## 1 Introduction  
China began to build BeiDou Navigation Satellite System (BDS) at the end of the 20 th century according to the three-step development strategies [1]. As planned, the first-generation BDS (BDS-1), the second-generation BDS (BDS-2), and the third-generation BDS (BDS-3) were completed successively in 2003, 2012, and 2020, with the corresponding satellite constellations of 3 Geostationary Orbit (GEO) satellites, 5 GEO satellites+5 ICSO (Inclined Geosynchronous Orbit) satellites+4 MEO (Medium Earth Orbit) satellites, and 3 GEO+3 IGSO+24 MEO satellites, respectively. Currently, the global Positioning, Navigation, and Timing (PNT) services of BDS are supported by signals on frequencies B11 (1561.098 MHz), B2I (1207.14 MHz), B3I (1268.52 MHz), B1C (1575.42 MHz), B2a (1176.45 MHz), and B2b (1207.14 MHz) [2, 3, 4, 5, 6, 7]. Among these services, the Precise Point Positioning (PPP)-B2b enhancement service is of great significance, and also it is considered to be the core support for smart city development in China. PPP, which was proposed by [PERSON] et al. [8] in 1997, is the favored technology for high-accuracy positioning applications. The corresponding model was furtherly developedin the works [8; 9; 10]. PPP can provide an accurate positioning solution using only a single GNSS receiver by utilizing precise satellite products with about two weeks delay [11; 12; 13]. Consequently, PPP is mainly for applications in post-processing currently [14; 15]. To satisfy the demands of real-time PPP, BDS-3 transmits the orbit/clock corrections of broadcast ephemeris by B2b signal [16; 17; 18; 19]. Multi-GNSS Experiment (MGEX)/iGMAS stations were adopted in [17] to verify the real-time PPP positioning performance using PPP-B2b service in static and simulated-kinematic modes by comparing with the solutions based on Geodetic Benchmark (GBM) final products. It is shown that the positioning performance of real-time PPP is slightly worse than the post-processing PPP in general, according to the statistical results. However, the convergence time of real-time PPP is slightly shorter for the BDS-only in a static model. [PERSON] et al. [16] compared PPP-B2b service with Real-Time Service (RTS) provided by Centre National d'Etudes Spatiales (CNES). Based on the analysis from six stations distributed in China, the positioning accuracy of BDS-3-only PPP with PPP-B2b service in kinematic mode can achieve decimeter-level positioning results, which is consistent with the accuracy of GPS PPP using products of CNES. However, such a PPP-B2b service-based PPP cannot maintain positioning accuracy and continuity in urban environments [20; 21], such as under bridges or trees, etc. In order to overcome the shortcomings of PPP in those circumstances, an Inertial Navigation System (INS) is integrated. INS is capable of providing position, velocity, and attitude results by using measurements from Inertial Measurement Units (IMU) without external observations. However, the position errors of INS will accumulate rapidly over time [22; 23]. Meanwhile, integrating PPP and INS can estimate and compensate IMU errors to restrain the divergence [20; 22; 24]. According to previous works, more reliable position results can be obtained by PPP/INS [20; 21; 25; 26; 27; 28; 29]. [PERSON] et al. [25] investigated the Loosely Coupled Integration (LCI) of Single Frequency (SF) PPP/INS, which was validated by a flight experiment. Results showed that the SF-PPP-only positioning performance is visibly improved in the horizontal and vertical components. LCI mode cannot work when there are not enough GNSS observations. [PERSON] in [26] further applied the Tightly Coupled Integration (TCI) of PPP and INS using different grade IMUs and different cut-off satellite angles. The results showed that reliable results could be obtained even if the number of satellites is less than 4. In [27], TCI was compared with LCI by using a tactical-grade IMU to illustrate the benefits of TCI.