## 1 Introduction  
With the rapid development of unmanned aerial vehicles (UAVs), unmanned ships (USVs), autonomous driving, and other technologies, there is a growing demand for high-precision real-time navigation. The Global Navigation Satellite System, as a mainstream means of navigation, has attracted much attention in the industry due to its global coverage, long-term effectiveness, and all-weather working capability. A GNSS, as a standard navigation sensor, is able to provide reliable positioning services in most situations. However, in complex environments such as urban canyons and tunnels, GNSS signals are susceptible to occlusion, leading to navigation interruptions [1]. In addition, GNSS signals increase in noise when subjected to interference, which, in turn, affects navigation accuracy [2, 3]. More importantly, GNSSs are unable to provide all of the navigation status information required for certain carrier control, such as precise horizontal attitude angles [4]. Therefore, a single GNSS may have limitations in continuous navigation missions. In order to overcome the shortcomings of a single sensor and improve the overall performance of the navigation system, it is necessary to introduce other sensors for assistance. Inertial Measurement Units (IMUs), consisting of gyroscopes and accelerometers, do not rely on external signals and offer higher autonomy, faster update rates, and more stable short-term accuracy. Although IMUs suffer from errors accumulated over time, their fusion with a GNSS can fully utilize their respective advantages and complement each other [5]. The integrated system composed of a GNSS and an inertial navigation system (INS) is superior to single-element navigation systems in terms of stability and accuracy. With the advancement of GNSS receiver and Micro-Electro-Mechanical System (MEMS) technology, the cost of combined satellite-inertial navigation systems has been reduced significantly, which paves the way for their wide application in smart driving vehicles. Currently, the combined navigation schemes based on the integration of a GNSS and an INS are mainly categorized into loosely coupled (LC), tightly coupled (TC), and deeply coupled (DC) forms based on the level and complexity of their combination [6]. In the loosely coupled scheme, the GNSS and INS operate as two independent systems, with the GNSS being responsible for providing long-term corrections of position and velocity and the INS providing short-term, high-precision data. Due to its simple structure and redundancy, the LC scheme is currently the most widely adopted navigation scheme. However, the LC scheme suffers from the problem of serial filtering in data processing and cannot effectively utilize GNSS data to assist the INS for navigation when the number of visible satellites is less than four. Compared to the LC scheme, the deep-coupling scheme fuses GNSS and IMU data in the signal processing stage, and its distinctive feature is that it utilizes the velocity information of the INS to assist the tracking loop of the GNSS receiver, which enhances the receiver's anti-jamming capability, improves the dynamic performance, and reduces the dynamic error. However, this scheme requires the high computational capability of the hardware and is difficult to realize, so it is mainly used in the military and aerospace fields. For civilian carriers, the performance and cost-benefit ratio of the DC scheme still need to be further evaluated. The TC scheme fuses GNSS and IMU data at the algorithmic level with high accuracy and robustness, and even when the satellite observation is poor, the TC combined system does not need the complete GNSS information to assist the INS, and fusion processing can be carried out when visible satellites are fewer than four [7]. Although TC schemes are able to maintain combined navigation in environments where GNSS signals are obstructed, errors due to non-line-of-sight (NLOS) reception in such environments can be tens of meters or more, with multipath effects being particularly severe.