# FOG De-Noising Algorithm Based on Augmented Nonlinear Differentiator and Singular Spectrum Analysis
## 1 Introduction  
Fiber optic gyroscopes (FOGs) are rotation sensors. By using optic wave information, FOGs can detect the phase shift induced by the so-called Sagnac effect [1]. FOGs have already been widely used in industrial and military applications due to the advantages of long life, simple structure, dynamic range and short start-up time. The precision of FOGs output signal would be degraded due to errors. There are two types of error, which are deterministic error and stochastic error [2, 3]. Deterministic errors are caused by bias, misalignment, and scale factors, which can be reduced by appropriate calibration methods. The stochastic errors are caused by environmental temperature variations, imperfect fabrication, and other electronic equipment interference, which mainly consisted by temperature drift and random noise. The drift can be compensated by establishing a temperature model. However, the temperature drift is submerged in noise, therefore it is necessary to reduce the noise at first. Many studies havebeen explored to cancel out the random noise to improve the precision of temperature drift modeling and compensation. Multi-scale transformation method is a widely used technique for FOG de-noising, such as wavelet-based techniques [4; 5], mode decomposition-based techniques [6; 7; 8], and singular spectrum analysis (SSA) [9; 10]. By using multi-scale transformation methods, the signal can be decomposed from time-domain into frequency-domain, and then the high frequency noise can be extracted and eliminated, which are successfully applied for FOG de-noising especially for static signals, but fails in highly dynamic conditions. Optimal estimation method, such as Kalman filter, is another widely used technique for FOG de-noising [11; 12]. To solve the divergent problem of Kalman filter, adaptive Kalman filters have been proposed [13; 14; 15], such as innovation based adaptive estimation, multiple models based adaptive estimation, and residual based adaptive estimation. Experimental results in literatures show that the Kalman filter based technique is promising for FOG de-noising both in static and dynamic conditions. However, the adjusting Kalman filter parameters for real-time filtering application still need to be improved. Moreover, many other de-noising methods have been reported for FOG in the literature, such as time-frequency peak filtering [16], forward linear predication [17], and hybrid de-noising algorithms [18]. These algorithms are available for FOG de-noising but still with the problems of complex model or time delay. Recently, tracking differentiators have been widely used in signal tracking and differential estimation [19]. Additionally, the application of tracking differentiators on de-noising has attracted increasing attention from research community due to the excellent noise suppression ability. Many researchers have dedicated to developing various differentiators to achieve a satisfactory signal tracking and noise suppression result with good convergence property, such as sliding mode technique-based differentiator [20], finite-time-convergent differentiator [21], sigmoid tracking differentiator [22], and augmented nonlinear differentiator (AND) [23]. It is notable that the AND has the characteristics of global fast convergence and simple structure with promising noise-attenuation ability among the existed tracking differentiators, but the application of AND on gyroscope de-noising has never been reported. Compared to the widely used Kalman filter based de-noising method, tracking differentiators have the advantage of simple structure without pre-designed model. Tracking differentiators has excellent advantages in signal de-noising.