# A Phase Correlation Anti-Noise Displacement Estimation Method Based on PSD Phase Screening
## 3 Experiment and Analysis
### Real Data Verification
#### 3.2.2 Results and Discussion  
In total, 5579 images were processed by the five employed methods to obtain the displacement sequence of pixel units. Then, the real size of each pixel was calculated according to the real size \(d_{real}\) of the target in the image and the pixel size \(d_{pixel}\) of the target, according to Equation (8). In this paper, \(d_{real}=20\) mm amd \(d_{pixel}=142.014\) pixels, so we obtain \(d=0.141\) mm/pixel. According to the calculated scale parameters, the displacement sequence in pixel units is converted into millimeter units, and the displacement sequence is shown in Figure 13b. \[d=\frac{d_{real}}{d_{pixel}} \tag{8}\]  
In order to evaluate the accuracy of the displacement results obtained by the proposed method, the input displacement sequence used to control the vibration of the shaking table was derived and compared with the displacement sequence calculated by the proposed method. The derived original vibration input sequence of the shaking table is shown in Figure 13a. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Size (length \(\times\) width) & 4 m \(\times\) 4 m \\ Number of degrees of freedom & 3 directions and 6 degrees of freedom \\ Degree of freedom of two shakers’ linkage & 12 degrees of freedom \\ The distance of two shakers & 6–25 m (adjustable) \\ Maximum load & 30 ton \\ Maximum displacement and maximum acceleration of X & 250 mm, \(\pm\)0.8 g (fully loaded) \\ Maximum displacement and maximum acceleration of Y & 250 mm, \(\pm\)0.8 g (fully loaded) \\ Maximum displacement and maximum acceleration of Z & 160 mm, \(\pm\)1.6 g (fully loaded) \\ Sine wave vibration speed & 750 mm/s \\ Operating frequency range & 0.1–50 HZ \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main technical parameters of shaking table of high-speed railway shaking-table test system. Since the input frequency is 1000 HZ, and the image shooting frequency is about 200 HZ, it is necessary to down-sample the displacement sequence of the shaking table to make the sampling frequency of the two sets consistent. At the same time, the collected image contains some non-vibrating parts on the shaking table, so it is necessary to locate the vibrating parts from the displacement sequence calculated by the proposed method, and then the corresponding accuracy can be evaluated. The processed displacement sequences calculated by these five phase correlation methods are shown in Figure 14a, the absolute error of those method is shown in Figure 14b, and the average absolute error is shown in Table 4. \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Average Absolute Error (mm)** \\ \hline Local up-sampling & 0.041 \\ SVD & 0.085 \\ RANSAC & 0.024 \\ SVD + RANSAC & 0.064 \\ Ours (PSD + SVD) & **0.018** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average absolute error of each phase correlation method, where the bold font is the minimum error value among the five methods. Figure 14: The experimental results of the high-speed railway multi-functional shaking-table test system; where (**a**) is the displacement sequence calculated by each phase correlation method and the input displacement sequence of the shaking table, (**b**) is the absolute error of the displacement sequence of each phase correlation method. Figure 13: The original displacement sequence; where (**a**) is the input displacement sequence used to control the vibration of the shaking table, (**b**) is the displacement sequence calculated by the improved phase correlation method in this paper. From the comparison chart of the displacement sequence (as shown in Figure 13a), the displacement sequence obtained by the improved phase correlation method proposed in this paper is consistent with the control sequence of the shaking table. From the comparison chart of the absolute error sequence (as shown in Figure 13b), it can be seen that the fluctuation is smaller, and the absolute error of our method is also smaller compared to the others.