## 1 Introduction  
In an optimal scenario for general bridge health monitoring systems, the ideal is for the bridge owner to have access to comprehensive response data (including displacement, acceleration, strain, inclination, etc.) across the entire bridge structure. This would enable a more thorough assessment of the service status and precise detection of any damage [1; 2]. However, budget constraints often limit the number of sensors that can be deployed to specific locations on the bridge. To address this challenge, scholars have recently turned to data fusion research [3], aiming to estimate unknown structural dynamics from the limited measured data available. The key problem of data fusion is securing the transfer matrix that correlates mode shape functions with various response indicators, such as displacement [4], strain [5], inclination [6], and acceleration [7]. For example, one could compute the unknown acceleration at a specific site by simply multiplying the measured strain from different locations with a transfer matrix. However, the application of conventional mode shape identification techniques, such as the Stochastic Subspace Identification (SSI) [8] and eigensystem realization methods [9], is challenging for medium- and short-span bridges. Firstly, these methods struggle with identifying the low-frequency responses that predominantly affect strain and inclination measurements. Secondly, these methods necessitate a substantial number of sensors to maintain accuracy, which conflicts with the reality of limited sensor deployment. In light of these limitations, three main categories of data fusion methods have been proposed: those based on finite element models [10], Bayesian approaches [11], and machine learning techniques [12]. The finite element model-based approach necessitates an accurate finite element model of the target bridge [13; 14]. This model serves as the foundation for calculating mode shape functions associated with various monitoring indices, including strain, inclination, and acceleration. It also facilitates the derivation of the transfer matrix that links these different indices. For example, [PERSON] et al. [15] developed a displacement-strain transfer matrix utilizing finite element models. An analogous strategy [16] involves estimating the external load from the finite element model and sensor responses, followed by a comprehensive finite element analysis to estimate the entire bridge's response. Subsequent research in this area has focused on two main aspects: (1) refining the model updating process [17] to enhance the accuracy of the finite element model and (2) advancing signal processing techniques [18] to mitigate measurement noise. A common de-noising technique involves integrating measured strain and acceleration data to estimate bridge displacement through methods such as regularization or Kalman filters [19]. Both strain and acceleration mode shapes are determined using finite element models. Moreover, the regularization process can be augmented with direct measurements obtained from advanced equipment like vision cameras [20] and millimeter wave radars [21], further enhancing the precision of the data fusion process. However, constructing an accurate finite element model is challenging in practical engineering scenarios, as conventional model updating techniques can be exceedingly time-consuming. To address this issue, data fusion methods incorporating surrogate models have been introduced. Bayesian-based methods offer an alternative to finite element modeling by constructing surrogate models, such as state-space models, directly from empirical data. For example [22], to infer bridge displacement, initial displacement estimates from a GPS device can be integrated with the double integration of measured accelerations to formulate a state-space model. These preliminary displacement measurements are instrumental in updating the state-space model.