## 1 Introduction  
Effective positioning and navigation are vital for autonomous systems, such as unmanned driving and intelligent vehicles, especially in complex urban environments [1, 2, 3]. The realization of autonomous transportation systems depends on multi-sensor information fusion from the inertial measurement unit (IMU), global navigation satellite system (GNSS), and vision sensor measurements [4]. However, due to the disturbance caused by complex environments, vehicle sensors are prone to significant errors and even failures [5]. An inertial navigation system (INS) is a good choice for urban positioning because of its short-time high precision characteristic. Nevertheless, the errors in INS measurements will accumulate over time and may have a sudden increase affected by the fluctuation or vibration of the transport systems without auxiliary sensors [6]. GNSS has the ability to provide high-precision navigation information and compensates for the accumulation of INS errors through an integrated navigation scheme, but its signals are susceptible to external environmental influence [7]. Affected by occlusion from complex environments, such as high-rise buildings and tunnels, GNSS may become completely ineffective. Therefore, the urban environment has a significant impact on the navigation accuracy of GNSS [8]. Visual navigation systems have attracted significant attention in autonomous systems, and LiDAR is widely used due to its high precision and high-frequency data acquisition capability. LiDAR alone for navigation may be difficult due to the loss of features or the insensitivity to dynamic targets in urban environments [9]. Considering the disturbance under complex urban environments, an effective fault detection and adaptive integrated navigation method is necessary for vehicle safety. Integrated navigation schemes based on multi-source information fusion for vehicle navigation have been extensively investigated. Considering the difficulties of accurate modeling and prediction for external dynamic disturbance, the traditional extended Kalman filter (EKF) algorithm fails to satisfy the robustness requirements [10; 11]. To address this problem, the adaptive Kalman filter (AKF) provides a solution. [PERSON] et al. introduced an improved multi-rate strong tracking cubature Kalman filter (CKF) to estimate the system covariance adaptively [12]. Also, a dual optimization scheme comprising a CKF-multiple layer perceptron and radial basis function-CKF was proposed to maintain system accuracy during GNSS denying [13]. The factor graph algorithm is featured due to its multi-source asynchronous information fusion and plug-and-play abilities. It has been widely applied in navigation and simultaneous localization and mapping (SLAM) areas for data optimization [14]. As a probability graph model, the factor graph is able to estimate and update the state variables through graph modeling of mathematical problems. A direct method for navigation is constructing the multi-source navigation system under factor graph modeling and using graph optimization as a filter for information fusion. [PERSON] proposed an inertial/visual integrated navigation system which describes sensor error models of factor nodes and estimates the system states through the factor graph optimization algorithm [15]. To verify the effectiveness of the factor graph model, [PERSON] et al. compared the factor graph algorithm with EKF using dataset experiments. The results showed that as an information fusion strategy, the factor graph performs better in disturbed environments owing to its historical information fusion ability [16]. Additionally, the sliding window algorithm enables the factor graph to marginalize information, thus reducing the computational burden of the whole system and improving the real-time performance. Another application of factor graphs is solving the SLAM backend optimization problem.