gnss orbit modeling: non-conservative forces and ... · 3.1 model: ceres data and box-wing...

Institute for Astronomical and Physical Geodesy

Colloquium Satellite Navigation Munich, 24.01.2012

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GNSS Orbit Modeling:

Non-conservative Forces and

Deviations from Nominal Attitude

M.Sc. Carlos Javier Rodriguez Solano

Acknowledgements:

Univ.-Prof. Dr.phil.nat. Urs Hugentobler

Dr.-Ing. Peter Steigenberger

Colloquium Satellite Navigation



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Content

● Master Thesis: Rodriguez-Solano CJ, Hugentobler U, Steigenberger P (2012) Impact of albedo radiation on GPS satellitesGeodesy for Planet Earth, IAG Symposia 2009, Vol. 136, Springer

● PhD 1st year:Rodriguez-Solano CJ, Hugentobler U, Steigenberger P, Lutz S (2011) Impact of Earth radiation pressure on GPS position estimatesJournal of Geodesy, doi: 10.1007/s00190-011-0517-4

● PhD 2nd year:Rodriguez-Solano CJ, Hugentobler U, Steigenberger P (2012)Adjustable box-wing model for solar radiation pressure impacting GPS satellitesAdvances in Space Research, accepted



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Content1. Basic concepts

1.1 Satellite – Earth – Sun geometry1.2 Nominal attitude of GNSS satellites

2. Motivation2.1 Orbit related frequencies in geodetic parameters2.2 SLR – GPS residuals

3. Earth radiation pressure3.1 Model: CERES data and box-wing satellite3.2 Impact on GPS orbits and SLR measurements3.3 Impact on geodetic parameters

4. Solar radiation pressure4.1 Adjustable box-wing model4.2 Impact on GNSS orbits

5. Non-nominal attitude5.1 Solar panel rotation lag angle5.2 Yaw maneuvers during eclipse seasons

6. Conclusions & Outlook



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1. Basic Concepts● Non-conservative forces = non-gravitational forces

● For GNSS satellites, at an altitude of ~20,000 km,non-conservative forces are very important forprecise orbit determination and predictionmismodeling issues or no models are usedgravitational forces have a low contribution to the orbit error budget

● IGS (International GNSS Service) provides most precise orbits:~ 2.5 cm for GPS~ 5.0 cm for GLONASS

● Basically two types of models:empirical models, based on in-orbit behavioranalytical/physical models, based on pre-launch information



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1. Basic Concepts● Modeling of non-conservative forces is a complex task!

● Acceleration due to solar radiation pressure

● Satellite attitude, orientation in space

● Satellite properties



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1.1 Satellite – Earth – Sun geometry

● β0 Sun elevation angle above the orbital plane● Δu Argument of latitude w.r.t. argument of latitude of Sun● ψ Angle satellite – Earth – Sun, ε = π – ψ● XYZ Body-fixed orthogonal frame● DYB Sun-fixed orthogonal frame



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● β0: Sun elevation angle above the orbital plane

GPS orbital planes for 2007

● Period of β0: ~351 days 1.04 cycles per year

● GPS draconitic year rotation period of the Sun around GPS constellation

1.1 Satellite – Earth – Sun geometry



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1.2 Nominal attitude of GNSS satellites● Satellites accomplish at any time two conditions:

- navigation antennas point to the Earth navigation signals- solar panels point to the Sun power supply

yaw-steering attitude



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2. Motivation

● GPS draconitic year:~351 days 1.04 cpy

● Station coordinatesRay et al. (2009)

● Geocenter positionHugentobler et al. (2006)

2.1 Orbit related frequencies in geodetic parameters



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2.2 SLR – GPS residuals● SLR – GPS range residuals based on reprocessed orbit series 1995.0 – 2009.0

from ESOC (ESA)

● A bias of ~1.8 cm and eclipse season (attitude) effects remain



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● Acceleration not taken into account by all IGS analysis centers

● Irradiance [W/m2] at satellite position:– Earth scattering properties approximated as a Lambertian sphere– Earth reflected radiation in the visible (albedo)– Earth emitted radiation in the infrared

● Types of radiation models:1) Analytical: constant albedo, Earth as source point

2) Numerical: latitude-, longitude- and time-dependent reflectivity and emissivity from NASA CERES project

