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Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters
Tracking and Drift Correction of EFFPI Sensor Systems
P. Chawah
Toulouse
ParisAngers
MontpellierRustrel
2P. Chawah [email protected]
Paper context
LINESLaser INterferometry
Earth Strain
OPTICS GEOPHYSICS
for
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
3P. Chawah [email protected]
Paper context
LINESLaser INterferometry
Earth Strain
OPTICSEFPI sensors
GEOPHYSICS
for
x(t)
SeismometersTiltmetersstrainmeters
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
Photo-detector
Laser diode
s(t)
Φ(t)
Currentmodulation
I(t)
Q(t)
Kalman filter
arctan
Φ(t)x(t)
novelty
4P. Chawah [email protected]
Current modulation
=
Wavelength modulation
=
Phase modulation m(t)
PD output model
Sinusoidal Fm
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
5P. Chawah [email protected]
Synchronous quadrature demodulation
AI (t)
AQ (t)
x(t)<<
x(t)<<
x(t)<<
BI (t)
BQ (t)
Homodyne demodulation
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
6P. Chawah [email protected]
Synchronous quadrature demodulation
2
2
2
2
Virtual displacement carrier
Homodyne demodulation
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
7P. Chawah [email protected]
Homodyne demodulation
Synchronous quadrature demodulation
2
2
2
2
OPM + temperature instability
+ fiber torsion + pressure
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
P. Chawah [email protected]
Kalman filter
We need a system that is adaptative is dynamic tracks the Lissajous parameters in real time
8
conic equation+
Elliptic path
Constrained optimization problem
Kalman Filter+
Mathematical model
I(t)
Q(t)
New samples
Update parameters
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
P. Chawah [email protected]
Kalman filter
9
I(k)
Q(k)
Conic equation for ellipse constraint
+
Kalman Filter+
Conic / Cartesian parameters conversion+
Instantaneous normalization
I’(k)
Q’(k)
Arctan (Q’k / I’k) unwrap Filter m1 xk
222 QγfQγeIγdIQγb)Q(Iγa
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
10P. Chawah [email protected]
Kalman filter efficiency
Simulated noisy Lissajous plot
Estimation by KF of the clean Lissajous
Behavior of the Kalman filter after a sudden change of the ellipse parameters
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
11P. Chawah [email protected]
Displacement estimation results
Experimental result: Response of the EFFPI sensor for an impulse displacement (nm)
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
Validation with apiezo-electric instrument : fig(a) Green: EFFPI displacement estimationBlue: capacitive sensor measurements
fig(b) Blue – Green
2nm peak to peak
12P. Chawah [email protected]
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.
Perspectives
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
13P. Chawah [email protected]
Thank you Any questions ?
Any suggestions ?
http://lsbb.oca.eu/spip.php?article101
For more informations
http://www.gm.univ-montp2.fr/spip/spip.php?article1018
“Real Time and Adaptive Kalman Filter for Joint Nanometric Displacement Estimation, Parameters Tracking and Drift Correction of EFFPI Sensor Systems"
