Multi-Source Fusion Monitoring of Global and Local Inclination in Historic Buildings Using EKF with Fractional-Order State Modeling

Historic buildings exhibit coupled response characteristics during long-term service, characterized by slowly varying global inclination evolution superimposed with local component-level deformation. Meanwhile, multi-source measurements are susceptible to environmental noise and structural non-integrality, which poses challenges to obtaining stable and physically interpretable inclination measurements. To address these issues, this study proposes a multi-source fusion monitoring method for global inclination and local deformation of historic buildings using an extended Kalman filter with fractional-order state modeling (FEKF). A state-space model incorporating global inclination, local component-level additional deformation, and their projection relationships is established, in which global inclination information derived from Global Navigation Satellite System (GNSS) and local observations obtained from inclinometers are formulated within a unified measurement framework. Fractional-order dynamics are introduced into the state evolution model to represent the long-memory and non-stationary characteristics of structural responses in historic buildings. By adopting a finite-memory approximation, the fractional-order model is embedded into the extended Kalman filtering framework, enabling joint estimation and physical decoupling of multi-source measurements. Numerical simulation results demonstrate that the proposed method can stably separate global inclination and local deformation components under noisy conditions, while improving the stability of global inclination estimation. Further validation using measured data from a historic building shows that the fusion results effectively suppress high-frequency disturbances in GNSS measurements and allow reliable reconstruction of local component-level inclination responses, indicating good stability and practical applicability. These results demonstrate that the proposed approach provides a physically consistent and robust solution for long-term posture and deformation monitoring of historic buildings.