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Data fusion is an important issue in bridge health monitoring. Through data fusion, specific unknown bridge responses can be estimated with measured responses. However, existing data fusion methods always require a precise finite element model of the bridge or partially measured target responses, which are hard to realize in actual engineering. In this study, we propose a novel data fusion method. Measured inclinations across multiple cross-sections of the target bridge and accelerations at a subset of these sections were used to estimate accelerations at the remaining sections. Theoretical analysis of a typical vehicle-bridge interaction (VBI) system has shown parallels with the blind source separation (BSS) problem. Based on this, Independent Component Analysis (ICA) was applied to derive surrogate inclination mode shapes. This was followed by calculating surrogate displacement mode shapes through numerical integration. Finally, a surrogate inter-section transfer matrix for both measured and unmeasured accelerations was constructed, enabling the estimation of the target accelerations. This paper presents three key principles involving the relationship between the surrogate and actual inter-section transfer matrices, the integration of mode shape functions, and the consistency of transfer matrices for low- and high-frequency responses, which form the basis of the proposed method. A series of numerical simulations and a large-scale laboratory experiment were proposed to validate the proposed method. Compared to existing approaches, our proposed method stands out as a purely data-driven technique, eliminating the need for finite element analysis assessment. By incorporating the ICA algorithm and surrogate mode shapes, this study addresses the challenges associated with obtaining accurate mode shape functions from low-frequency responses. Moreover, our method does not require partial measurements of the target responses, simplifying the data collection process. The validation results demonstrate the method’s practicality and convenience for real-world engineering applications, showcasing its potential for broad adoption in the field.