1. Real Time and Adaptive Kalman Filter for Joint
Nanometric Displacement Estimation, Parameters
Tracking and Drift Correction of EFFPI Sensor Systems
P. Chawah
Paris Patrick.chawah@eseo.fr
Angers
Montpellier
Rustrel
Toulouse

2. Paper context
LINES
Laser INterferometry for Earth Strain
OPTICS GEOPHYSICS
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" 2

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. PD output model
Current modulation
=
Wavelength modulation
=
Phase modulation
m(t)
Sinusoidal
Fm
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" 4

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. Homodyne demodulation
Synchronous quadrature demodulation
2
2
2
2
Virtual displacement carrier
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" 6

7. Homodyne demodulation
Synchronous quadrature demodulation
2
2
2
2
+ temperature + fiber torsion
OPM instability + pressure
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" 7

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 parameters
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" 8

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 xk
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" 9

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
Lissajous
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" 10

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 – Green
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" 11

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. 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?article1018
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" 13