( )( )

( )( ) ( ) rhR

EAhEE

sunEAERM ˆ

41sincos

32, 22 ⎥⎦

⎤⎢⎣⎡ −

++−+

=− παψψψπ

παψ

r

AE = πRE2, RE = 6378 km, ESUN = 1367 W/m2, h = satellite altitude, α = albedo (≈ 0.3)

3. Earth radiation pressure



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3.1 Model: CERES data and box-wing satelliteCERES(Clouds and Earth´sRadiant Energy System)NASA EOS project

Reflectivity (visible)

Emissivity (infrared)

CERES data, monthly averages, July 2007



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● 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 ψ, the angle satellite – Earth – Sun

3.1 Model: CERES data and box-wing satellite



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3.1 Model: CERES data and box-wing satellite

Earth shadow

Solar panels maximal exposure

● Earth radiation pressure acceleration = irradiance (CERES data) + box-wing satellite

● GNSS satellites with different β0 angles:β0 ~ 0° for GPS-IIA, GPS-IIR and GLO-Mβ0 ~ 50° for GLONASS



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3.2 Impact on GPS orbits and SLR measurements● Computation of GPS orbits as done by CODE for one year (2007) of tracking data

● Orbit differences = perturbed orbit (Earth radiation pressure) – reference orbit

SVN35

SVN36



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3.2 Impact on GPS orbits and SLR measurements● SLR – GPS residuals for year 2007

● GPS satellites with laser retro-reflector array: SVN35 / SVN36 or PRN05 / PRN06

Without Earth radiation pressure

With Earth radiation pressure

With T20

Without T20

With T20

● Earth radiation pressure = CERES data + box-wing model + antenna thrust

● T20 model a priori solar radiation pressure model (Fliegel et al., 1992)



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3.3 Impact on geodetic parameters



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3.3 Impact on geodetic parameters ● Reprocessing of 9 years (2000-2008) of GPS tracking data

● Reduction of orbit related errors in North-component daily coordinates



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3.3 Impact on geodetic parameters ● Almost no improvement of GPS-derived geocenter (Z-component)

● Cause for remaining errors on SLR – GPS bias, coordinates and geocenter?

Modeling of solar radiation pressure



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4. Solar radiation pressure● CODE empirical model:

• 5 empirical acceleration parameters [m/s2] per arc• constant and periodic in DYB directions

● Analytical models:• knowledge e.g. from satellite manufacturers• nominal attitude• physical interaction between radiation and satellite surfaces

● Examples: T20/T30 (Fliegel et al., 1992, 1996)UCL (Ziebart et al., 2005)

• 3 stochastic pulses per day- radial- along-track- cross-track



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4.1 Adjustable box-wing model● Physically based model:

Simple box-wing model for SRP

● Four main surfaces:

• Solar panels front • Bus +X side• Bus +Z side• Bus –Z side



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● Physically based model:Simple box-wing model for SRP

● Four main surfaces:

● Model capable of fitting the GNSS tracking data

adjusting the optical properties of the satellite’s surfaces

● Additionally: Adjustment of y-bias and stochastic pulses

● Model tests based on IGS tracking data of full year 2007

• Solar panels front • Bus +X side• Bus +Z side• Bus –Z side

4.1 Adjustable box-wing model



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● Models tested and working for:

GPS IIR GLONASSGPS IIA GLONASS-M

box-wing cylinder-wing



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● Results for all GPS satellites as function ofβ0: the Sun elevation angle above the orbital plane

● Reflectivity: fraction of specularly reflected photons

● +Z surface: pointing always to the Earth (navigation antennas)

GPS IIAGPS IIR

+Z bus reflectivity




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● Absorption + diffusion highly constrained, correlation with other parameters

● +Z surface: pointing always to the Earth (navigation antennas)

● Modeling problems for Block IIR satellites

GPS IIAGPS IIR

+Z bus absorption + diffusion




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● Absorption + diffusionhigh constrained, correlation with other parameters

● –Z surface: pointing always away from the Earth

● Asymmetry between +Z and –Z surfaces of Block IIR satellites

GPS IIAGPS IIR

–Z bus absorption + diffusion




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4.2 Impact on GNSS orbits● Orbit prediction error after 7 days, for all GPS satellites

