Interactive Filtering-Graph-Optimization Method for Resilient GNSS/PDR Integrated Navigation

Given the superiority of global consistency and plug-and-play capability, factor graph optimization (FGO) has been extensively studied in multisensor integrated navigation. However, due to the lack of an error covariance matrix for evaluating the posterior state estimate, FGO cannot construct test statistics that perfectly meet theoretical requirements for fault detection and exclusion (FDE). Filtering-based algorithms possess a mature theoretical foundation. Therefore, using filtering to assist FGO algorithm for FDE is a feasible approach. Based on this, an interactive filtering-graph-optimization (IFGO) framework for global navigation satellite system (GNSS)/pedestrian dead reckoning (PDR) integrated navigation systems is proposed in this article. First, the proposed algorithm implements parallel computation of extended Kalman filter (EKF) and FGO within the GNSS/PDR integration framework. Then, the algorithm uses the fault-free and deviation segments of the IGG-III function to generate equivalent weight factors to adjust the observation noise matrix of EKF and FGO in real time to reduce the influence of observation biases. Furthermore, the solutions from the EKF are used as the iteration initial values for the FGO. Ultimately, to solve the problem that loosely coupled GNSS/PDR is easily affected by long-term multiepoch anomaly observation, the prediction innovation is used to reconfigure the anomaly observation, and the reconfigured observation is fed into FGO to realize navigation and positioning. The proposed algorithm is implemented in two types of GNSS/PDR factor graph models: 1) FGO-GNSS/PDR with position constraint (P-FGO) and 2) FGO-GNSS/PDR with stride length constraint (S-FGO). The experimental results show that the proposed algorithm reduced the maximum error by 7.8% and the average error by 12.3% compared with the P-FGO; it reduced the maximum error by 50.03% and the average error by 15.06% compared with the S-FGO. At the same time, the proposed algorithm improved computational efficiency by 81.64% and 33.83% compared with P-FGO and S-FGO, respectively.