Accurate measurements and calibrations of the MICROSCOPE mission. Gilles METRIS on behalf the MICRSCOPE Team

Transcription

1 Accurate measurements and calibrations of the MICROSCOPE mission Gilles METRIS on behalf the MICRSCOPE Team 1

2 Testing the universality of free fall by means of differential accelerometers in space 1,2 Galileo Galilei «Free fall» in space = 1 = 2 Microscope mg 1 mi mg 2 ' 1,2 mi differential accelerometer = 2 sensors (test masses) sensor 1 sensor 2 differential accelerometer 2

3 Applied acceleration!! i = [T] GO i gravity gradient +( S i )! g EP violation!! +[In] GO i +2[ ] GO i + GO! i! F + M +! p! fp i m i inertial accel. and relative motion non grav. forces including propulsion NG perturbations on the test mass! g S (m i ) local gravity (satellite and the rest of the payload) X j6=i! fe j M electrostatic forces on other proof mass «applied» accelerations equilibrated by the measured «electostatic» acceleration 3

4 Differential acceleration between two test masses 2! (d) = [T](O 12 = forb + fspin in the instrument frame! [In] O 1 O 2 gradients: gravity and inertia +( 2 1 )! g (O 12 ) EP violation!! 2[ ] O 1 O 2 O 1 O 2 2! p (d) 2! g (d) S relative motion of the test masses di erential perturbations on the masses The potential EP violation signal is their but: We do not measure the difference of acceleration but we compute the difference of two measurements! Each of this measurement is affected by the sensor characteristics 4

5 Sensor model sensor (test mass) k theoretical acceleration (input):! (k) measured acceleration (output):! (k)! (k)! = B (k) +[M] (k) [ ] (k)! (k)! (k) + Q + hn (k)i (k)! Biais ê DC part of the acceleration not known precisely Scale factors + axis coupling (symmetric matrix) Test mass rotation Quadratic terms Negligible (will be checked by in flight calibration) Angular to linear acceleration coupling Negligible because dω/dt 0 [M] (k) [ ] (k) =[Id]+[dA] (k) 5

6 The differential measured acceleration 2 (d) x =2B (d) x + x g x + y g y + z g z + x S xx + y S xy + z S xz + (ac 13 y + ac 12 z )S yz + ac 12 y S yy + ac 13 z S zz +( ac 13 y + ac 12 z +2nd 11 ) x ( z 2ac 13 x +2nd 12 ) y +( y 2ac 12 x +2nd 13 ) z +2 ac 13 y + ac 12 z x 2 z 2ac 13 x y +2 y 2ac 12 x z mc 11 x,inst mc 12 y,inst mc 13 z,inst (c) (c) (c) +2 ad 11 x + ad 12 y + ad 13 z! + K (1) (1) 2 (1) x b 0x 2xx K (2) 2xx K 1x (1) (2) x b 0x (2) K 1x (2)! 2 estimated by calibration observed or/and computed negligible at Fep Target: accuracy ó ms -2 in acceleration 6

7 The fep frequency The EP signal, collinear to the gravity vector, follows the direction of the Earth centre, seen from the satellite. This direction rotates at the orbital frequency and, if the satellite is not rotating, the EP signal has the frequency fep = forb which will be well determined If the satellite rotates, the signal is modulated and the EP signal has the frequency fep = forb + fspin This fact is used to Optimize the accuracy of the experiment around the fep frequency To discriminate the EP signal from some other perturbing signals 7

8 Needs for calibration Gravity gradient 8

9 Auxiliary data required g : gravity acceleration at the instrument position projected in the instrument frame Requires a gravity model (mainly Earth) Requires the instrument position S : gravity gradient projected in the instrument frame + symetric part of the gradient of inertia Ω : angular velocity Ω : angular acceleration Requires the instrument orientation 9

