## 5 Discussion  
One of the main limitations of the use of RAR measurements for bridge monitoring is the capability to only estimate the LOS of the displacement. This limits the possibility of obtaining a full picture of the bridge vibrations. Although the vertical displacements are usually the most significant component, the horizontal displacements (longitudinal and lateral) cannot be neglected. A possible approach to overcome such a limitation is to use different radar sensor measuring simultaneously from different positions: the integration of all measurements allows to decompose the measured displacement in its different components. In this work, we have used a single RAR system measuring from different positions. The in situ data provided by an existing SHM system of the bridge were used to check that both lateral and longitudinal displacements are negligible with respect the vertical ones. Hence, all the measurements were projected to the vertical direction.  
The results obtained in view S1 and view S2a were compared with the results obtained using external sensors mounted on the bridge. In view S1, the dynamic responses to ambient noise are within \(\pm\)0.3 mm, which, in fact, are uncertainty of the displacements measurement and the result agree with the rigid characteristic of the bridge; In view S2a, we first analyze the horizontal displacements achieved by the in situ sensors and then the displacement obtained from the RAR and the in situ measurements are compared, the results confirms the assumption that the train-induced displacements are vertical. The main difference between the in situ and the RAR measurements is the sampling frequencies, the high frequency of the radar measurements are capable of illustrating the maximum train-induced displacements.  
Two measurements of the same section of the bridge with perpendicular LOS (view S2b and view S3) were performed in order to emulate the measurement of a two-RAR system. Although the two measurements were not simultaneous, we compared measurements with similar loads on the bridge. The loading cases of 16 carriages high-speed trains passing on the bridge (track 2), N2S) were chosen. Due to the fact that the train-induced lateral displacements are within 0.1 mm (see Figure 8a), Figure 19  
Figure 18: Comparison of vertical displacement histories of the bridge deck at (light blue) upstream and (orange) downstream swath.  
depicts the converted displacement in the vertical direction. In Figure 19a, the three radar bins (number 26, 27 28) have exactly the same displacement behavior, while the magnitudes of vibration are different. This is because the bins have different distances from the pier 1/0: the farer the distance, the larger the magnitude. In Figure 16b, the displacements have a similar behavior of that shown in Figure 16a. The largest displacements are related to the part of the eccentric train loading of the bridge: the farer to the eccentric loading, the smaller the displacement.  
Due to the fact that the train-induced displacements are in a 2D plane of the bridge deck, while the two radar LOS displacements are on the two perpendicular lines in the plane, a quantitative analysis of the two measurements becomes complicated.  
The RAR can only measure in the LOS and cannot measure the displacements perpendicular to the LOS. Usually, the displacements in the bridge lateral direction can be considered uniform. However, if a bridge is quite wide, e.g., including multiple tracks/lanes, the displacement can be laterally nonuniform. Setting a measurement perpendicular to the bridge longitudinal direction allows monitoring such variations.