Enhancing Positioning Accuracy of Wrist-Worn Instrumentation: A Factor Graph-Based Fusion of GNSS and Inertial Measurements

Accurate trajectory measurement and positioning using consumer-grade wrist-worn devices present significant challenges due to the inherent noise, bias, and drift of low-cost MEMS inertial sensors, as well as the uncertainty of GNSS signals in obstructed environments. While pedestrian dead reckoning (PDR) is a common technique, it suffers from cumulative measurement errors, whereas standalone GNSS is susceptible to signal outages. To address these instrumentation limitations, this paper proposes a robust PDR/GNSS integrated measurement method based on factor graph optimization (FGO). Unlike traditional filtering approaches, the proposed framework models the positioning problem as a joint optimization of GNSS observations, PDR-derived motion states, and velocity constraints within a globally consistent graph. Specifically, to mitigate the systematic errors in inertial measurements, a step frequency detection and adaptive step length estimation model is developed, effectively serving as an in-run calibration for the wrist-worn inertial measurement unit (IMU). The FGO framework then optimally estimates the trajectory by minimizing the measurement residuals through a nonlinear least-squares optimization using the Levenberg–Marquardt algorithm. Experimental validation conducted in diverse scenarios demonstrates that the proposed method significantly reduces the measurement uncertainty, achieving average positioning error reductions of 34.1%, 12.6%, and 29.8% in open, GNSS-challenged, and transition environments, respectively, compared to conventional methods. These results confirm the efficacy of the proposed approach in enhancing the measurement accuracy and reliability of wearable instrumentation without reliance on external infrastructure.