An Innovative Gradual De-Noising Method for Ground-Based Synthetic Aperture Radar Bridge Deflection Measurement  
[PERSON]  
1 School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, No.1 Zhanlanguan Road, Beijing 100044, China; [EMAIL_ADDRESS]  
[PERSON]  
1 School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, No.1 Zhanlanguan Road, Beijing 100044, China; [EMAIL_ADDRESS]  
[PERSON]  
2  
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have gradually become the dominant approach in bridge dynamic-deflection monitoring. Common non-contact techniques include Laser Doppler Vibrometers (LDV) [12], Global Positioning Systems (GPS) [13], and visual measurement methods [14]. Despite their advantages, these non-contact methods are characterized by low sampling frequencies. Ground-Based Synthetic Aperture Radar (GB-SAR) is a sophisticated remote sensing technique that has been increasingly utilized for monitoring the dynamic deflection of bridges. GB-SAR can utilize radar signals to measure and monitor the physical characteristics and movements of structures. It operates by emitting radio waves towards a target and analyzing the reflected signals to detect minute changes in the target's position over time. GB-SAR allows for bridge deflection monitoring without the need for physical contact with the structure, ensuring that the measurement process does not interfere with the bridge's operation or integrity [15]. With its ability to detect submillimeter-level changes, GB-SAR provides high-precision measurements that are crucial for accurately assessing the dynamic behavior of bridges under various load conditions [16]. Unlike optical sensors, GB-SAR can operate effectively in any weather conditions, including rain, fog, or darkness, due to the radar's ability to penetrate these atmospheric obstacles. Additionally, GB-SAR can acquire data in real-time, providing immediate insights into the bridge's dynamic response to traffic and other external factors [17]. This is particularly useful for monitoring during critical events or for rapid assessment following incidents. In essence, GB-SAR is a powerful tool for bridge deflection monitoring, offering a combination of precision, reliability, and adaptability that is unmatched by many traditional monitoring methods. Its application in this field is crucial for maintaining the structural integrity and safety of bridges [18]. Despite its advantages, when monitoring bridge deflection with GB-SAR, the radar system is susceptible to complex environmental noises, which can introduce noises into the monitoring signals [19]. The noises can arise from various sources, such as nearby systematic errors, construction activities, or even the movement of vehicles on or near the bridge. Furthermore, the environmental noise encountered in such scenarios often exhibits nonlinear and Gaussian characteristics, adding to the complexity of the signal processing. These noise types can obscure the true deflection signals, leading to inaccurate measurements and misinterpretations of the bridge's dynamic response [20]. The presence of such noises necessitates robust signal processing techniques to ensure reliable and accurate monitoring. Bridge deflection monitoring using GB-SAR comprises a nonlinear time-series signal. Noise reduction methods for nonlinear signals can be divided among the time domain method, frequency domain method, and time-frequency domain method [21; 22; 23]. For noise-reduction in the time domain [24], the moving average and Savitzky-Golay filter, was well as total variation de-noising methods, etc. are usually used.