## 1 Introduction
Furthermore, [PERSON] [24] studied the integration of GPS PPP and MEMS (micro-electro-mechanical System)-based inertial system, the results of which suggested that decimeter-level positioning accuracy was achievable for GPS outages within 30 s. [PERSON] et al. [23] analyzed the integration of multi-GNSS PPP with MEMS IMU. The results showed that the position RMS improved from 23.3 cm, 19.8 cm, and 14.9 cm for the GPS PPP/INS tightly coupled integration to 7.9 cm, 3.3 cm, and 5.1 cm for the multi-GNSS PPP/INS in the north, east, and up components, respectively. PPP-AR/INS tightly coupled integration is able to realize stable centimeter-level positioning after the first AR and achieve fast re-convergence and re-resolving after a short period of GNSS outage [25]. [PERSON] et al. [26] analyzed the performance of the tightly coupled integration of RTK/INS constrained with the ionospheric and tropospheric models. [PERSON] et al. [27] realized the tightly coupled integration of multi-GNSS PPP/INS with atmospheric augmentation. Taking the advantages of PPP-RTK over PPP and RTK into consideration, the integration of multi-GNSS PPP-RTK and MEMS IMU still needs further research. The performance of GNSS/INS tightly coupled integration could deteriorate even if there were short periods of GNSS signal outages and the positioning accuracy was terrible during long periods of GNSS signal outages, as the drift of INS accumulates rapidly. Therefore, other aiding sensors are required to limit the drift errors of INS when the GNSS signals are blocked. On the one hand, a camera is suitable for solving this problem since visual odometry (VO) can estimate the motion of a vehicle with a slow drift. On the other hand, the model of the monocular camera is relatively simple, but it lacks the metric scale, which can be recovered by IMU. Consequently, a monocular camera is usually integrated with IMU to achieve accurate pose estimations. The fusion algorithms of IMU and vision are usually based on an extended Kalman filter (EKF) [28; 29; 30] or nonlinear optimization [31; 32]. The former method usually carries out linearization only once, so there may be obvious linearization errors for vision data processing. The latter method utilizes iterative linearization, which can achieve higher estimation accuracy but is subject to an increased computational burden. The multi-state constraint Kalman filter (MSCKF) is a popular EKF-based visual-inertial odometry (VIO) approach, which is capable of high-precision pose estimations in large-scale real-world environments [28]. MSCKF maintains several previous camera poses in the state vector by a sliding window and forms the constraints among multiple camera poses by using visual measurements of the same feature point across multiple camera views. Accordingly, the computational complexity is linear with the number of feature points. On the one hand, VIO can provide accurate pose estimations when GNSS is unavailable. On the other hand, VIO or VI-SLAM (simultaneous localization and mapping) can only achieve an estimation of motion and provide the relative position and attitude and there are unavoidable accumulated drifts over time. Consequently, the integration of GNSS, INS, and vision is receiving increasing interest [33; 34; 35; 36]. [PERSON] et al., 2005 used a six-degrees-of-freedom (DOF) SLAM to aid GNSS/INS navigation by providing reliable navigation solutions in denied and unknown environments GNSS. Then, [PERSON] et al. integrated GNSS with vision for low GNSS visibility [34], and proposed the selective integration of GNSS, INS, and vision under GNSS-challenged environments [2], which was able to improve the positioning accuracy compared with nonselective integration. However, in most of these studies, only the position provided by the GNSS or pseudo-range measurements were utilized in the fusion of GNSS, INS, and vision. The application of the carrier phase in multi-sensor fusion is less studied.