## 1 Introduction  
According to the experience of the first generation of the Chinese BeiDou Navigation Satellite System, the development of the second generation has been separated into two phases: (1) service for the Asia-Pacific region by the end of 2012 (BeiDou-2) and (2) global coverage by the end of 2020 (BeiDou-3) [1,2]. The BeiDou-2 constellation that provides the regional service consists of three types of satellites: geostationary orbit (GEO), inclined geosynchronous orbit (IGSO), and medium Earth orbit (MEO). The constellation for regional service consists of 14 satellites, including five GEOs (pseudo random noise (PRN) C01-C05), five IGSOs (PRN C06-C10), and four MEOs (PRN C11-C14) [3]. Because the M05 satellite (PRN C13) had already stopped transmitting signals since 21 October 2014, a new IGSO (106) was launched to supply regional coverage and has been in service since March 2016. With the development of BeiDou-2, many studies have been carried out on various aspects of this system. In comparison with the Global Positioning System (GPS) and the GLObal Navigation Satellite System (GLONASS), BeiDou-2 satellite pseudorange observations show obvious systematic biases in different frequencies for different constellations, which were first mentioned by [PERSON] et al. [4] and [PERSON] et al. [5], and then were subsequently diagnosed and modeled using piece-wise linear functions with respect to satellite elevations by [PERSON] [6]. As for the BeiDou precise orbit determination (POD) research, six MGEX (Multi-GNSS Experiment) analysis centers (ACs) have been routinely providing GNSS precise orbit and clock products since 2012 on the basis of MGEX stations, namely, the Center for Orbit Determination in Europe (CODE), GeoForschungsZentrum Potsdam (GFZ), Centre National d'Etudes Spatiales / Collecte de Localisation Satellite (CNES/CLS), the Japan Aerospace Exploration Agency (JAXA), Technische Universitat Munchen (TUM), and Wuhan University (WHU). [PERSON] et al. [7] assessed BeiDou orbits provided by MGEX ACs, which showed that the precision of day boundary discontinuities for all AC products were on the decimeter to meter scale for GEOs, 1-3 dm for IGSOs, and 10-27 cm for MEOs. Moreover, the performance of precise point positioning (PPP) by the BeiDou-2 system has also been assessed. The horizontal and vertical positioning accuracies were found to be better than 1 cm and 3 cm in static mode, and better than 2-3 cm and 10 cm in kinematic mode. The PPP convergence time for the BeiDou-2 system was only about 50 min [8; 9; 10]. To implement the plan for global service, five next-generation experimental satellites (two IGSOs and three MEOs), named BeiDou-3e [11], have been launched since 2015 to test satellite payloads and global service signals. Inter-satellite link (ISL) payloads have been assembled on the experimental satellites, and observational data of ISL has been obtained and processed for autonomous orbit determination [12]. The BeiDou-3e satellites transmit signals at five frequencies, namely, BII and B3I legacy signals, similar to those from BeiDou-2 satellites, as well as modernized signals in the B1C, B2a, and B2b bands. Furthermore, [PERSON] et al. [11] investigated the consistency of the carrier phase for BeiDou-3e satellites using the differential ionosphere-free combination with respect to the triple-frequency carrier phase using ionosphere-free and geometry-free combination. No significant bias variations were observed for any of the next-generation BeiDou-3e satellites, although these have been found in BeiDou-2 and GPS Block IIF satellites signals owing to unstable inter-frequency clock offsets. [PERSON] et al. [13] calculated the BeiDou-3e orbit and assessed its precision by overlapping comparison and satellite laser ranging (SLR) based on nine BeiDou-3e stations and 52 BeiDou-2 stations, and the precisions of the radial components for BeiDou-3e IGSOs and MEOs were 10 cm and 40 cm, respectively. [PERSON] et al.