## 1 Introduction  
The safety of existing road bridges has been a priority issue in engineering for decades because none can deny that bridge deterioration is a real threat to our lives and economies. This safety problem is mainly a concern among bridge owners and investors who are worried about the rapid deterioration of aged bridges if not routinely inspected and treated appropriately. In addition, the number of skilled engineers who can appropriately inspect bridges is still limited. Since resources such as engineers and budgets are limited, it is necessary to classify (1) bridges that should be repaired as soon as possible and (2) bridges that are damaged but should be just monitored without immediate repair. For the latter, developing a system to detect the damage progress at an early stage is necessary. An option as a specific method for realizing early damage detection is vibration-based SHM (structural health monitoring) [1; 2; 3; 4]. In vibration-based SHM, sensors are usually installed on a bridge [3; 4]. Measured vibration data is often used to extract the natural frequencies [5] and other modal pa rameters [6]. Modal parameters are fundamental properties of a structure that reflect its structural condition [2]. When a structure experiences damage, these parameters may shift [7] because the stiffness decreases. Identifying such changes promptly and precisely is crucial for maintaining the system's structural integrity. There are many signal-processing methods for determining structural models from collected data. Structures are often considered a system. In this idea, forces acting on the structure are inputs, while vibration responses are outputs. The system parameters are mechanical parameters, such as mass, damping, and stiffness of the structure. In SHM, estimating these parameters only from the outputs is necessary. If the inputs are wind- and traffic-induced vibrations, they are often treated as white noise [6; 8; 9] to make system identification based on the output data alone. Examples of parametric methods in the time domain include the AR (autoregressive) [10] and SSI (stochastic subspace identification) methods [11]. On the other hand, the FDD (frequency domain decomposition) method [12] derives a singular value spectrum through the SVD (singular value decomposition) of the cross-power spectrum matrix of the multipoint responses. These schemes provide all information about the system parameters of the target structure. Vibration-based SHM for bridges used to be intended mainly for constantly monitoring large-span bridges instead of routine inspections [2; 3; 4]. Thus, if applying SHM to many aged short-span bridges widely distributed in local areas, the cost of installing sensors on each bridge would make the SHM implementation difficult. The applicability of this direct approach to the large numbers of old bridges poses various feasibility concerns related to bridge location, sensor affordability, and installation conditions. Another drawback to the traditional SHM method is the absence of information related to the intact version of the target bridge. These problems call for an alternative bridge monitoring method that is easy to be implemented, cost-effective, able to estimate current performance, and applicable to short-span bridges. One option to be expected to overcome these issues is to apply drive-by bridge monitoring technology. Drive-by bridge monitoring uses vehicle vibration data to evaluate bridge health conditions, as shown in Figure 1. This kind of technique has been investigated for decades [13; 14]. The most known in this regard is the indirect approach proposed for the first time by [PERSON] et al. [15]. This method uses only vehicle vibration to estimate the bridge's natural frequency. They apply the Fourier transform to the vehicle acceleration response and extract the bridge frequency. The obtained spectrum of their study has three predominant frequencies: vehicle drive frequency, two shifted bridge frequencies, and the vehicle's natural frequency.