Illustration ©ESA
Outline
1. Mission Goal
2. Gravity Sensor System
3. Ground Processing
4. Conclusions
Mission Goal
The Geoid
Physical
Height
Topography
Mean Ocean Surface
Dynamic Ocean
Topography
Geometric
Height
Sea Surface
Height
Geoid
Geoid Height
Ellipsoid
Equipotential Surface
Reference of Physical Height Systems
Mission Goal
1-2 cm in Geoid corresponding to 1-2 mGal in Gravity
with 100 km spatial Resolution
[mGal]=[10-5 m/s2]
[mGal]=[10-5 m/s2]
Mission Goals
1-2 mGal in Gravity
[mGal]=[10-5 m/s2]
Illustration ©ESA
Arctic Gravity Project
-160
0
160 [mGal]
Mission Goals
The Earth Gravity Field (Equipotential Surface)
seen on Ground
Mission Goals
The Earth Gravity Field (Equipotential Surface)
seen at Satellite Height
The Gravity Sensor System
Observing the Earth Gravity Field from Space
Gravitational Forces:
Earth
Moon
Sun
Planets
& Indirect Effects
Center of Mass
in Free-Fall
The Gravity Sensor System
Observing the Earth Gravity Field with GOCE
Non-Gravitational (Surface) Forces:
Atmospheric Drag
Solar Radiation Pressure
Earth Albedo
Drag-Free in Flight Direction
Zero-drag satellites or equivalently "drag-free satellites" are satellites where the
payload follows a geodesic path through space only affected by gravity and not
by non-gravitational forces such as drag of the residual atmosphere, light
pressure and solar wind.
Test Mass in Center of
Mass in Free-Fall
The Gravity Sensor System
Observing the Earth Gravity Field with GRACE
Non-Gravitational (Surface) Forces:
Atmospheric Drag
Solar Radiation Pressure
Earth Albedo
Test Mass in Center of
Mass in Free-Fall
The Gravity Sensor System
Key Features
1. The first Gravity Gradiometer in Space with High Precision Thermal Control
Pictures ©ESA
The Gravity Sensor System
Key Features
1. The first Gravity Gradiometer in Space with High Precision Thermal Control
2. Newly developed European Space GPS-Receiver with Geodetic Precision
Pictures ©ESA
The Gravity Sensor System
Key Features
1. The first Gravity Gradiometer in Space with High Precision Thermal Control
2. Newly developed European Space GPS-Receiver with Geodetic Precision
3. Very Low Orbit in 260 km Height with Drag Compensation
Illustration ©ESA
Picture ©ESA
The Gravity Sensor System
Key Features
1. The first Gravity Gradiometer in Space with High Precision Thermal Control
2. Newly developed European Space GPS-Receiver with Geodetic Precision
3. Very Low Orbit 260 km with Drag Compensation
4. Smooth Spacecraft Attitude Control System
Radial
Along Track
Cross Track
Picture ©ESA
The Gravity Sensor System
Key Features
1. The first Gravity Gradiometer in Space with High Precision Thermal Control
2. Newly developed European Space GPS-Receiver with Geodetic Precision
3. Very Low Orbit 260 km with Drag Compensation
4. Smooth Spacecraft Attitude Control System
5. Largest Carbon Construction of a Satellite for Stiffness and Thermal Stability
Pictures ©ESA
INCOSE 2008 System Engineering for our Planet, Utrecht, The Netherlands, Academic Forum, 17.6.2008
The Gravity Sensor System
Gravity Gradiometer – Primary Sensor
Observation
6 Accelerometers
measure Accelerations in
3 Directions.
Measurement Accuracy:
10-12 ms-2
Differential Mode
Accelerations
By Subtraction of
Accelerations along 1
Gradiometer Arm.
Gravity Gradients
Common-Mode
Accelerations
By Computation of Mean
Value of Accelerations
along 1 Gradiometer Arm.
Divide differential
Accelerations by Arm
Length and correct for
rotational Accelerations
The Gravity Sensor System
Gravity Gradiometer – Primary Sensor
Measurement Bandwidth of the Gradiometer: 5mHz bis 0,1 Hz,
corresponds to wavelenghths of about 1500 km to 80 km.
The Gravity Sensor System
Satellite-to-Satellite Tracking – Secondary Sensor
Observation of the low Fequencies
Step 1:
Compare true Orbit with
computed Orbit using aprioiri Gravity Field
Orbit Perturbation
GPS
Constellation
Step 2:
Analysis of Orbit
Perturbations to
improve Gravity Field
Computed Orbit
True Orbit
Illustration ©ESA
The Gravity Sensor System
System Approach
translational
forces
angular
forces
star
sensors
GPS/GLONASS
SST -hl
A
B
GRAVITY GRADIOMETER
measures:
gravity gradients
angular acceleration
common mode acc.
drag control
Illustration ©ESA
angular control
*
*
The Gravity Sensor System
System Approach
Ground Processing
Gradiometry
a  V  r    r    (  r)
the linear
acceleration of
accelerometer
proof mass
induced by the
gravity
potential
the linear
acceleration of
accelerometer
proof mass
induced by
satellite angular
accelerations
the centrifugal
acceleration of
accelerometer
proof mass
induced by
satellite angular
rotation
with
V


