Positioning Error Limits and Noise Analysis in Hybrid MZ-Sagnac Interferometric Distributed Optical Fiber Sensing System

In hybrid MZ-Sagnac interferometric distributed optical fiber sensing system, positioning accuracy is crucial for practical engineering applications. Beyond identifying disturbance locations, quantifying positioning error is essential to evaluate the reliability of the results, which is critical for real-world engineering. In this paper, the factors influencing positioning error is analyzed, and a comprehensive assessment of the system accuracy is provided. The Cramer-Rao lower bound and correlator performance estimate methods are employed to evaluate positioning accuracy. The analysis reveals that positioning error is influenced by the signal-to-noise ratio (SNR) and signal bandwidth, and system noise is served as a key limiting factor. Various noise sources are analyzed, and strategies for noise mitigation are discussed. A theoretical derivation of noise propagation is conducted, leading to the determination of the minimum detectable phase. The experimental setup involves measuring system noise and evaluating positioning performance by placing the optical fiber in a soundproof room and introducing external disturbances at various positions along the fiber. Results show that the system phase noise level is measured at approximately 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> rad at 1 kHz. With a sensing fiber length of 70 km and an SNR of 30 dB, the positioning error for signals with varying bandwidths is demonstrated to be less than 10 m.