A GNSS/accelerometer integrated deformation monitoring model using fractional Kalman filtering

Abstract The integration of GNSS and accelerometer data has become a well-established approach for deformation monitoring. However, its accuracy and reliability are often limited by factors such as anomalous observation errors, uncertainty errors, and model structural errors. To overcome these limitations, this paper proposes a deformation monitoring model based on a fractional Kalman filter (FKF) that integrates GNSS and accelerometer data. Firstly, by introducing a fractional-order state-space framework, a discrete state equation is established, and both GNSS displacements and accelerometer observations are incorporated into a unified measurement process to formulate the observation equation. Secondly, a dual-filter architecture is implemented, consisting of a global filter that fuses both data types and a local filter that performs high-frequency predictions using only accelerometer data. This design maintains output frequency and provides optimal estimates of deformation parameters, including translation, settlement, and tilt. Finally, simulations and field experiments demonstrate that the proposed method achieves higher accuracy than traditional integer-order KF, with the FKF exhibiting slower root mean square error (RMSE) growth under increasing noise. Over a 5 min period, displacement and tilt angle RMSE values reached 5.3 mm and 0.0337°, respectively, representing improvements of approximately 34.8% in displacement and 26.4% in tilt angle estimation compared to conventional methods.