Comparison of FGO and KF for PDR-GNSS Fusion Under Different PDR Errors

Smartphone-based positioning, heralded for its widespread accessibility, encounters challenges due to its reliance on global navigation satellite systems (GNSSs) in unfavorable conditions such as urban canyons, tunnels, and indoor areas. Even in clear-sky conditions, signal distortions, interruptions, and the limitations of cost-effective smartphone GNSS prompt researchers to explore alternative positioning methods. This has led to the adoption of sensor fusion techniques, often integrating the inertial measurement unit (IMU) for its complementary features with GNSS. In pedestrian localization, the fusion of pedestrian dead reckoning (PDR) and GNSS, traditionally employing the Kalman filter (KF) as the main fusion algorithm, has been standard practice. The emerging factor graph optimization (FGO) algorithm has recently gained attention for its better accuracy for inertial navigation system (INS)-GNSS fusion architectures, especially under GNSS outliers. However, the FGO implementation for PDR-GNSS fusion architecture has been less investigated, and little is known about its performance under different PDR outliers. As the different gait dynamics of humans and transient variations in the way the smartphone is carried, the PDR system can generate short and high errors (SHEs) or continuous and low errors (CLEs). We analyze the improvement of FGO over KF in mitigating these PDR errors in the PDR-GNSS fusion architectures for smartphone-based positioning. Since FGO is a smoothing technique and KF is a filtering method, for a fairer comparison, we also implemented a smoothed KF (SKF) using the Rauch–Tung–Striebel smoother (RTSS) technique. Our investigation, involving ten individuals with diverse heights, genders, and gait patterns in walking and running motions, underscores FGO’s superior performance in the presence of PDR errors and across various pedestrian and motion scenarios, achieving a stable 25% improvement for the mean position error and 30% for the median position error in comparison to KF, 24% mean improvement, and 32% median improvement in comparison to SKF. Furthermore, the convergence time for FGO after the SHE PDR errors is comparably shorter than SKF and KF.