# 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
From the average absolute error (as shown in Table 4), the average absolute error of the displacement sequence calculated by our method is the smallest, and the experimental results show that the proposed PSD-based phase correlation method has the advantages of high precision and strong anti-noise performance. In addition, from Figure 14 and Table 4, it can be found that: (1) The displacement results obtained by the SVD method have the worst accuracy, which indicates that in the case of severe noise, the use of SVD cannot restore the cross-power spectral matrix to a state of clean stripes, so the SVD method alone cannot obtain accurate displacement results; thus, it is necessary to combine the RANSAC method on this basis to obtain more accurate displacement results. (2) In this experiment, the photographed scene is sprayed with digital speckle, which enriches the texture of the scene. Therefore, even if there is a lot of noise under high-frequency shooting, the five methods in this experiment can obtain satisfactory accuracy. However, the method in this paper is still better, which further reveals that the proposed method is more resistant to noise. (3) In this experiment, the accuracy obtained by the SVD + RANSAC method is worse than that obtained by using the RANSAC method alone, which seems to be contrary to the conclusion obtained in the simulation experiment. This is due to the fact that the displacement that occurs is smaller compared with that of the simulation experiment. In the case of small displacement, the width of the stripes corresponding to the cross-power spectral matrix is larger (even larger than the image width or height), which leads to the clean stripes of the cross-power spectrum matrix restored by SVD being inaccurate (as shown in Figure 15, where (a) is the original cross-power spectrum matrix, and (b) is the cross-power spectrum matrix restored  
in the subsequent steps. The simulated data experiments and high-speed rail laboratory experiments have validated the robustness of the proposed method. By comparing with other typical four phase correlation methods, the experimental results show that the proposed method has high resistance to noise and can accurately estimate displacement in the case of serious noise interference, compared to the existing phase correlation methods. Since the proposed method is a visual-based method, there are certain requirements for the monitoring scene: one is that the scene can be imaged; at the same time, it has to be ensured that the displacement size (pixels) will not exceed the detectable range of the phase correlation method. In general, the proposed method can be inserted as a module to an existing DIC tool, to monitor structures' displacement that can be clearly imaged, and the imaging resolution can meet the accuracy requirements. The proposed method can avoid noise affection. However, it is a method based on digital image, thus, if the images are not captured with an optimal light source, the promising results could not be obtained. In such situation, an auxiliary artificial light source is needed to ensure the image quality of the measured surface or targets. The proposed method still needs to be improved in some aspects. When using PSD for phase screening, the excessive screening phenomenon may occur and generate a too-small screened area. That means the amount of data utilized for displacement estimation would be limited, resulting in unsatisfying estimation results. In addition, because the calculation process of PSD is time-consuming, the efficiency of the proposed method has to be improved in the future. Conceptualization, Y.Z. ; methodology, Y.Z., J.C. and W.D. ; software, Z.Y. and J.C.; validation, Z.Y. ; writing--original draft preparation, Y.Z., Z.Y. and J.C.; writing--review and editing, L.X., S.C. and W.D. All authors have read and agreed to the published version of the manuscript.