Real Time and Adaptive Kalman Filter for Joint   Nanometric Displacement Estimation, ParametersTracking and Drift Correcti...
Paper context                                                 LINES                         Laser INterferometry          ...
Paper context                                                                                 LINES                       ...
PD output model                 Current modulation                          =             Wavelength modulation           ...
Homodyne demodulation           Synchronous quadrature demodulation                                                       ...
Homodyne demodulation           Synchronous quadrature demodulation                                        2              ...
Homodyne demodulation           Synchronous quadrature demodulation                              2                        ...
Kalman filter  We       need a system that        is adaptative        is dynamic        tracks the Lissajous paramete...
Kalman filter                                                                                                             ...
Kalman filter efficiency                                                                                                  ...
Displacement estimation results                                                                  Experimental result: Resp...
Perspectives     Optimize the sensor :        Phase drift correction caused by the temperature         fluctuations     ...
Any questions ?                  Thank you                                                               Any suggestions ?...
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Conf limerick 2011

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Conf limerick 2011

  1. 1. Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, ParametersTracking and Drift Correction of EFFPI Sensor Systems P. Chawah Paris Patrick.chawah@eseo.fr Angers Montpellier Rustrel Toulouse
  2. 2. Paper context LINES Laser INterferometry for Earth Strain OPTICS GEOPHYSICSP. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 2
  3. 3. Paper context LINES Laser INterferometry for Earth Strain OPTICS GEOPHYSICS EFPI sensors Laser diode Current modulation Seismometers Tiltmeters strainmeters novelty Φ(t) Φ(t) Kalman I(t) filter x(t) s(t) x(t) arctan Photo-detector Q(t)P. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 3
  4. 4. PD output model Current modulation = Wavelength modulation = Phase modulation m(t)Sinusoidal FmP. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 4
  5. 5. Homodyne demodulation Synchronous quadrature demodulation x(t)<< AI (t) BQ (t) x(t)<< AQ (t) BI (t) x(t)<<P. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 5
  6. 6. Homodyne demodulation Synchronous quadrature demodulation 2 2 2 2Virtual displacement carrierP. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 6
  7. 7. Homodyne demodulation Synchronous quadrature demodulation 2 2 2 2 + temperature + fiber torsion OPM instability + pressureP. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 7
  8. 8. Kalman filter  We need a system that  is adaptative  is dynamic  tracks the Lissajous parameters in real time conic equation I(t) + Elliptic path Constrained optimization problem Q(t) Kalman Filter + New Mathematical model Update samples parametersP. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 8
  9. 9. Kalman filter I’(k) I(k) Conic equation for ellipse constraint γa (I 2 Q 2 ) γb IQ γd I γe Q γf Q2 + Kalman Filter + Conic / Cartesian parameters conversion Q(k) + Q’(k) Instantaneous normalization Arctan (Q’k / I’k) unwrap Filter m1 xkP. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 9
  10. 10. Kalman filter efficiency Simulated noisy Behavior of the Kalman filter after a sudden Lissajous plot change of the ellipse parameters Estimation by KF of the clean LissajousP. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 10
  11. 11. Displacement estimation results Experimental result: Response of the EFFPI sensor for an impulse displacement (nm) Validation with a piezo-electric instrument : fig(a) Green: EFFPI displacement estimation Blue: capacitive sensor measurements fig(b) 2nm peak to peak Blue – GreenP. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 11
  12. 12. Perspectives  Optimize the sensor :  Phase drift correction caused by the temperature fluctuations  Increase the range – Mechanical solutions, – Optical solutions, – Signal processing solutions.  Implement the EFFPI sensor on Geophysical instruments  Validation of the equipment for long time periods in  The underground low-noise Laboratory (LSBB Rustrel, France),  Seismic sites.P. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 12
  13. 13. Any questions ? Thank you Any suggestions ? For more informations Patrick.chawah@eseo.fr http://lsbb.oca.eu/spip.php?article101 http://www.gm.univ- montp2.fr/spip/spip.php?article1018P. Chawah “Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation,Patrick.chawah@eseo.fr Parameters Tracking and Drift Correction of EFFPI Sensor Systems" 13

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