## 1 Introduction
Since drive-by monitoring is an indirect approach [13], estimated modal parameters only suggest the possibility of bridge damages and never identify the damages. Furthermore, there is no information about the dynamic characteristics of the intact state of old bridges because the aging bridges have been in service for a long time. In most cases, it is identified that the first vibration mode is sensitive only to global stiffness reduction, while the extraction of a higher mode sensitive to local stiffness reduction is still a challenge. Due to the limitation of feature-value-based monitoring, an alternative concept is required for bridge health screening. Thus, the implementation of effective monitoring on many bridges should be based on a direct evaluation of the bridge's structural performance. This implies that it is preferable to estimate and evaluate bridge stiffness directly. [PERSON] et al. [26] have proposed a method to estimate road profiles from vehicle vibration data without prior information about the vehicle's mechanical parameters. This method can identify the vehicle's mechanical parameters during estimating road unevenness. [PERSON] et al. [27], [PERSON] et al. [28], and [PERSON] et al. [29] have studied similar methods. While [PERSON] et al. [27] and [PERSON] et al. [28] have examined their schemes only numerically, [PERSON] et al. [26] and [PERSON] et al. [29] have verified the applicability of their method by using actual data. According to the experimental result, [PERSON]'s method can accurately estimate road profiles. In the field experiment, [PERSON] et al. [26] use a known size hump to decide the initial distribution of the vehicle parameters and update them by GA (Genetic Algorithm). [PERSON] et al. [27] extend [PERSON]'s method to use randomly-assumed initial parameters instead of using calibration data. In this study, while the prior probability distribution of each vehicle parameter is assumed to be the Gaussian distribution, the posterior distribution accurately indicates each correct value. [PERSON] et al. [29] also apply a random method to the actual vehicle vibration data for simultaneous vehicle identification and road profile estimation. The Monte Carlo-based schemes [27,29] show high accuracy in estimating road profiles and are verified numerically and experimentally to be applicable. Furthermore, the obtained high accuracies have increased momentum to extend the Monte Carlo-based schemes to bridge inspection. However, it is still necessary to improve the accuracy of extracting bridge responses as well as road profiles from vehicle vibrations. [PERSON] et al. [28] have tried to avoid the numerical integration process by introducing contact forces into the state variable vector of a vehicle model. The motivation of these existing studies [27,28] makes an input estimation process more accurate for extracting bridge information. Therefore, the authors have extended their methods [26, 27, 28, 29] and have proposed a novel scheme that can simultaneously estimate not only vehicle parameters but also bridge parameters. This scheme extension can be realized by adding a bridge simulation process. The extended method is called the PRE (numerical simulation-based vehicle and bridge parameter and road roughness estimation in VBI system) method [30, 31, 32] in this study. The uniqueness of the PRE method is that it includes the identification process of the bridge system. The proposed PRE method has a different purpose from similar previous studies. For instance, the publications [26, 27, 28, 29] use PRE-like schemes to estimate road unevenness, unlike the proposed method, which estimates bridge parameters as well as road unevenness. Therefore, the required accuracy of the proposed method for estimating vehicle inputs is much higher. The PRE method is probably the world's first drive-by scheme for simultaneously estimating vehicles, bridges, and road unevenness.