Flexible Vibration Sensing Using Kalman Smoother Integrated in ECL-Based Communication Systems

In this letter, we propose a flexible vibration-induced phase extraction scheme based on a three-pass Kalman smoother (KS) with scalar linear time-invariant model for integrated communication and sensing systems under commercial external-cavity lasers (ECLs). By differentiating the phase estimated by the carrier phase estimation (CPE) module, the laser phase noise is transformed into Gaussian noise. Then, the three-pass KS is used to estimate the differentiated vibration-induced phase. In the three-pass KS, the forward filter pass is used to obtain the posteriori estimates, the backward filter pass is employed to obtain the priori estimates, and the smoother pass is utilized to combine both posteriori and priori estimates. The vibration-induced phase can be obtained by integrating the estimated differentiated vibration-induced phase. In experiments, compared to conventional vibration-induced phase extraction scheme based on band-pass filter (BPF), the KS-based scheme achieves a 1.5dB sensing signal-to-noise ratio (SSNR) enhancement at 10 kHz without requiring vibration frequency or waveform information. Furthermore, the KS-based scheme enables frequency-modulated continuous wave (FMCW) vibration detection in the range of 200 kHz to 1 MHz with the same smoother parameters used for sinusoidal vibration detection, highlighting the flexibility of the KS-based scheme. This flexible vibration-induced phase extraction scheme provides a feasible solution for intelligent sensing in future optical networks.