Predictions of the GOCE in-flight performances with the End-to-End System Simulator. Third International GOCE User Workshop

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1 Predictions of the GOCE in-flight performances with the End-to-End System Simulator Page 1 Giuseppe Catastini, Stefano Cesare, Simona De Sanctis, Massimo Dumontel, Manlio Parisch, Gianfranco Sechi Alcatel Alenia Space Torino, Italy Third International GOCE User Workshop ESA-ESRIN, Frascati, Italy 6 8 November 2006

2 GOCE Mission Key Features Orbit: Circular, Sun-Synchronous (96.5 ) Dawn-Dusk, at Altitude! 250 km (first measurement phase, beginning 2008, 6 months),! 260 km (second measurement phase, after long-eclipse season)! 270 km (third measurement phase, mission extension) Page 2 Attitude: Earth pointing Air drag: controlled in the flight direction Measurement Techniques and Instruments: q Satellite gradiometry " tri-axis gradiometer q High-low satellite-satellite tracking " SSTI

Payload Instruments Page 3 Satellite-Satellite Tracking Instrument

5 m accuracy) P/Y code range measure (<0.

Satellite position, velocity real-time measurement Electrostatic

3 Payload Instruments Page 3 Satellite-Satellite Tracking Instrument 12-channel, 2 frequencies GPS receiver C/A code range measure (<0.5 m accuracy) P/Y code range measure (<0.2 m accuracy, A/S off) carrier phase measure (%1 mm accuracy, L1, L2) Satellite position, velocity real-time measurement Electrostatic Accelerometer Tri-axial gradiometer 6 tri-axial accelerometers 0.5 m baseline mhz MBW measurement noise < 2#10-12 m/s2/$hz (US) < 4#10-12 m/s2/$hz (LS)

Level 1b Products GOCE Level 1b main products (obtained from the raw measurements of the gradiometer and of the SSTI after the application of the instrument transfer functions and calibration

4 Level 1b Products GOCE Level 1b main products (obtained from the raw measurements of the gradiometer and of the SSTI after the application of the instrument transfer functions and calibration parameters in the ground processing): q components of the gravity gradient tensor (a 3x3 matrix containing the second spatial derivatives of the gravitational potential) in the Gradiometer Reference Frame and in the J2000 Reference Frame, together with the transformation matrices. Applicable requirement: The measurement error spectral density of the gravity gradient tensor trace (nominally zero) shall not exceed this limit in the MBW Page 4 q SSTI measurements (in RINEX format) and derived positions and reconstituted satellite orbits in Earth Fixed Reference Frame. Applicable requirement: satellite geolocation accuracy < 10 m RMS all directions

5 GOCE End-to-END System Simulator: Top-Level Block Diagram Page 5 The GOCE End-to- End System Simulator is a detailed software model of the satellite, its payload, the orbit environment, the inflight calibration procedures and of the ground processing algorithms.

6 Page 6 Purpose of the GOCE E2E System Simulator: 1. Simulation of the in-flight behaviour of the GOCE system in the various operational modes in support to design and validation of: Ø Ø Ø Ø drag-free and attitude control algorithms in-flight calibration procedures of the gradiometer Level 0 to Level 1b ground processing algorithms performance requirements derivation and error budgets 2. Prediction of achievable mission performance on Level 1b products. 3. Simulation of long periods (up to 60 days) of in-flight measurement phases and production of the corresponding stream of the Level 1b products and ancillary data necessary to feed the Level 2 processing. 4. Data interpretation and identification of potential anomalies and corresponding solutions during the mission.

