Real time and adaptive Kalman filter for joint nanometric displacement estimation, parameters tracking and drift correction of EFFPI sensor systems

Abstract

This paper deals with the optimization of an Extrinsic Fiber Fabry-Pérot Interferometer used for very long term (more than one year) and high precision displacement measurements by a real time and adaptive estimation procedure based on a Kalman filter. By performing a sinusoidal laser diode current modulation, a wavelength modulation is created. The Kalman filter takes into account not only the correction of the measurement drift caused by the resultant Optical Power Modulation, but also the correction of the measurement noise and temperature fluctuations.The tracking algorithm is presented, the complete system has been set up, the Kalman filter and the demodulation are programmed on an FPGA board. Experimental results give an estimation error of about 2 nm for a 7000 nm displacement.

Onland and Offshore Extrinsic Fabry–Pérot Optical Seismometer at the End of a Long Fiber

“…We demonstrated that a synchronous quadrature demodulation -which allows to extract 2 intensity signals in approximate quadrature I(t) and Q(t) (equations 4 and 5) -coupled with fast and innovative real-time algorithms for instantaneous phase estimation, makes it possible to estimate the displacement of the target (Chawah et al (2011)).…”

Real-time FPGA-based Kalman filter for constant and non-constant velocity periodic error correction

“…There are two common ways to correct or compensate the periodic error to achieve more precise measurement: 1) design a novel optical configuration that eliminates the periodic error inherently [10,11,12,13,14], and 2) use a compensation algorithm applied to the measurement data to correct the periodic error electronically [15,16,17,18,19,20,21,22,23,24]. A novel optical configuration of interferometer would lead vastly large and complicated setup, and be more sensitive to environment.…”

“…Chawah, et al [23] established a system to estimate the coefficients and correct the error based on a Kalman filter on a computer. However, the measurement data has to be transferred from the data acquisition system (FPGA) to the computer for off-line processing.…”

“…Equations (17)(18)(19)(20)(21)(22)(23)(24) are recursively computed for each new value of (I x , I y ). After a certain number of iterations, the state or ellipse coefficients x converges to a constant value, thus the ellipse is optimally estimated and (A, B, D, E, F ) are ready to be used for correcting the periodic error.…”