Trajectory Smoothing Using GNSS/PDR Integration via Factor Graph Optimization in Urban Canyons

Smooth and accurate global navigation satellite system (GNSS) positioning for pedestrians in urban canyons is still a challenge due to the multipath effects and the nonline-of-sight (NLOS) receptions caused by the reflections from surrounding buildings. Factor graph optimization (FGO) attracts more and more attention in GNSS society for improving urban GNSS positioning by effectively exploiting the measurement redundancy from historical information to resist the outlier measurements. Unfortunately, the FGO-based GNSS standalone positioning is still challenged in highly urbanized areas. As an extension of the previous FGO-based GNSS positioning method, the potential of the pedestrian dead reckoning (PDR) model in FGO to improve the GNSS standalone positioning performance in urban canyons is exploited in this article. Specifically, the relative motion of the pedestrian is estimated based on the raw acceleration measurements from the onboard smartphone inertial measurement unit (IMU) via the PDR algorithm. Then, the raw GNSS pseudorange, Doppler measurements, and relative motion from PDR are integrated using the FGO. Given the context of pedestrian navigation with a small acceleration most of the time, a novel soft motion model is proposed to smooth the states involved in the factor graph model. This article verified the effectiveness of employing the PDR model in FGO step-by-step through two data sets collected in dense urban canyons of Hong Kong using smartphone-level GNSS receivers. The comparison between the conventional extended Kalman filter, several existing methods, and FGO-based integration is presented. The proposed method shows better results than the conventional FGO method in all test data sets, with at least a 22% decrease in the mean value of the positioning error. The proposed method reduces the average localization error from 31.64 m to 18.51 m in a deep urban area.