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Bragg wavelength detection in fiber Bragg grating sensor by combining nonlinear least squares with Kalman smoothing

In fiber Bragg grating (FBG) sensors, detecting the Bragg wavelength accurately could be difficult due to a low signal-to-noise ratio (SNR) in the FBG spectrum. Two common sources of noise are the general random noise from the broadband sources and the interferometric noise caused by the residual reflections in the sensor system. Conventional filtering techniques could be quite effective in removing random Gaussian-white noise, but not so for the interferometric noise, which is very structured. On the other hand, parameter estimation techniques such as nonlinear least squares can be used to identify the parameters in the interferometric noise and remove it accordingly. However, since the parameter estimation problem is nonlinear, the larger the number of parameters, the higher the chance that the algorithm will get trapped into a local minimum and fail to identify the correct parameters. In this paper, it is proposed to combine the nonlinear least squares method with a Kalman smoother. Hence, the number of parameters to be estimated by the nonlinear least squares algorithm will be greatly reduced. To do this, a continuous-time linear time-varying state-space model is derived for the FBG spectrum and then the model is discretized so that the Kalman smoother can be applied. An interesting point to note is that this model is linear time-varying instead of nonlinear, thus not requiring an extended Kalman filter. Computer simulations are provided in the paper to demonstrate the effectiveness of the proposed method, followed by applications to real experimental data. Improvements in the accuracy of Bragg wavelength detection are observed.