# FOG De-Noising Algorithm Based on Augmented Nonlinear Differentiator and Singular Spectrum Analysis
## 4 Experimental and Verification  
In this section, the output of FOG is employed for verifying the effectiveness of SSA-AND de-noising algorithm. Figure 4 is the experimental setup of FOG. The equipment is mainly including: Temperature control cabinet, a single axis FOG sensor, data acquisition system, computer, and (alternating current) AC-(direct current) DC converter. The diameter of the FOG is 11.5 cm, and the height is 2.5 cm. In this work, two set of data are collected from two different FOGs with temperature changing from +10 \({}^{\circ}\)C to \(-\)10 \({}^{\circ}\)C to +10 \({}^{\circ}\)C, where the temperature change rate is less than 1 \({}^{\circ}\)C /min. The two FOGs are the same type but different production batch. Figure 5a is the collected data from FOG1, and Figure 6a is FOG2. From the two figures we can see that, during the temperature variation, there is an obvious drift trend which is submerged in large noises. To extract the precise drift, it is necessary to eliminate the noises effectively. The de-noising procedure by using SSA-AND algorithm for FOG output signal is the same as Section 2. The comparison results are shown in Figures 5 and 6. Figure 4: Experimental equipment arrangement of fiber optic gyroscope (FOG). Figure 5: Comparison results of different de-noising methods for the signal of FOG1: (**a**) original signal; (**b**) signal de-noised by AND with \(R\) = 0.5, the red circle shows the signal delay happens when using AND; (**c**) signal de-noised by DFA-VMD; (**d**) signal de-noised by EMD-FLP; (**e**) signal de-noised by ARKF; (**f**) signal de-noised by SSA-AND. AND: augmented nonlinear differentiator; DFA-VMD: detrended fluctuation analysis-variational mode decomposition; ARKF: adaptive robust Kalman filter; EMD-FLP: empirical mode decomposition-forward linear prediction; SSA-AND: singular spectrum analysis-augmented nonlinear differentiator. From Figures 5 and 6, all the de-noising methods can eliminate the noise of FOG output in some degree. Figures 5b and 6b both show that when AND is used for de-noising alone, the signal delay phenomenon occurred, while there is almost no signal delay by using the proposed SSA-AND algorithm. From the step 3 of SSA-AND algorithm we know that after calculation of correlation coefficients, the strongest correlated component will remain entirely, which would ensure both no obvious signal delay after signal reconstruction and no damage of useful low frequency information. Compared to DFA-VMD algorithm, the de-noising result of SSA-AND algorithm seems better. According to the process of DFA-VMD algorithm, the function of DFA is defined to select the relevant modes to construct the de-noised signal, which means that the components with smaller DFAs would be abandoned, and the rest of components remained for reconstruction, therefore the noise in the remained components will be reserved. While in the process of SSA-AND, almost all the components would be processed by AND except the component with the biggest correlation coefficient, and the smaller correlated components would be suppressed strictly, therefore the de-noising performance of SSA-AND algorithm is better. The principle of EMD-FLP algorithm decomposes the signal into IMFs by EMD and then filter each IMF by FLP, which is similar as our proposed SSA-AND algorithm. However, there is no selection criterion for the parameters of FLP for each IMF which means that it is hard to select the best parameters just by experience, therefore the de-noising result of EMD-FLP algorithm is not optimal. Compared to AND, DFA-VMD, and EMD-FLP, a better de-noising result can be obtained by using ARKF. But the de-noising result of ARKF is still not as smooth as SSA-AND algorithm, that is because ARKF is de-noising the signal in time-domain directly, while the SSA-AND algorithm is decomposing the time domain signal into different components firstly and then each component is de-noised independently which makes the de-noising process more specific.