7 Page 7 Models and algorithms included in the GOCE E2E System Simulator: n Environmental models:!egm96 Earth gravitational potential model, complete to degree, order 360!MSIS90, Hickey (short-term fluctuations), HWM93 atmospheric models n Orbital propagator based on the EGM96 Earth gravity field model n Functional models of the GOCE Payloads (Gradiometer and SSTI) n Functional models of Drag Free and Attitude Control sensors, actuators n GOCE satellite configuration files (mass properties, satellite shape, aerodynamic properties, magnetic dipole) n Drag Free and Attitude Control algorithms for all the operational modes n Calibration algorithms for the Gradiometer instrument n Ground processing algorithms for scientific products up to Level 1b n Failure Detection and Isolation algorithms

8 Gradiometer Model Accelerometer proof mass with sensing/control electrodes Y # Pitch X! Roll " Yaw Z Page 8 Pair 14 ARF i th np = Acelerometer i th ARF nominal position ARF i th dp = Acelerometer i th ARF displaced position

9 Page 9 Accelerometer Functional Scheme

10 Page 10 Detailed model of one accelerometer implemented in Matlab- Simulink The model can run at 1 khz (for accelerom. behaviour investigation) and at 200 Hz (for longduration runs)

11 Accelerometer overall measurement noise modelled in the E2E Simulator Page 11 Ultra Sensitive axis noise spectral density [m/s 2 /Hz 1/2 ] Less Sensitive axis noise spectral density [m/s 2 /Hz 1/2 ]

in-flight calibration simulation Spectral density of the

cold-gas thrusters (Y, Z axes) for the acc.

12 Shaking pattern of the acc. proof mass for the nonlinearity detection Page 12 Gradiometer in-flight calibration simulation Spectral density of the satellite linear shaking by the ion thuster (X-axis) and the cold-gas thrusters (Y, Z axes) for the acc. scale factors and misalignment determination Signature of the acc. nonlinearity in the output signal (DFACS channel)

13 Gradiometer in-flight calibration simulation (cont d) Step 1 Determination of the Inverse Calibration Matrices, assuming unitary absolute scale factors Step 1 and Step 3 are in turn iterative procedures which normally converges after ~10 iterations. The overall process converges normally after 2-3 iterations of the Step 2 & Step 3 loop. Step 2 Determination of the transverse absolute scale factors, using the ICMs determined at Step 1 Repetition of Step 2 with the ICMs determined at Step 3 NO Iterative procedure for the determination of the accelerometer scale factors and sensitive axes misalignment in the Gradiometer Frame Step 3 Page 13 Update the determination of the Inverse Calibration Matrices, starting from the ICMs determined at Step 1 and the transversal absolute scale factors determined at Step 2 Convergence? YES STOP

14 Drag-free control performance simulation Page 14 Time history of the residual linear accelerations of the satellite [m/s 2 ] Spectal density of the residual linear accelerations of the satellite [m/s 2 /Hz 1/2 ]

15 Satellite-Satellite Tracking Instrument Model Page 15 GPS satellites visible from the receiving antenna installed on GOCE vs mission time

16 Page 16 Error contributors to the satellite position determination, implemented in the E2E System Simulator Level 1b Error on Satellite Position Satellite-to-Satellite Tracking GPS Ionosphere Satellite Instrument Errors System Errors Correction Error Errors GPS IGS Ground Reference Station Antenna Center of Phase - COM Receiver Noise, Bias Co-ordinate Errors Position Knowledge Error GPS Antenna Center of Phase Location Error GPS Satellite Ephemeris Errors Satellite Attitude Measurement Error Multipath Effects

17 Page 17 Level 1b Error on GGT trace I C S P Instrument Errors Instrument-Satellite Satellite Errors Processing Errors Coupling Errors I.1 Accelerometer Noise C.1 Coupling with Common-mode accelerations S.1 Platform Self Gravity P.1 Centrifugal Accelerations Recovery Error I.2 Accelerometer Position Stability I.3 OAGRF-GRF Alignment and Alignment Stability I.4 Gradiometer Self Gravity I.5 Coupling with Gradiometer Magnetic Field I.6 Acc. Noise Coupling with Scale Factors and Misalignments C.1.1 Coupling with non-gravitational Linear accelerations C.1.2 Coupling with COM Location and Stability in the OAGRFs C.2 Coupling with Differential-mode accelerations C.2.1 Coupling with Satellite Angular accelerations C.2.2 Coupling with Centrifugal Accelerations and GGT C.3 Quadratic Coupling C.4 Coupling with Accelerometer Misplacement C.5 Coupling with Platform Magnetic Field C.6 Acc. Noise Coupling with Scale Factors, Misalignment Knowledge C.7 Coupling with High Frequency Noise Error contributors to the gravity gradient measurement, implemented in the E2E System Simulator and in a semi-analytical performance budget C.8 Coupling with Differential Transfer Function C.9 Angular-Linear Acceleration Coupling at Accelerometer Level

