Newcastle, 30.06.2010
● Acceleration over one year in a sun-fixed coordinate system, E1-S2
Box-wing: along track acceleration
Twice per revolution
Box-wing: cross track acceleration
Once per revolution
4 Acceleration on the Satellites
Institute for Astronomical and Physical Geodesy 34
Newcastle, 30.06.2010
Earth radiation pressure [m/s2]
From 0.5x10-9 to 2.5x10-9
Solar radiation pressure [m/s2]
From 9.5x10-8 to 10.5x10-8
4 Acceleration on the Satellites
Institute for Astronomical and Physical Geodesy 35
Newcastle, 30.06.2010
● Orbit differences = perturbed orbit (with albedo) – reference orbit (without albedo)
-0.0165 +/- 0.0017 0.0005 +/- 0.0023 0.0001 +/- 0.0010
-0.0164 +/- 0.0016 0.0006 +/- 0.0023 0.0002 +/- 0.0009
-0.0186 +/- 0.0036 -0.0001 +/- 0.0062 -0.0004 +/- 0.0074
-0.0179 +/- 0.0037 -0.0000 +/- 0.0056 -0.0002 +/- 0.0075
5 Impact on the Orbits
Institute for Astronomical and Physical Geodesy 36
Newcastle, 30.06.2010
● Orbit differences effect of different models, PRN05
5 Impact on the Orbits
Num. (const. albedo) model
Box-wing analytical model
Latitude dependent albedo
CERES data
Institute for Astronomical and Physical Geodesy 37
Newcastle, 30.06.2010
5 Impact on the Orbits
● Orbit differences effect of different models, PRN05
Block specific properties
Box-wing numerical model
Antenna thrust
Institute for Astronomical and Physical Geodesy 38
Newcastle, 30.06.2010
● SLR validation: SLR measurements – GPS orbits
● SLR-GPS orbit anomaly mean reduction of 16 mm - 11 mm albedo - 5 mm antenna thrust
● Scale parameter: 0.00163 +/- 0.00160 mm/KmComparison SLRF2005 and ITRF05RS
Red: with a priori ROCK model
Blue: no a priori ROCK model
5 Impact on the Orbits
ITRF05
Institute for Astronomical and Physical Geodesy 39
Newcastle, 30.06.2010
5 Impact on the Orbits
Institute for Astronomical and Physical Geodesy 40
Newcastle, 30.06.2010
5 Impact on the Orbits
Institute for Astronomical and Physical Geodesy 41
Newcastle, 30.06.2010
6 Impact on the Orbits
Institute for Astronomical and Physical Geodesy 42
Newcastle, 30.06.2010
6 Impact on the Orbits
Institute for Astronomical and Physical Geodesy 43
Newcastle, 30.06.2010
6 Impact
top related