Real-time Factor Graph Optimization Aided by Graduated Non-convexity Based Outlier Mitigation for Smartphone Decimeter Challenge

Real-time reliable navigation in urban environments has received academic and commercial interest over recent years. Unfortunately, commercial sensors such as smartphones are implemented with low-cost antennas and chips for receiving satellite signals and suffered from severe signal degrading caused by the non-light-of-sight (NLOS) and multi-path effect. Many conventional methods like extended Kalman filter (EKF) would always perform poorly in the urban environment. Factor graph optimization (FGO) has recently proved its reliable navigation performance in urban environments, utilizing the multi-epoch GNSS measurements to estimate the user position simultaneously. Furthermore, recent studies verified that outlier mitigation technologies using graduated non-convexity (GNC) could effectively improve GNSS positioning performance. However, those studies are mainly concerned with batch optimization which makes the computational load significant and leads to large time consumption, especially while the system integrates the GNC-based robust function in optimization for outlier mitigation. For smartphones application, this study proposed a real-time sliding window-based FGO with the implementation of GNC for outlier mitigation to guarantee reliability and low time consumption. This paper verifies the effectiveness of the contributions of this paper step by step using datasets in Shang Hai and Los Angeles. We also discussed the impact of the different sizes of sliding windows in terms of positioning error and time consumption.