## 1 Introduction  
Railway bridges are excited to forced vibrations during train crossings, which can lead to a destabilization of the ballast bed, especially in the case of resonance excitation [1]. Thus, instability of the rail position may occur, eventually leading to safety issues for trains and passengers, respectively. Generally, in the case of designing new railways and operational planning of existing bridges, for example, due to the introduction of new rolling stock or an increase in operational speed, a computational verification of serviceability must be carried out. In this context, it must be verified that the maximum occurring vertical bridge deck accelerations do not exceed the limit accelerations specified in the standards, the Eurocode EN 1990:2002/A1:2005/AC:2010 [2], and additionally, on a national level, the RW 08.01.04 [3] to be applied in Austria, in order to exclude any possible risk to the longitudinal, transversal and vertical track stability, the fatigue strength of the supporting structures, and the riding comfort in passenger traffic, or the storage safety regarding freight traffic. The forced vibration responses of railway bridges depend dominantly on the bridge's natural frequencies and damping characteristics. Resonance vibrations occur if one of the trains crossing excitation frequencies meets one of the bridge's eigenfrequencies, and they are associated with detrimental large vibration amplitudes [4; 5]. Hence, the knowledge of the bridge's natural frequencies is vital to evaluate train-induced vibrations and to ensure the bridge's serviceability. To determine the natural frequencies of existing bridges, classical in situ measurement methods, such as the ambient vibration test [6], forced vibration test [7], impact vibration test [8], and train excitation test [9] have been frequently applied. These classical measurement methods are often referred to as the direct approach since they usually require many sensors directly installed in the bridge structure. Contrary to the classical time-consuming in situ measurement methods, [PERSON] et al. [10] proposed to determine the natural frequencies of a road bridge from the measured dynamic response of crossing vehicles and later verified the proposed method through in situ tests [11]. The proposed technique, named vehicle-based indirect Structural Health Monitoring (iSHM) or 'drive-by' bridge SHM, provides a promising method, namely by using the indirect measurements from a moving vehicle [12; 13; 14; 15; 16; 17]. The approach uses sensors that are installed on traveling vehicles to collect the bridge response during the train crossing event, which is referred to as the indirect method of bridge response measurements. In comparison to conventional bridge SHM, the concept of vehicle-based iSHM shows many advantages in terms of being low-cost, time-saving, and highly efficient. Therefore, this method has recently received extensive attention and achieved great development. However, currently, no regulation and/or standard exists for the application of the iSHM method. Most related investigations focus on extracting the bridge's dynamic properties with indirect measurements of train vibrations, i.e., natural frequencies [18; 19; 20; 21; 22; 23], damping ratios [24; 25; 26], and mode shapes [27; 28; 29; 30; 31]. The change of those modal properties is frequently used for bridge damage detection [32; 33; 34; 35; 36; 37]. However, in the application of the vehicle-based iSHM method to railway bridges, several challenges arise in extracting the natural frequencies, corresponding mode shapes, and damping ratios from the recorded sensor signals.