Fig. 1. Schematic diagram of heterodyne interference quadrature demodulation. NLL, narrow linewidth laser; OC, optical couple; AOM, acousto-optic modulator; FBG, fiber Bragg grating.

Fig. 2. Reflection intensity spectrum and reflection phase spectrum of the FBG.

Fig. 3. Algorithm flow chart of self-Bayesian estimation.

Fig. 4. Numerical validation of algorithm validity. (a) The curve of theoretical posteriori variance $P_k$ and actual variance of the filtered signal ${\widehat{x}}_k$ with respect to the initial value of the variance $Q$. (b) Variance iterative procedure. (c) True value, observation 1, observation 2, and posterior value in the time domain. (d) Fluctuation differences among observation 1, observation 2, posterior value, and true value.

Fig. 5. Demodulation results under different signal frequencies and vibration amplitudes.

Fig. 6. Vibration signal sensing system. BPD, balanced photodetector; OPM, optical power meter; PZT, piezoelectric ceramic sensor; FBG, fiber Bragg grating; AWG, arbitrary waveform generator; DAQ, data acquisition system.

Fig. 7. Noise distributions of phase demodulation and intensity transformation. (a) Noise scatter diagram, (b) cross-correlation diagram, and (c) two-dimensional probability density distribution of two types of noise.

Fig. 8. Experimental results and errors. (a) Phase demodulation, intensity transformation, and self-Bayesian estimation at 200-kHz driving frequency in the time domain. (b) Fluctuation differences between the three results and the standard input sinusoidal signal. (c) The probability density function (pdf) of the fluctuation differences.

Fig. 9. Power spectral density (PSD) curves of the three results. (a) Phase demodulation spectrum of FBG at 200-kHz driving frequency. (b) Intensity transformation spectrum of FBG at 200-kHz driving frequency. (c) Self-Bayesian estimation at 200-kHz driving frequency.

Fig. 10. (a) Variances and (b) SNRs of the three results and their (c), (d) density curves.

Fig. 11. (a) SNRs and (b) variances of different frequencies.

Fig. 12. (a) Variances, (b) SNRs, and (c) amplitudes of demodulation results of different voltages.