Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

Overview of GOCE Gradiometer Cal/Val Activities

J. Bouman, P. Brieden, G. Catastini,

S. Cesare, R. Floberghagen, B. Frommknecht,

R. Haagmans, M. Kern, D. Lamarre, J. Müller,

G. Plank, S. Rispens, C. Stummer,

C.C. Tscherning, M. Veicherts, P. Visser

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

GOCE Cal/Val LP Symposium 2010

• The in-flight calibration of the GOCE gradiometer (Cesare et al)• Alternative in-flight calibration of the gradiometer using ESA's L-Method

(Lamarre and Kern)• Quality assessment of GOCE gradients (Müller and Brieden)• A methodology to use terrestrial gravity data sets for regional validation

of GOCE products in central Europe (Schäfer et al) • First results using ESA's internal calibration method GRADNET

(Kern et al)• External calibration of GOCE differential accelerations (Rispens)• Validation of GOCE with terrestrial gravity data in Norway

(Gerlach and Pettersen)• External calibration of the GOCE gravity gradients at the High-Level

Processing Facility (Bouman et al)

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

• 6 accelerometers measure in 3 orthogonal directions• Each accelerometer has two ultra-sensitive axes and

one less-sensitive axis• OAG: One-Axis Gradiometer• GRF: Gradiometer Reference Frame

Gradiometer

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

• Ideal accelerometer measurements:- Gravity gradients- Rotational terms- Drag, solar radiation pressure, thruster action, …- Vibrations, self-gravity, …

• Common and differential accelerations- Common = sum averaged drag etc- Differential = differences averaged gravity gradients

and rotational terms• Pair of two accelerometers is OAG (One-Axis

Gradiometer)

Single accelerometer and pairs

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

1. different scale factors 2. axes are not perfectly aligned 3. sensitive axes are not mutually

perpendicular 4. internal dynamics 5. accelerometers do not occupy

their nominal positions 6. origins of the 3 OAGRFs do not

coincide and their axes are not aligned

7. gradiometer configuration is time-varying

Measurements with a real gradiometer have errors due to:

Real gradiometer measurements

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

Acceleration measured by the accelerometer Ai:

ai = ([K]i + [dR]i + [dS]i)ai + [K2]iai2 + bi + ni

ai = true accelerationa’i = measured acceleration[K]i = scale factor matrix[dR]i = rotation matrix (misalignment)[dS]i = accelerometer inter-axis coupling matrix[K2]i = quadratic factor matrixbi = biasni = noise

Real gradiometer measurements

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

1. On-ground verification2. In-flight accelerometer calibration

• Quadratic factors• Calibration parameters (matrix)• Accelerometer or satellite shaking

3. External calibration and validation• Accelerations or gravity gradients• External gravity data and models

GOCE Calibration Steps

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

• Verification of design/manufacturing tolerances and of stability (e.g. K2)

• One-Axis Gradiometer (OAG) baselines were measured on ground and these values are used in flight

On-ground verification

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

Two operations:• Quadratic factor (K2) adjustment• Scale factor, coupling & misalignment determination

- Baseline method- ESA L-method- GRADNET

In-flight calibration

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

• Feed-back loop non-lineara = K0 + K1 V + K2 V2 + …

• Physically reduce K2 to zero (acceptable level) by test mass position adjustment

• Test mass shaking

In-flight calibration: quadratic factors

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

• For each OAG, common and differential:- Couplings- Misalignments- Scale factors

• 54 calibration parameters (3*18)• Relation between measured and corrected common &

differential accelerations for one OAG (ij = 14, 25, 36):

In-flight calibration: Inverse calibration matrices

36,25,14,,

,

,

,

,

,

,

,

ij

a

a

a

a

a

a

a

a

ijd

ijcij

ijd

ijc

ijd

ijcij

ijd

ijc MIM

Three 6x6 calibration matrices Mij (scale factors, misalignments & couplings).Inverse calibration matrices MIij must be known to recover actual accelerations from the measured ones.

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

• Calibration matrices for each OAG determined separately (iterative process)

• Satellite shaking enables relative calibration (all ICM elements except common scale factors)

• Star sensor data used to determine 9 absolute (common) scale factors

• Empirical relation between scale factors needed

ZX

Yd

Y

XdY

Z

Xd

X

ZdX

Y

Zd

Z

Yd

La

La

La

La

La

La

--- ,14,,25,,36,,14,,25,,36,

In-flight calibration: baseline method

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

• Equations in GRF instead of OAG (72 parameters)• 54 parameters are estimated• Co-estimate STR – gradiometer misalignment

1. Relative scale factors, relative positions and relative misalignments

2. One absolute scale factor, misalignment with respect to star tracker

ESA-L & baseline ICMs agree except for large differences in common scale factors

In-flight calibration: ESA-L method

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

• Accelerometers form a gradiometer network• Use redundancy within the network

ESA-L & GRADNET agree wellGradiometer scale factors stable to better than 10-3

In-flight calibration: GRADNET

x(GRF)

y(GRF)

z(GRF)

(a3x + a6x) / 2 = (a1x + a4x) / 2

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

• External calibration of accelerations• External calibration and validation of gravity gradients (GOCE Cal/Val Team)

- Global gravity field models- Using GOCE GPS data- Using terrestrial gravity data- Validation in crossovers

External calibration

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

Use GG from model to calibrate GOCE GG

GG scale factor determined up to 10-3 level

External calibration:Global gravity field models

GOCE

Model

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

External calibrationGOCE GPS and terrestrial gravity data

• GOCE GPS data- Estimation of global 80 x 80 gravity field combining GOCE GPS

data and GGs- GG scale factors co-estimated

• Terrestrial gravity data

For each track in area GG SF estimated

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

External calibrationValidation in crossovers (XO)

Basic ideaIdentical measurement position→ identical gravity gradient: Vij,1 = Vij,2

Tasks• Interpolation of XO position and GG

measurement along time series• Reduction of altitude and attitude

effects in measurementsXO-differences fit very well with GG noise level

VXX, VYY: 98% < 15 mEVZZ: 98% < 25 mE

Bouman et al, GOCE Calibration, ESA Living Planet Symposium 2010, Bergen, Norway

• GOCE calibration is done in 3 steps:- On-ground verification- In-flight calibration- External calibration and validation

• Absolute calibration requires reliable standard: not trivial

• Result:- Gravity gradient data of good quality- Improved gravity field information

GOCE Calibration Splinter Meeting:Thursday 10 AM, Room Bøygen, Grieghallen

Summary