A Method for Event Localization in Sagnac Loop Sensing System Using Sparse Signal Recovery

Efficient localization of events within optical fiber sensing systems is essential for many applications like pipeline monitoring and intrusion detection, where fast and accurate responses are crucial. This paper proposes a method for applying sparse signal recovery (SSR) in an optical fiber Sagnac interferometer (SI) loop-based sensing system for event detection and localization. The SSR data processing techniques have emerged to meet the demand for applications like medical imaging, wireless communication, and astronomy. This is because of the SSR's ability to (i) reconstruct signals from incomplete or noisy measurements, (ii) focus on the essential parts of the signal that make the detection more robust against noise, and (iii) process signals by acquiring fewer measurements. Here, we develop a new method for event localization in an SI loop-based sensing system using SSR. The performance of the proposed method was evaluated through simulations and experiments by characterizing (i) the statistics of the detected location; using the Average Location of the Event and Standard Deviation (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\sigma }$</tex-math></inline-formula>), and (ii) the quality of the detection system; using the Probability of False Alarm and the Probability of Detection (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {PD}$</tex-math></inline-formula>). In the simulation, which included <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {2000}$</tex-math></inline-formula> tests for both single-event and two-event scenarios, the results indicated that (i) for a single event, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\sigma }$</tex-math></inline-formula> is between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {0}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {\pm 50}$</tex-math></inline-formula> m when the Signal-to-Noise Ratio (SNR) exceeds <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {10}$</tex-math></inline-formula> dB and within <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {\pm 400}$</tex-math></inline-formula> m at an SNR of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {-10}$</tex-math></inline-formula> dB, with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\sigma }$</tex-math></inline-formula> decreasing significantly as the SNR increases, eventually reaching zero; (ii) for two events, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\sigma }$</tex-math></inline-formula> is between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {0}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {\pm 100}$</tex-math></inline-formula> m when the SNR exceeds <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {10}$</tex-math></inline-formula> dB, and within <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {\pm 600}$</tex-math></inline-formula> m at an SNR of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {-10}$</tex-math></inline-formula> dB. Experimental evaluations were conducted with five scenarios for a single event and three scenarios for two events, demonstrating a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {PD}$</tex-math></inline-formula> of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {100}$</tex-math></inline-formula>% in the experimental setup of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {106.245}$</tex-math></inline-formula> km of loop length (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {\sim\! 50}$</tex-math></inline-formula> km of effective sensing distance). Additionally, we explored the feasibility of the SSR method when integrating simultaneous sensing and data communication within the SI loop-based system by modifying the setup to support both functions.