A Multi-Stage Framework for GPS Trajectory Reconstruction Using Consumer-Grade Wearable Devices

Global Navigation Satellite System (GNSS)-based measurements are widely used for sports monitoring and outdoor activity analysis; however, consumer-grade smartphones often produce degraded trajectories, inaccurate elevation profiles, and unreliable pace estimates. This study proposes a multi-stage framework for reconstructing low-fidelity GNSS running trajectories using an averaged high-fidelity wearable GNSS reference proxy. The framework combines activity-window selection, trajectory filtering and route-consistent projection, reference-based elevation correction, and pace reconstruction using two complementary approaches: a Linear Acceleration Influence Model and a Physics-Based Model. The methodology was validated using three high-fidelity and three low-fidelity recordings collected on a shared 5.726 km route. Within the common activity window, raw low-fidelity observations had a pooled nearest-route RMSE of 30.72 m, whereas retained route-consistent assignments had a residual RMSE of 14.84 m. Aggregate pace agreement improved from 2.40 to 1.74 min/km RMSE and from 32.84% to 25.46% MAPE. Raw smartphone elevation had a pooled RMSE of 190.27 m relative to the adopted reference profile, supporting reference-based elevation substitution. A constant-velocity Kalman RTS baseline reduced positional RMSE from 30.72 to 29.05 m (5.4%), whereas the complete route-association procedure eliminated severe backtracking that remained after distance thresholding alone. The proposed framework provides a transparent and reproducible solution for reconstructing sparse consumer-grade GNSS activities while preserving explicit uncertainty.