# Intelligent Environment-Adaptive GNSS/INS Integrated Positioning with Factor Graph Optimization
## 1 Introduction  
Global navigation satellite systems (GNSSs) are a widely recognized navigation technology that has been applied in various fields, including robotics, the military, and agriculture. Intelligent transport systems (ITSs) are one of the most popular research areas due to the pros of autonomous vehicles. However, the system performance highly depends on positioning accuracy. In urban canyons, GNSS signals are susceptible to multipath and non-line-of-sight (NLOS) effects due to the reflection and blockage of signals from high-rise buildings [1]. The multipath effect may cause meters of positioning error, while an NLOS signal can seriously deteriorate the GNSS positioning accuracy to errors of a hundred meters [2, 3]. Numerous research has been proposed to enhance the accuracy and reliability of GNSS positioning results. The 3D-mapping-aided (3 DMA) GNSS approach is one of the popular methods applied in urban areas. Researchers [4, 5] employed a 3D building model incorporated with the ray tracing technique to predict the transmission path of the GNSS signal and correct the NLOS delay. [PERSON] et al. [6] developed an algorithm that matches images taken by a fisheye camera with skymasks generated by 3 DMA to decide the position and heading of the fisheye image. However, this method requires an up-to-date 3D building model and strong computational power to simulate the path and process the image. Another popular approach is multi-sensor fusion. The developmentof GNSSs, inertial navigation systems (INSs), and light detection and ranging (Lidar)-integrated systems have enhanced the positioning continuity and accuracy during GNSS outage periods and under challenging environments [7; 8]. [PERSON] et al. [9] adaptively fused GNSS, Lidar, inertial measurement unit (IMU), and real-time kinematic (RTK) sensors according to an uncertainty estimation algorithm to prevent system failures in various scenes. [PERSON] et al. [10] proposed a tightly coupled GNSS-visual-inertial fusion system to cope with challenging environments for positioning. However, incorporating multiple sensors results in increased cost, which forms a barrier to integration into commercial products, whereas GNSS/INS integration is more economical and widely applicable in the industry. Enhancing the positioning accuracy of GNSS/INS integration using various algorithms has attracted researchers' interest. The coupling methods can be divided into loosely coupled (LC), tightly coupled (TC), and ultra-tightly coupled (UTC) depending on the type of GNSS data used to perform integration. LC integration utilizes the position information of GNSS receivers, while TC integration uses the raw GNSS measurements such as pseudo-range and Doppler observables [11; 12]. In UTC integration, in-phase (I) and quadrature-phase (Q) components of the signal are directly fed into the filter [13]. However, it requires adjustment on receiver architectures, which limits its applicability with general equipment. The traditional KF method and its extensions, such as extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman Filter (CKF), are the most common integration algorithms. The effectiveness and robustness of KF-based algorithm have been verified by several studies [14; 15; 16; 17; 18; 19; 20]. [PERSON] et al. [17] employed EKF to integrate linearized correlator outputs and INS measurements. Nevertheless, EKF might cause large errors during the linearization process. Instead of approximating non-linear functions by a Taylor series expansion, UKF adopts probability distribution to represent the non-linearity [18]. A derivative UKF of TC integration was proposed by [PERSON] et al. [19] to achieve at least a second-order accuracy of the Taylor series. CKF features more accurate state estimation using the cubature technique [20], and the research work by [PERSON] et al. [21] proved that CKF further reduces the positioning error and computational time compared with UKF.