GPS IIAGPS IIRCODE model Box-wing model

Eclipse seasons yaw maneuvers



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4.2 Impact on GNSS orbits● Orbit prediction error after 7 days, for all GLONASS satellites

GLONASSGLONASS-MCODE model Box-wing model

● Similar performance between CODE and box-wing model



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4.2 Impact on GNSS orbits● Box-wing minus CODE differences of few centimeters in the orbits

● Radial shift of Block IIA orbits in the “correct” directionFurther reduction of SLR – GPS bias possible

GPS IIA, PRN 06 GPS IIR, PRN 17



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● Acceleration from different solar radiation pressure models:

Analytical/physical models

Empirical models

Adjustable box-wing

GPS IIA

GPS IIR

4.2 Impact on GNSS orbits



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5.1 Solar panel rotation lag angle● Box-wing model (alone) is not enough to fit GNSS tracking data ● Solar panel rotation around y-axis lagging by few degrees behind motion of the Sun



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5.1 Solar panel rotation lag angle

GPS IIA: 1.5 ± 0.5 deg

GPS IIR: 0.4 ± 0.3 deg

GLONASS: 3.6 ± 0.8 deg

GLONASS-M: 0.3 ± 0.1 deg

● Estimated angle deviation from nominal attitude● Results for all GPS and GLONASS satellites for 2007



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http://www.russianspaceweb.com/uragan.html

GLONASS GLONASS-M




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● How to validate that orbit gets more physical?

● Improvement visible in radial pseudo-stochastic pulses

● CODE empirical model:

GPS IIAGPS IIR




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● Box-wing model:

GPS IIAGPS IIR




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● Box-wing model without rotation lag:

GPS IIAGPS IIR




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5.2 Yaw maneuvers during eclipse seasons● GPS IIA satellites (Bar-Sever, 1996):

• Finite hardware yaw rate noon turn• Occultation of Sun sensors shadow-turn• Yaw angle at shadow end post-shadow recovery



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● GPS IIR satellites (Kouba, 2009):• Finite hardware yaw rate noon turn• Finite hardware yaw rate shadow-turn

5.2 Yaw maneuvers during eclipse seasons



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5.2 Yaw maneuvers during eclipse seasons● GLONASS-M satellites (Dilssner et al., 2010):

• Finite hardware yaw rate noon turn• Occultation of Sun sensors shadow-turn



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5.2 Yaw maneuvers during eclipse seasons● Specially problematic post-shadow recovery of GPS IIA satellites

● Yaw angle during maneuvers used in adjustable box-wing model

● For example, acceleration caused by +Y surface:



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5.2 Yaw maneuvers during eclipse seasons

● Impact on GPS IIA orbits:

● However, no improvementachieved on orbit predictions:

Further investigations needed!



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6. Conclusions & Outlook● Non-conservative forces play a key role for GNSS precise orbit determination

● Mismodeling effects of Earth radiation pressure and solar radiation pressure:Orbit differences at the few cm levelSystematic effects on orbitsPotential to solve problems on SLR, station coordinates and geocenter

● Attitude of satellite is needed for non-conservative force modelsDeviations from nominal attitude degrade accuracy of modelsSolar panel rotation angle, not previously identified for GNSS satellites

● Long time series to be computed with new solar radiation pressure model

● Importance of other effects?Shadowing between satellite surfacesThermal (heating/cooling) effects



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References● Bar-Sever YE (1996) A new model for GPS yaw attitude. Journal of Geodesy 70(11):

714-723

● Dilssner F, Springer T, Gienger G, Dow J (2010) The GLONASS-M satellite yaw-attitude model. Advances in Space Research 47(1): 160-171

● Kouba J (2009) A simplified yaw-attitude model for eclipsing GPS satellites. GPS Solutions 13(1): 1-12

● 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

● Ray J, Altamimi Z, Collilieux X, van Dam T (2008) Anomalous harmonics in the spectra of GPS position estimates. GPS Solutions 12: 55-64

● Ziebart M, Adhya S, Sibthorpe A, Edwards S, Cross P (2005) Combined radiation pressure and thermal modelling of complex satellites: Algorithms and on-orbit tests. Advances in Space Research 36: 424-430

gnss orbit modeling: non-conservative forces and ... · 3.1 model: ceres data and box-wing...

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