Accurate and smooth global navigation satellite system (GNSS) positioning for pedestrians in urban canyons is still a challenge due to the multipath effects and the non-light-of-sight (NLOS) receptions caused by the reflections from surrounding buildings. The recently developed factor graph optimization (FGO) based GNSS positioning method opened a new window for improving urban GNSS positioning by effectively exploiting the measurement redundancy from the 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, this paper exploits the potential of the pedestrian dead reckoning (PDR) model in FGO to improve the GNSS standalone positioning performance in urban canyons. 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. The effectiveness of the proposed method is verified step-by-step through two datasets 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 results reveal that the existing FGO-based GNSS standalone positioning is highly complementary to the PDR's relative motion estimation. Both improved positioning accuracy and trajectory smoothness are obtained with the help of the proposed method.

翻译：在城市峡谷中，由于周围建筑物反射引起的多路径效应和非视距（NLOS）接收，实现行人高精度和平滑的全球导航卫星系统（GNSS）定位仍然是一个挑战。近年来发展的基于因子图优化（FGO）的GNSS定位方法，通过有效利用历史信息的测量冗余来抵抗异常测量，为改善城市GNSS定位开辟了新窗口。然而，基于FGO的独立GNSS定位在高城市化区域仍面临挑战。作为先前FGO-GNSS定位方法的扩展，本文探索了行人航迹推算（PDR）模型在FGO中的应用潜力，以提升城市峡谷中独立GNSS定位性能。具体而言，通过智能手机内置惯性测量单元（IMU）的原始加速度测量值，利用PDR算法估计行人的相对运动；随后将原始GNSS伪距、多普勒测量与PDR相对运动通过FGO进行融合。针对行人导航中大多数时间加速度较小的特点，提出了一种新颖的软运动模型来平滑因子图模型中的状态变量。通过在香港密集城市峡谷中使用智能手机级GNSS接收机采集的两组数据集，逐步验证了所提方法的有效性。本文对比了传统扩展卡尔曼滤波、若干现有方法与基于FGO的融合方法。结果表明，现有FGO独立GNSS定位与PDR相对运动估计具有高度互补性。借助所提方法，定位精度和轨迹平滑性均得到提升。