Vxx
Vxy

V

Vyy
Vzy
Not taking into account accelerometer bias and scaleVyx
factors, misalignments, centre of mass displacements, etc.
zx
Vxz
Vyz 

Vzz 

Ground Processing
Gradiometry
a  V  r    r    (  r)

a
 Vxx
x



  


y

a
   yx
 V 


V z
a


x
z





observed
accelerations
V
xy
V

yy
V
zy

V  
xz

V  
yz
V
zz

0
 
 
 

z
z
y
0

x

  
y 

 
x
 

0  
 

2  2
y
z
 
x y
 
x y
2  2
x
z
 
x z
 
y z
gravity
gradients
angular
accelerations
angular rates

 r 


 
  
 x
 
 r y
z 

2
2
y
    
y  z 
 r
x



 
x z
offset
from CoM
Ground Processing
Gradiometry
Common-Mode Accelerations
X GRF
X1
A1

O1
A6
Y6
X6
X5
Y1
O6
Z1
A5
Y5
Z5
OGRF
X2
A3
A2
O2
Y2
X4
Z2
Y3
O4
Y4
in analogy


ac,1,4,x ; ac,1,4, y
;
ac,1,4,z
ac,2,5,x ;
ac,2,5, y
; ac,2,5,x
ac,3,6,x ;
ac,3,6, y
; ac,3,6,z
Z3
ZGRF
YGRF

X3
O3
A4


O5
Z6


1
a1,x  a 4,x 
2
1 V  2  2 L x 1 V  2  2  L x 

xx
y
z
xx
y
z 

2
2 2
 2

L x V  2  2  V  2  2  0

y
z
xx
xx
y
z
4
a c,1,4,x 
Z4
Ground Processing
Gradiometry
Differential-Mode Accelerations
1
a d,1,4,x  a1,x  a 4,x 
2
1 V  2  2 L x 1 V  2  2  L x 


y
z
xx
xx
y
z 

2
2 2
2


L
L
 x 2Vxx  22y  22z  x Vxx  2y  2z
4
2

X GRF

X1
A1
O1
A6
Y6
X6
O6
Z1
A5
O5
Z6
Y5
Z5
a d,1,4,z 
OGRF
X2
A3
A2
O2
Y2
X4
Z2
Y3
O4







L
1
a1,z  a 4,z  x Vzx  y  x z
2
2


ad ,1,4,x ; ad ,1,4, y ;
ac,1,4,z
Z3
ZGRF
YGRF
Y4
X3
O3
A4


X5
Y1

ad ,2,5,x ;
ad ,2,5, y
; ad ,2,5,z
ad ,3,6,x ;
ad ,3,6, y
; ad ,3,6,z
Z4
Ground Processing
Gradiometry
Correction for Gradiometer
Imperfections due to:
 scale factors
 misalignments
 non-orthogonality
Example: Accelerometer Pair 1-4
 a c 


,1 4
 d ,1 4 


M
a
measured accelerations
ij
 a c

,1 4
 a d
,1 4


 ac 


,1 4
a
 d 
,1 4
true accelerations

M I ij
 a c 


,1 4
  d ,1 4 
a
measured accelerations
Ground Processing
Gradiometry
Angular Accelerations
X GRF
2x  -
X1
A1
2a
d ,3,6, y
Lz
O1
A6
Y6
X6
X5
Y1
O6
Z1
x  -
A5
O5
Z6
Y5
-V yz   yz 
a
d ,3,6, y
Lz
Z5
OGRF
X2
A3
A2
O2
Y2
X4
Z2
y  
ad ,1,4,z
O3
A4
Y3
O4
Z4
Lx

Ly
ad ,2,5,z
Ly
ad ,3,6,x
Lz
Z3
ZGRF
YGRF
Y4
X3

2ad ,2,5,z
z 
a
d ,1,4, y
Lx

a
d ,2,5, x
Ly
 V zy -  yz
Ground Processing
Gradiometry
X GRF
Gravitational Gradients
X1
A1
O1
X6
A6
Vxx  
Vxy  
Vxz  
2ad ,1,4,x
d ,1,4, y
Lx
a
d ,1,4,z
Lx
Z1
O5
 