10 Orbite restitution Motivation: T ij Δ j = 2 V g x i x j Δ j must be substracted to the measured acceleration Err (T ij Δ j ) = T ij Err(Δ j ) + 3 V g x i x j x k Δ j Err (position) Δ j = O(20µm) and frequency considerations lead to the specifications : Frequency Radial Tangent Normal DC 100 m 100 m 2 m f ep 7 m 14 m 100 m 2 f ep 100 m 100 m 2 m 3 f ep 2 m 2 m 100 m Not too stringent, in principle, with GPS but the computation must take into account the thrust on the satellite commended by the drag-free system. Performance evaluation è no problem 10

11 Attitude Motivation: Projection of the gravity gradient in the instrument frame è attitude [A] Computation of the gradient of inertia è [In] =[A] [Ä] T =d/dt([ω])+[ω] [Ω] < rd/s 2 (inertial & rotating modes) < rd/s (rotating mode) so that : Ω^ Δ and Ω^ ( Ω^ Δ) is equivalent to an attitude stability of the instrument better than 0.16µrad 16 m/s 2 This is a real challenge 11

12 Solution (courtesy P. Prieur, CNES) 1 : on board attitude and angular acceleration control Hybridation of the star trackers (low frequencies) and the acceloremeter (high frequencies) Red : real time attitude performance Blue : a posteriori attitude knowledge performance Above : versus time over 20 orbits Under : versus frequency 12

13 Solution (courtesy P. Prieur, CNES) 1 : on board attitude and angular acceleration control Hybridation of the star trackers (low frequencies) and the acceloremeter (high frequencies) 2 : on ground attitude restitution Hybridation frequency by frequency Red : real time attitude performance Blue : a posteriori attitude knowledge performance Above : versus time over 20 orbits Under : versus frequency 13

14 Exemple of calibration Correction of the gravity gradient effects e = fep Gravity gradient (20 mm) EP Corrected gravity gradient (0.1 mm) 14

15 Calibration of the other parameters E. Hardy thesis 15

16 Conclusion The MICROSCOPE mission is optimized to discriminate an EP signal at the fep frequency Measurement of environment data (position of the masses, position of the satellite, attitude, temperature ) are planed Dedicated calibration sessions have been designed and included in the mission scenario The performances are verified: At the sub-system level : Return from previous missions On ground tests Simulations At the global level : Analytical error budget => worst case (see P. Touboul) Spin mode : 1, over 20 orbits and 0, over 120 orbits Inertial mode : 1, over 120 orbits Numerical simulations (for calibration and EP test) è 0, => Monte Carlo simulations are planed 16

17 Thank you for your attention 17

18 Treatment of the data gaps Lack of data can exist due to accelerometer saturations or transmission problems The duration of the gaps could extend from 1s (frequently) to 1mn (up to once per orbit) and even more (rarely). This can increase the projection of some perturbations on the Fep frequency (cf presentation by E. Hardy) To limit this effect, different actions are planed (cf presentation by E. Hardy) To fill the short gaps by reconstructing the lacking data To remove a whole number of orbits in case of large gap The corresponding data will be well flagged 18

19 How to handle the differential signal? Example of equation to solve : Design matrix A gx t1 )... gx( t ) ( 1 N Txx( t1 )... Txx( t ) N Txz( t )... Txz( t ) N observations Y Δ δ Δγ x( t 1 ) x. z. Δγ x( t ) parameters X N X =( A PA) T 1 A T PY P : weight matrix = inverse of the covariance matrix Difficulties : - P non diagonal for non white noise - Covariance matrix difficult to know accurately - Even if known, heavy inversion (typical dimension = ) 19

20 Transformation of the linear system First method Second method A X = Y Discret filter (e.g. Butterworth passeband pass, order 4) A X = Y FFT + band selection A F X = Y F ~ A X = ~ Y Inversion X=( AT F A 1 F) A T F Y F Inversion in the frequency domain X= ~ A ~ A ) A ~ TY ~ ( T 1 20

21 Simulations 21