In-flight performance prediction Page 18 Gravity gradient measurement error prediction obtained with the E2E System Simulator, compared with the semi-analytical

18 In-flight performance prediction Page 18 Gravity gradient measurement error prediction obtained with the E2E System Simulator, compared with the semi-analytical performance budget. Error spectral density of Uzz (radial component of the GGT) [me/hz 1/2 ] Error spectral density of the GGT trace (Uxx + Uyy + Uzz) [me/hz 1/2 ]

19 In-flight performance prediction Long (60 days) simulation statistics Page 19 n The simulator runs on a DELL Precision 670, equipped with dual Xeon GHz, 2 GB of RAM, 400 GB of HD, OS Red Hat Enterprise Linux 3.0, kernel n The run time performance of the simulator is minutes (%13.6 days) in the case a 200 harmonics gravity field is used for the orbit propagation. n The science_60days simulation generates the following amount of data:!about 6 GB of telemetry data (binary format) for the STR and the EGG!about 14 GB of SSTI telemetry data (ascii SP3 and RINEX format)!about 2 GB of ancillary data (binary format) n The Post-processing module generates: about 32 GB of data (binary format) for the EGG about 10 GB of data (ascii format) for the navigation solution and the orbital infos

In-flight performance prediction Performance prediction from a 60-days mission simulation l Begin of the mesurement phase: March 2008 l Orbit

20 In-flight performance prediction Performance prediction from a 60-days mission simulation l Begin of the mesurement phase: March 2008 l Orbit altitude: 240 km (worst case for the environmental conditions) Page 20 Error spectral density of Uxx, Uyy, Uzz Error spectral density of Uxy, Uxz, Uyz

21 In-flight performance prediction Page 21 The ultra-sensitive axes of the six accelerometers are arranged to measure with the highest precision the in-track, cross-track and radial gravity gradient components (Uxx, Uyy, Uzz), and the off-diagonal component in the in-trackradial plane (Uxz). The components Uxy and Uyz are measured with the less sensitive axes of the accelerometer, and thus with lower precision (factor ~200). Z GR X GR A 3 A 4 Z J2000 A 5 Z O X 1 X GR A 1 Y GR A 2 A 6 O O u A 6 X 6 Y 1 O 1 A 1 Z 1 X 5 X O Y O Y 6 O 6 Z 6 Y 5 O 5 A 5 Z 5 X 2 O GR X 3 X J2000! i Y J2000 Y GR Y 2 A 2 O 2 Y 4 Z 2 X 4 O 4 Y 3 Z 4 O 3 A 3 Z 3 Z GR A 4

22 In-flight performance prediction Page 22 Effect of the gradiometer calibration on the gravity gradient measurement

23 In-flight performance prediction Gravity gradient [ measurement error composition Instrument Errors ] ) z H ( t r q s / E m D S Gravity Gradient Tensor Trace r o r r e Page 23 Instrument- Satellite Coupling Errors Satellite Errors Processing Errors Total Trace Errors t n e m e r u s a e m T G G Trace Error Requirement frequency [mhz]

In-flight performance prediction Page 24 Performance prediction in the Level 1b orbit determination from SSTI data Time history over 60 days of the satellite COM position determination error along

24 In-flight performance prediction Page 24 Performance prediction in the Level 1b orbit determination from SSTI data Time history over 60 days of the satellite COM position determination error along the X- axis of the Earth- Centered Earth Fixed frame Time (days) Error in the satellite COM position in the Earth-Centered Earth Fixed frame: = 3.90 m 1' (X axis); = 3.95 m 1' (Y axis); = 5.65 m 1' (Z axis)

MICROSCOPE Mission operational concept

MICROSCOPE Mission operational concept PY. GUIDOTTI (CNES, Microscope System Manager) January 30 th, 2013 1 Contents 1. Major points of the operational system 2. Operational loop 3. Orbit determination