## 1 Introduction  
High-speed trains produce strong dynamic effects on the bridge girders; and, conversely, the running stability of high-speed trains poses new requirements for the girder deformation of operating bridges [1]. With the continuous expansion of the high-speed railway network in China, a large number of bridges carrying multiple railway tracks are being put into operation. Monitoring bridge displacements is a difficult task for the bridge SHM systems [2]. Displacements of railway bridges and subsidence in the transition zones have been monitored using satellite SAR interferometry [3; 4; 5]. The dynamic impact of trains on high-speed railway bridges is an important problem in the design and evaluation of such bridges. High-speed trains excite the vibrations of the bridge structures, which can affect the performance and service-life of bridges. Moreover, the bridge vibration in turn greatly affects the running safety and stability of high-speed trains. Therefore, the train-induced vibration of bridges must be measured and evaluated in the operation of high-speed railway bridges. Pointwise sensors, such as total station [6], accelerometers [7] and global navigation satellite system (GNSS) [8; 9; 10] are widely used for bridge dynamic data acquisition. These sensors are reliable but need to be installed in contact with the surveyed structure and their placement is often time consuming and sometimes unpractical. Video techniques [11] have the advantage of establishing a good compromise between the acquisition frame rate and the resolution, while many factors, such as artificial lights, light refraction phenomena, variation of the natural light, fog and precipitation may affect the precision of video systems. Laser sensors can be used for remote monitoring; however, they are sensitive to dust and abrupt changes of the atmospheric conditions, often resulting inadequate for in-field application [12], and also low cost camera based image processing has been experienced, see [13]. In the past decade, a coherent microwave sensor has been investigated to monitor the vibration characteristics of civil structures; the first pioneering experiment dates back to 1999 [14]. Reviews of this technique, called ground-based radar interferometry, are provided in [15; 16; 17]. With the development of commercial systems [18; 19], the dynamic response of a variety of structures, such as chimneys [20], wind farms [21], towers [22; 23], urban buildings [22; 23; 24] and cables [22; 23], has been described. The technique demonstrated to have a high sensitivity to displacements, which under the best measurement conditions can be down to a few microns. The interest in the dynamic behavior of bridges using ground-based radar interferometry has increased in recent years [23; 25]. Ref. [26] report a method to detect both the vertical bending and the torsional movements of a section of a bridge. In the former application, the radar sensor was put below the bridge, as far as possible from the deck. In this configuration, the radar line-of-sight (LOS) was almost parallel to the bridge longitudinal direction. Due to the 1D characteristic of the radar, the radar reflecting signals with the same LOS distance were imaged in the same elemental unit, namely the radar range-bin. Therefore, different displacement behaviors in the bridge lateral direction, e.g., displacements due to trains passing in different tracks could not be distinguished. In ([27]) the authors used the IBIS-S system to study the dynamic impact of kinematic excitations during passage of low speed (\(<\)120 km/h) trains on the corrugated steel plate culverts; the sensor was set perpendicular to the railway, while difference of dynamic performance of the two tracks were not considered during the analysis. Radar systems using the synthetic aperture radar (SAR) technique, such as IBIS-L and GPRI [25], have the ability of acquiring 2D SAR images: they can distinguish targets in the range and azimuth directions.