Optimized IDW Algorithm for Accurate GPS-IMU Time Synchronization Using Acceleration and Temporal Factors

Abstract

Accurate time synchronization of global positioning system (GPS)-inertial measurement unit (IMU) sensor data is critical in dynamic applications such as autonomous driving and UAV navigation, where rapid acceleration variations challenge traditional interpolation methods. This study proposes time difference and acceleration rate-inverse distance weighting (TDAR-IDW), an adaptive algorithm that integrates time difference and acceleration variation into an exponential weighting framework. Unlike conventional IDW, TDAR-IDW employs dual-factor weights: ${w} _{{t}_{i}}={e}^{-\alpha \text {(}\Delta {t}_{i}\text {)}^{p}}$ and ${w} _{{a}_{i}}={e}^{-\beta \text {(}\Delta {a}_{i}\text {)}^{q}}$ to prioritize temporally proximate data and suppress erratic motion effects. These weights are dynamically fused via state-dependent exponents, enabling real-time adaptation under varying motion conditions. Experimental validation on a GPS-IMU platform (1-Hz GPS and 100-Hz IMU) confirms TDAR-IDW’s superiority over linear interpolation, spline interpolation, and traditional IDW. Under rapid acceleration, TDAR-IDW reduces the roll angle error by 92.3% and the pitch angle error by 75.0%, achieving near-perfect Pearson correlations ( $\rho \gt 0.999$ ). For gradual changes, roll and pitch angle errors decrease by 69.0% and 77.1%, respectively, while the total acceleration field prediction mean absolute error (MAE) improves by 34.9%. The error distribution interquartile range (IQR) is reduced by 58%, reinforcing the algorithm’s stability and robustness. By addressing polynomial instability and static weight coupling in existing methods, TDAR-IDW provides a scalable and computationally efficient solution for multisensor fusion in dynamic Internet of Things (IoT), robotics, and intelligent transportation systems.