Objective High sensitivity, large dynamic range, and anti-electromagnetism interference are advantages of interferometric fiber-optic hydrophones. In the fields of marine resources exploration and seabed geological exploration, it has a good application potential. Phase generated carrier (PGC) modulation and demodulation technology have the advantages of high sensitivity, easy multiplexing, and good linearity. Interferometric optical fiber hydrophones commonly employ this signal detection technology. PGC demodulation approach includes internal and external modulation. PGC demodulation results can be affected by laser intensity modulation and laser phase excursion caused by directly modulating laser, fluctuations in direct-current laser intensity, alternating-current laser intensity, phase modulation depth, and phase delay due to laser transmission delay, circuit transmission delay, etc. Several viable approaches to eliminating these factors' influence have been researched by numerous previous studies. However, most of them only focus on some of the abovementioned nonlinear factors and one case of PGC internal or external modulation. We hope to propose an approach to eliminate the effects of the abovementioned nonlinear factors. Furthermore, we hope that this approach can be employed in both PGC internal and external modulations. Methods To eliminate these effects, a PGC demodulation approach based on extended Kalman filter parameter estimation (PGC-EKF) is proposed in this study. The traditional PGC demodulation process is modified in this study using the characteristics of the PGC demodulation model that considers the influence of nonlinear factors. In the modified PGC demodulation process, the PGC demodulation problem can be transformed into the estimation of four demodulation model parameters D, E-x/E-y, sin(theta(x)-theta(y)) and cos(theta(x)-theta(y)). In this study, an ellipse fitting algorithm based on an extended Kalman particle filter is introduced to estimate the model's parameters. An ellipse fitting algorithm can be employed to map the four demodulation model parameters into five elliptic equation coefficients a, b, c, d, and e to obtain the four demodulation model parameters. Furthermore, the EKF algorithm is employed to estimate the elliptic equation coefficients. After obtaining the five elliptic equation coefficients, we use the undetermined coefficient approach to obtain the mapping from the five elliptic equation coefficients a, b, c, d, and e to the four demodulation model parameters D, E-x/E-y, sin(theta(x)-theta(y)) and cos(theta(x)-theta(y)). The existing relational expression between the coefficients of the general equation of an ellipse and the parameters in its corresponding parameter equation is simplified using the undetermined coefficient approach, the incorrect part of the existing derivation results is corrected, and further derivation is performed in combination with the model's characteristics used in this study. After obtaining the demodulation model parameters, the acoustic signal to be measured can be obtained using the PGC arctangent (PGC-Atan) approach. Results and Discussions The simulation experiment is conducted under the conditions that the acoustic signal's frequency to be measured is 500 Hz, the sampling frequency is 250 kHz, and the carrier frequency is 25 kHz. The simulation experimental results show that the EKF-based ellipse fitting estimation algorithm fits the estimation result curves of the four demodulation model parameters well with the actual values set in the simulation and can track the fluctuations of the four demodulation model parameters well (Fig. 4). The relative estimation errors of estimation results of four types of demodulation model parameters D, E-x/E-y, sin(theta(x)-theta(y)) and cos(theta(x)-theta(y)) are 0.07 %, 0.39 %, 0.59 %, and 0.28 %, respectively (Table 2). The mean square errors of the estimation results of four types of demodulation model parameters D, E-x/E-y, sin(theta(x)-theta(y)), and cos(theta(x)-theta(y)) are 1.00 X 10(-)(10), 3.80 X 10(-9), 5.70 X 10(-)(10), and 2.69 X 10(-)(10) (Table 2). The experiment is conducted under the conditions that the laser's center wavelength is 1550 nm, the linewidth is 1.9 kHz, the output power is 15 mW, the acoustic signal's frequency to be measured is 100 Hz, the sampling frequency is 500 kHz, and the carrier frequency is 31. 25 kHz. The experimental findings are as follows: the signal demodulated directly according to the traditional PGC-Atan approach has significant waveform distortion and AC interference, which is reflected in the spectral lines of low-frequency and high-order harmonic components with high intensity in its frequency spectrum (Fig. 10). The waveform distortion and AC interference in the time domain are suppressed in the PGC-EKF approach's demodulation results proposed in this study, and the intensity of the low-frequency component and high-order harmonic component in the corresponding frequency spectrum is considerably reduced (Fig. 12). In the PGC-Atan approach, the signal-to-noise ratio (SNR), total harmonic distortion (THD), and signal-to-noise and distortion (SINAD) of the demodulation results are 21. 29 dB, - 9. 56 dB, and 9. 28 dB, respectively (Table 4). Additionally, in the PGC-EKF approach, the SNR, THD, and SINAD of the demodulation results are 30.13 dB, - 28. 81 dB, and 26.44 dB, respectively (Table 4). The SNR, THD, and SINAD of the PGC-EKF approach's demodulation results are better than those of the PGC-Atan approach. Conclusions In this study, the traditional PGC demodulation process is modified to eliminate the effects of laser intensity modulation, laser phase excursion, fluctuations in DC laser intensity, AC laser intensity, phase modulation depth, and phase delay on PGC demodulation results. An ellipse fitting algorithm based on EKF parameter estimation is applied to the modified demodulation model, and a PGC demodulation approach based on EKF parameter estimation is proposed in this study, which can be used for both PGC internal and external modulations. The existing relational expression between the coefficients of the general equation of an ellipse and the parameters in its corresponding parameter equation is simplified, the incorrect part of the existing derivation results is corrected, and further derivation is performed in combination with the model' s characteristics employed in this study. The experimental results show that the PGC-EKF approach proposed in this study improves the demodulation results' SNR by 8. 84 dB, reduces the THD by 19. 25 dB, enhances the SINAD by 17.16 dB, and significantly improves the system performance compared with the traditional PGC-Atan demodulation approach. This demonstrates that the PGC-EKF can efficiently demodulate the signal to be measured, suppress the AC interference and waveform distortion of the demodulated signal caused by the abovementioned nonlinear factors, and eliminate the low-frequency and high-order harmonic components in the demodulated signal frequency spectrum.
