High-spatial-resolution localization algorithm based on cascade deconvolution in a distributed Sagnac interferometer invasion monitoring system.

In the Sagnac fiber optic interferometer system, the phase difference signal can be illustrated as a convolution of the waveform of the invasion with its occurring-position-associated transfer function h(t); deconvolution is introduced to improve the spatial resolution of the localization. In general, to get a 26 m spatial resolution at a sampling rate of 4×10⁶  s^-1, the algorithm should mainly go through three steps after the preprocessing operations. First, the decimated phase difference signal is transformed from the time domain into the real cepstrum domain, where a probable region of invasion distance can be ascertained. Second, a narrower region of invasion distance is acquired by coarsely assuming and sweeping a transfer function h(t) within the probable region and examining where the restored invasion waveform x(t) gets its minimum standard deviation. Third, fine sweeping the narrow region point by point with the same criteria is used to get the final localization. Also, the original waveform of invasion can be restored for the first time as a by-product, which provides more accurate and pure characteristics for further processing, such as subsequent pattern recognition.