## 1 Introduction  
Fiber optic sensor system design of the point and/or quasi-distributed type is impossible without solving the key problem for this type of system, which is finding the central wavelength in the reflection spectrum with the most accuracy. Thus, the shift of the central wavelength of a fiber optic sensor based on a resonant structure (a fiber Bragg grating (FBG) [1; 2; 3], a Fabry-Perot interferometer [4; 5; 6], or a ring resonator [7; 8; 9; 10]) or other types of resonators [9; 11] determines the magnitude of the physical impact. In addition, temperature [9; 12; 13], pressure [14; 15], deformation [16; 17], friction, wear, and other types of impacts [18; 19] are all determined using information about the position of the sensing element's reflection spectrum. The primary factor limiting the estimation accuracy of the physical impact magnitude in fiber optic sensor systems is the inadequate resolution of the devices used to measure the spectral properties of such sensors. Increasing the resolution of a device's built-in spectrum analyzer can improve its technical capabilities, but this usually comes at a cost that rises almost exponentially. Diverse methods have been proposed to improve the precision of determining the position of the sensing elements' spectra. Thus, the sub-pixel spectrum processing tech niques [20; 21; 22] made it possible to increase the resolution by one or two orders of magnitude [23]. Meanwhile, after adjusting for the nonlinear spectrum distortions in charge-coupled devices depending on the signal accumulation time, the resolution can be improved by another order of magnitude but only in an extremely narrow frequency range [24]. Due to additional mathematical processing of the data, the maximum results obtained indicated that the physical resolution of the devices could be increased by nearly two orders of magnitude [23; 24]. However, the achieved capabilities to determine the magnitude of the spectral shift are insufficient for some applications. The spectral shift can be determined with greater precision with the help of sensitive elements with narrow spectral characteristics. Fiber Bragg structures with discrete phase shifts, whose reflection spectra are an order of magnitude narrower than those of fiber Bragg gratings [25; 26; 27], and optical elements based on ring resonators, whose Fano resonance has a very narrow reflection spectrum [8; 11; 28], fall into this category of sensitive elements. However, high-resolution spectrum analyzers are also needed when working with sensitive elements that exhibit narrow spectral characteristics. Microwave-photonic methods [20; 29; 30] are another way to improve the accuracy of measurements. These methods work by transferring the measurement process from the optical range of the electromagnetic spectrum to the microwave one. Although microwave-photonic methods are highly accurate for physical parameters determination, they do necessitate upgrading to new technologies and replacing the current hardware and software of measurement instruments. A number of researchers have proposed the artificial intelligence algorithms to determine a central wavelength of sensors based on fiber Bragg gratings (Table 1). [PERSON] et al. [31] proposed to use a fully connected (FCC, fully connected cascade) neural network trained by the Neuron-by-Neuron algorithm to approximate the FBG reflection spectrum and eliminate spectrum distortions, the spectra of which were obtained with a resolution of 1 pm. They managed to achieve an error in the FBG central wavelength determination of 1.45 pm using the approximation of the FBG spectrum curve using the neural network. [PERSON] et al. [32] used a feed-forward neural network (BPNN) with an L-M optimization algorithm to determine the temperature using FBG. Based on the experimental data of the FBG reflectance spectra, the achieved accuracy was 0.2081 \({}^{\circ}\)C (root-mean-square error, RMSE), 0.8943 \({}^{\circ}\)C (max absolute error) or 2.081 pm (RMSE), 8.943 pm (max absolute error) on the training set.