## 1 Introduction  
Autonomous driving, unmanned aerial vehicles (UAVs), and the Internet of Things (IoT) are technologies that have developed rapidly in recent years. Precise navigation and positioning in complex environments are receiving increasing attention. However, any one sensor alone is not able to provide position solutions with high accuracy, availability, reliability, and continuity at any time and in all environments [1]. The integration of different sensors, for example, the integration of GNSS, INS, and vision, has become a trend [2; 3; 4]. GNSS (global navigation satellite system) is an efficient tool for providing precise positioning regardless of time and location and it is widely used in transportation. [PERSON] et al. [5] proposed the precise point positioning (PPP) technique, which has received much attention in recent years for its low costs, global coverage, and high accuracy [6; 7]. Though PPP can provide centimeter-level positioning for real-time kinematic applications, a nearly 30 min convergence time has limited its applications in UAVs and other technologies. Thus, great efforts have been focused on improving the PPP performance, especially to accelerate its convergence, and promoting various methods, e.g., multi-GNSS combination, ambiguity resolution, and atmospheric augmentation. [PERSON] et al. [8] presented a comprehensive analysis of quad-constellations with PPP. The results showed that in comparison with the GPS-only solution, the four-system combined PPP can reduce the convergence time by more than 60% on average in kinematic mode. For ambiguity resolution, [PERSON] et al. [9] proposed the uncalibrated phase delay (UPD) method. Then, [PERSON] et al. [10] proposed the integer phase clock method, and [PERSON] et al. [11] proposed the decoupled clock model to facilitate PPP ambiguity resolution (PPP-AR). It was proved that these three PPP-AR methods can dramatically accelerate the convergence and improve the positioning accuracy of PPP [9; 10; 11; 12]. The undifferenced and uncombined data processing strategy has received increasing interest [13; 14; 15; 16; 17; 18]. First proposed by [PERSON] et al. [19], PPP with ambiguity resolution and atmospheric augmentation is nowadays widely regarded as PPP-RTK (real-time kinematic). As PPP-RTK weakens the influence of the long convergence time in PPP and regional service coverage in RTK, it is regarded as a promising technique for high-precision navigation in mass market applications, including vehicle platforms. As a result, some regional authorities have developed their own PPP-RTK augmentation services, e.g., QZSS centimeter-level accuracy service (QZSS CLAS) began offering PPP-RTK services in 2018 [20]. Chinese BDS also intends to provide its satellite-based PPP-RTK service in the future. However, the performance of GNSS is limited by non-line-of-sight (NLOS) conditions, which means PPP-RTK cannot work very well in challenging environments such as urban areas [21]. When the satellite signals are blocked by buildings or other structures, PPP-RTK fails to provide positioning results if there are less than four satellites available and the performance is terrible due to frequent re-convergence and gross errors. Inertial navigation systems (INS) are immune to interference and can output navigation states continuously without external information. However, the accuracy degrades fast over time due to the accumulated errors. Integrating GNSS with INS can minimize their respective drawbacks and improve the performance of GNSS or INS alone. There are two common integration strategies for PPP with INS, tightly coupled integration and loosely coupled integration [22]. Moreover, it has been proved that the tightly coupled integration of PPP/INS performs better than loosely coupled integration, especially under GNSS-challenged environments [23].