# Fault Detection of Resilient Navigation System Based on GNSS Pseudo-Range Measurement
## 1 Introduction  
Navigation and positioning are necessary capabilities for autonomous systems to complete remote tasks [1]. Global navigation satellite system (GNSS) provides high-precision positioning, navigation and timing (PNT) services. Based on the association and integration of satellite navigation systems and other industries, GNSS has become the technical support of the modern information industry, big data service and artificial intelligence technology. An autonomous navigation system with a flexible framework and that is suitable for a variety of environments is closely related to modern science, economy and society. Building resilient navigation systems is the future development trend of the autonomous navigation system, which ensures that users can continuously obtain high-quality PNT information in a complex environment. Due to the respective shortcomings of INS and GNSS, the positioning and attitude of autonomous vehicles are estimated generally by fusing multi-sensor information from inertial navigation system (INS), GNSS and other sensors [2, 3]. Due to environmental disturbance or carrier vibration, the sensors of autonomous vehicles are prone to more significant errors or even faults [4]. Under the influence of vehicle fluctuation, the error of the inertial navigation system will increase suddenly, and even calculation failure will occur. GNSS signals are vulnerable to electromagnetic interference [5]. If fault information is not processed, the fault measurement will pollute the results of fused navigation and positioning states. Therefore, effective fault detection and isolation methods and robust navigation estimation under unknown interference are important for autonomous system safety. Because of the advantages of the plug-and-play capability and its resilient structure, the factor graph method has gradually attracted the attention of scholars at home andabroad in recent years [6; 7; 8]. Factor graph theory was first studied in the field of coding theory. In 1981, [PERSON] introduced a bipartite graph called a \"Tanner graph\" to describe the parity check matrix in the coding field [9]. [PERSON] et al. combined the characteristics of the Wiberg graph, Tanner graph and other graph models and put forward the concept of a factor graph [10]. [PERSON] et al. proposed a factor graph information fusion model based on an inertial/visual integrated navigation system [11]. [PERSON] et al. proposed a simultaneous localization and mapping (SLAM) method to optimize the image plane with the least square method [12]. [PERSON] et al. studied a method of constructing a factor graph based on INS, which was to make full use of INS measurement in the navigation system and avoid wasting measurement information [13]. [PERSON] et al. improved the traditional factor graph fusion method and realized integrated navigation and precise positioning based on the multi-source navigation information of UAVs [14]. To improve robust performance, the development of fault detection and adaptive fusion methods suitable for the factor graph framework should be studied. In safety critical applications (SCA), fault detection and isolation (FDI) is a key aspect in order to effectively improve the robustness of the system and prevent the navigation system from crashing due to sensor failure [15]. [PERSON] et al. proposed a new fault detection algorithm based on the multi-model algorithm, in which the Kalman filter in the system is replaced by the proposed model [16]. [PERSON] et al. designed a fault-tolerant Kalman filter scheme that included multiple filters based on the Chi-square method [17]. [PERSON] performed a statistical analysis on the separability of multiple faults in a GPS/INS combined system and found a significant relationship between the correlation and fault test value based on combined similarity [18]. [PERSON] et al. studied Kullback-Leibler divergence theory and proposed a relative navigation fault detection method [19].