Research on ESPRIT estimation algorithm for the central frequency of gain spectrum in Brillouin optical time-domain reflectrometry
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摘要:
在光纤布里渊光时域反射仪(BOTDR)系统中,对光纤中各处的布里渊散射谱中心频率的估计是测量的关键,也是最为费时的环节,导致BOTDR系统难以做到快速响应。本文研究了ESPRIT算法用来估计BOTDR系统中的布里渊散射谱中心频率,并与基于快速傅里叶变换(FFT)的频率估计算法进行了比较分析。结果表明,ESPRIT算法具有与补零FFT算法配合上洛伦兹频谱拟合所得结果相近的性能。由于ESPRIT算法对数据长度的要求较低,能够在短数据长度上获得较好的频率估计性能,因此能够在保证较高空间分辨率和测量性能的情况下,提高测量速度。
Abstract:In fiber-optic Brillouin optical time-domain reflectometer (BOTDR) system, the estimation of the center frequency of Brillouin scattering spectrum in fiber is the key and the most time-consuming part of the measurement, which makes BOTDR system difficult to achieve fast response. In this paper, estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm is proposed to estimate the center frequency of Brillouin scattering spectrum in BOTDR system. Due to fairly low requirement on data length, ESPRIT algorithm can obtain good frequency estimation over short data length, and makes it possible to increase measurement speed at high spatial resolution and measurement performance.
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Overview: Brillouin scattering based on distributed fiber-optic sensing system is very promising for wide range applications. Brillouin optical time-domain reflectometry (BOTDR) and Brillouin optical time-domain analyzer (BOTDA) are two widely employed schemes. Normally, BOTDR is of interest in practical implementation due to its single-end launch and receiving configuration, making it more robust in events of fiber fracture.
To recover temperature and strain information from Brillouin scattering signal in BOTDR, one has to obtain the distribution of Brillouin frequency shift along the fiber, which can be done by spectral analysis of Brillouin scattering signal to find the frequency of the peak of the Brillouin gain spectrum. In many schemes, a frequency scanning configuration is employed to find this Brillouin frequency shift by measuring the signal strength at various frequency points one by one. Obviously, such schemes take very long time to finish one measurement because tens of frequency points have to be measured. To shorten the measurement time, broadband schemes can be used by receiving all spectrum of the Brillouin scattering signal followed by spectral analysis through algorithms. Fast Fourier transform (FFT) is a popular algorithm in spectral analysis of Brillouin gain spectrum. However, to enhance the spatial resolution of BOTDR, one has to use data as few as possible, which results in great degradation of spectral resolution and hence temperature and strain resolution through FFT. Zero-padded FFT algorithm can be used to keep high spectral resolution but it increases computational complexity, imposing stringent requirement on computational resources.
In this paper, ESPRIT algorithm is proposed to estimate the center frequency of Brillouin scattering spectrum in BOTDR system. Experiments are set up to analyze the performance of three algorithms: FFT with Lorentz spectrum fitting, zero-padded FFT with spectrum fitting and ESPRIT. The linearity, accuracy and stability of these algorithms for the same data are compared. It shows that the performance of ESPRIT algorithm is much better than that of FFT with Lorentz spectrum fitting and is closed to that of zero-padded FFT algorithm with Lorentz spectrum fitting. ESPRIT algorithm works very well on short data length with a quite good performance of accuracy and stability. Moreover, the computational complexity decreases on short data length for ESPRIT, making fast measurement possible. Therefore, ESPRIT algorithm proposed in this paper can obtain good frequency estimation over short data length, making it possible to increase measurement speed at high spatial resolution and measurement performance.
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