2
y
Y6
2
z
Y5
Z6

a
d ,2,5,x
Ly
a
d ,3,6,x
Lz
 x y
 xz
Z5
OGRF
X2
A3
A2
O2

A5
O6
Lx
a
X5
Y1
Vyy  
Vzy  
2ad ,2,5, y
Y2
 2  2
x
Ly
a
d ,2,5,z
Ly

a
d ,3,6, y
Lz
Z2
X4
A4
X3
O3
Y3
Z3
O4
ZGRF
YGRF
Y4
Z4
z
  y z
Angular Rate Reconstruction
Vzz  
2ad ,3,6, z
Lz
 2  2
x
y
Ground Processing
Gradiometry
Angular Accelerations
from Gradiometer
 Noise specification for single
accelerometer within MBW (5–
100 mHz) 2e-12 m/s2 /Hz0.5
 Low frequency drift (1/f3)
Kalman Filter
with 3 individual
hybridisation
frequencies
Attitude Quaternions from
Star Sensor
 Accuracy of attitude measurements
< 3 arcsec for the boresight direction
< 24 arcsec for rotations about boresight
 White noise
0,2 mHz
MBW
y  
a
d ,1,4 , z
Lx

a
d ,3,6, x
Lz
Ground Processing
Gradiometry
X GRF
Gravitational Gradients
X1
A1
O1
X6
A6
X5
Y1
Z1
A5
O5
O6
Y6
Vxx  
2ad ,1,4,x
Y5
Z6
Z5
OGRF
 
2
y
Lx
X2
2
z
A3
A2
O2
Y2
Z2
X4
A4
X3
O3
Y3
Z3
O4
ZGRF
YGRF
Vxy  
Vxz  
a
d ,1,4, y
Lx
a
d ,1,4,z
Lx


a
d ,2,5,x
Ly
a
d ,3,6,x
Lz
 x y
 xz
Vyy  
Vzy  
2ad ,2,5, y
 2  2
x
Ly
a
d ,2,5,z
Ly

