A high-fidelity PGC-Arctan demodulation algorithm employing an extended Kalman filter and a combined modulation

Abstract

Ellipse fitting algorithms (EFAs) utilizing the traditional least squares method (LSM) are not robust in nonlinear systems and even fail when the input elliptic arc is short. To address the challenges, we propose a high-fidelity phase generated carrier (PGC) demodulation algorithm integrating the arctangent method, an extended Kalman filter (EKF) and a combined modulation. The EKF derives optimal state estimation from the nonlinear system by linearizing nonlinear functions, resulting in high accuracy in ellipse fitting. The laser undergoes internal modulation via a combination of low and high frequencies, which not only generates a phase carrier but also induces a large low frequency phase shift in the interferometric sensors. This shift guarantees the Lissajous arc length, thereby preventing fitting failures. The experimental results demonstrate that the EFA employing EKF is consistently superior to that utilizing LSM by comparing the eccentricities of the corrected Lissajous figures. Notably, the proposed algorithm has never failed due to the presence of the low frequency modulation. The average signal-to-noise-and-distortion of the demodulated signal of the proposed algorithm is 62.04 dB in the carrier modulation depth range of 1.5–3.0 rad, which is 46.79 dB higher than that of the PGC-LSM-Arctan demodulation algorithm. The proposed algorithm has promising application prospects in fiber optic sensors as it can effectively eliminate the nonlinear errors and has high robustness.