Y4
a
d ,3,6, y
Lz
Z4
z
  y z
Vzz  
2ad ,3,6, z
Lz
 2  2
x
y
Ground Processing
Ground Segment
Commands
RPF
Rules
Reference
Planning
Facility
@ESRIN
Reports
@ESRIN
FOS
Flight Operations
@ ESOC
Science Data
CMF
Archive
& User
Service
Housekeeping
Data & others
Main
Contractor
Satellite
Alenia
Calibr.
Rules
Calibration
Monitoring
Facility
@ESRIN
Telemetry
Monitoring
Products
Housekeeping
Data
PDS
Payload Data System
L0 to L1 Processing
@ ESRIN
L2 Products
Monitoring Products
L1 & L2
Products
Ancillary
Data
L1 Data
HPF
High-Level Processing
Facility
L1 to L2 Processing
@ EGG-C
Anillary
Data
Ancillary
Data
ILRS
IGS
ECMWF
Other
Ground Processing
Key Features
High Level Processing Facility
• Developped & operated
by European GOCE
Gravity Consortium
(EGG-C)
• EGG-C is a group of
European universities &
institutes with complementary expertise in
gravity field research
• Distributed system: 10
institues in 7 countries
• Independent validation by
overlap of expertise
Institute of
Astrodynamics and
Satellite Systems, Techn.
University Delft, The
Netherlands (FAE/A&S)
Project Management:
Netherlands Institute for
Space Research (SRON)
Institute of Theoretical
Geodesy, University
Bonn, Germany (ITG)
Astronomical Institute,
University Berne,
Switzerland (AIUB)
Institute of Geophysics,
University Copenhagen,
Denmark (UCPH)
GeoForschungsZentrum
Potsdam, Dept. 1 Geodesy
and Remote Sensing,
Germany (GFZ)
PI & Project Management:
Institute of Astronomical
and Physical Geodesy,
Techn. Univ. Munich,
Germany (IAPG)
Centre Nationale
d‘Etudes Spatiales,
Toulouse, France
(CNES)
Politechnico di Milano,
Italy (POLIMI)
Institute for Navigation and
Satellite Geodesy, Graz University
of Techn., Austria (TUG)
Ground Processing
High Level Processing Facility
GOCE Ground
Segment I/F
Central Processing Facility
De- Encoding, Archive, Data Distribution
Gravity Modeling:
Space-wise Approach
Gravity Modeling:
Direct Approach
Gravity Modeling:
Time-wise Approach
Product Validation and
Selection of Final Products
Scientific Pre-Processing
and External Calibration
Orbit Determination
(2 Methods)
External
Interfaces
Long Term
Archive
Calibration and Monitoring
Facility
Payload Data
System
External Data:
•IGS
•ILRS
•others
•IERS
•ECMWF
Central Processing Facility
Rolling Archive, De- and Encoding, XML, Aux. Data Archive, Data Distribution
Scientific Pre-Processing
and External Calibration
•Gradiometer External Calibration
•Corrections for Temporal Gravity
•Data Screening and Data Gaps
Orbit Determination
(kinematic and reduced dynamic)
•Rapid Science Orbits
•Precise Science Orbits
Gravity Modeling
Time-wise Approach
Gravity Modeling
Direct Approach
•SST: Orbit Perturbation
•SSG: Normal Equations
•Combination by Normals
Quick-Look and Precise Solutions:
•SST: Energy Conservation
•SGG: Semi-Anal. & Normals
•Combination by Normals
Gravity Modeling
Space-wise Approach
•SST: Energy Conservation
•SGG: Wiener Filtering
•Combination by Collocation
Product Validation and Selection of Final Products
•QL-Validation of Gravity Models
•Precise Validation of Gravity Field and Orbits
Rapid & Quick Look Processing
Off-line Processing Facility
Ground Processing
Gravity Gradient Product Reference Frames
OGRF
OLORF
XLNOF
ZLNOF
OLNOF
YLNOF
OIRF,OEFRF
Ground Processing
Gravity Gradient Products
Identifier
Description
EGG_NOM_2
Gravity Gradients in Instrument System:
 Externally calibrated and corrected gravity gradients
 Corrections to gravity gradients for temporal gravity variations
 Flags for outliers, fill-in gravity gradients for data gaps with flags
EGG_TRF_2
Gravity Gradients in Earth-fixed System:
 Externally calibrated gravity gradients in Earth fixed reference frame
including error estimates for transformed gradients
 Transformation parameters to Earth fixed reference frame
EGG_NOM_2 Data Content:
• GPS Time
• Corrected Gravity Gradients: Vxx, Vyy, Vzz, Vxy, Vxz, Vyz
• Standard Deviation for each Gravity Gradients (estimated)
• Flags for each Gravity Gradient
• Tidal Correction for each Gravity Gradient (Direct, Solid
Earth, Ocean, Pole Tide)
• Non-tidal Correction for each Gravity Gradient
• Correction for external Calibration
• Inertial Attitude Quaternions
EGG_TRF_2 Data Content:
• GPS Time
• Location in Latitude, Longitude, Height
• Corrected Gravity Gradients: Vxx, Vyy,
Vzz, Vxy, Vxz, Vyz
• Standard Deviation for each Gravity
Gradients (estimated)
• Flags for each Gravity Gradient
Ground Processing
Example: Raw Gravity Gradients with Bandpass Filter applied
Ground Processing
Orbit Products
Identifier
Description
SST_PSO_2
Precise Science Orbits (reduced dynamic and kinematic):
 GOCE precise science orbits final product
 Quality report for precise orbits
SST_AUX_2
Non-tidal Time-variable Gravity Field:
 Spherical harmonic coefficients of non-tidal potential from atmosphere,
ocean and GRACE time series every 6 hours
RMS of Kinematic vs. Reduced Dynamic Orbit for period 14.5.2009 to 21.6.2009 in Local Orbit System [m]
Radial [m]
Along-track [m]
Cross-track [m]
Ground Processing
Gravity Field Products
Identifier
Description
EGM_GOC_2
Gravity Field Model:
 Final GOCE Earth gravity field model as spherical harmonic series
including error estimates. Target: 1-2 cm / 1 mGal up to degree and order
200 corresponding to 100km spatial resolution.
 Grids of geoid heights, gravity anomalies and geoid slopes computed from
final GOCE Earth gravity field model including propagated error estimates
 Quality report for final GOCE gravity field model
EGM_GVC_2
Gravity Field Error Structure:
 Variance-covariance matrix of final GOCE Earth gravity field model
From
Simulations:
Left: Geoid
Height Error
Right: VarCov. Matrix
(Subset)
Ground Processing
Gravity Field Products
 Spherical harmonic series represents the main result of GOCE.
 For computation of derived quantities approximations are applied.
 Computation point on reference ellipsoid
 Spherical approximation of fundamental equation of physical
geodesy (approximating real plumb line by geocentric vector)
 For computing derived quantities on Earth surface use GOCE User
Toolbox together with topography information.
T 1 
P

T
 g P g 0  
h  0 h
h

Q
b
r


'
a
O
rN
S

T
 
g 
r
1 N
a REF 
2
a
REF
T
; 
1
N
a REF cos  
Ground Processing
Important Documents - See: http://earth.esa.int/GOCE/
Conclusions
 GOCE is designed to improve our knowledge of the Earth
gravity field by an order of magnitude.
 From the preliminary analyses we are confident to reach this
goal after completion of at least two measurement phases.
 It is expected that GOCE will open new views in various
Earth science disciplines.
 The EGG-C consortium is starting to operationally analyze
GOCE data during measurement phases.
 It is recommended to potential users to take a look to the
available products documentation in order to become
familiar.