## 1 Introduction  
With a view to the need for social and economic development as well as national security, China independently constructs and operates the BeiDou Navigation Satellite System (BDS), which is one of the Global Navigation Satellite Systems (GNSSs). BDS is an important national temporal-spatial infrastructure that is committed to providing all-weather and all-time positioning, navigation and timing (PNT) service with high accuracies for users all over the world. For the development and construction of BDS, great importance is attached by China. China has been exploring a path to develop a navigation satellite system suitable for its national conditions since the 1980s. A development strategy characterized by three steps was gradually formulated. The BeiDou navigation demonstration system (BDS-1) was built in the first step. In 1994, China started BDS-1 construction. In 2000, China launched two satellites in geostationary orbit (GEO), and then put BDS-1 into use. For the users in China, BDS-1 could provide timing, positioning, a wide-area differential as well as short-messagecommunication service with the use of an active positioning scheme. For the purpose of the further enhancement of BDS-1 performance, China launched the third GEO satellite in 2003. The regional BDS (BDS-2) was built in the second step. In 2004, China started BDS-2 construction. Fourteen BDS-2 satellites were launched by the end of 2012, including five GEO, five inclined geosynchronous orbit (IGSO) and four medium earth orbit (MEO) satellites. BDS-2 and BDS-1 adopted the compatible technical scheme, but for users in the Asia-Pacific region, the passive positioning scheme was further included to provide PNT, velocity measurement and short message communication service. The global BDS (BDS-3) was built in the third step. In 2009, China started BDS-3 construction. By 2020, BDS-3 will be completed in an all-round way (i.e., with full operational capability), with 30 launched satellites (24 MEO/3 IGSO/3 GEO). Two technical schemes, namely passive service and active service, were inherited for BDS-3. For global users, the PNT, international search and rescue, and global short-message communication service can be provided by BDS-3, while for users in China and adjacent regions, the regional short message communication, precise point positioning (PPP), ground-based augmentation, and satellite-based augmentation service can be further offered. China completed the basic constellation deployment of BDS-3 on 27 December 2018, and BDS-3 started to provide global services. The core constellation deployment of BDS-3 was completed on 16 December 2019 with a successful launch of the 24 th BDS-3 MEO satellite, and the performance of global services was further improved. On 23 June 2020, the last global networking satellite of BDS-3 was successfully launched, and the full constellation deployment of BDS-3 was officially finished. BDS-2 data processing has drawn a lot of attention from the GNSS community in the past several years [1; 2; 3; 4; 5]. With the availability of BDS-3 real data, many researchers focused on the various aspects of BDS-3, including broadcast ephemeris [6], satellite signals [7], global broadcast ionospheric delay correction model [8; 9], satellite-induced code bias [10], time group delay (TGD) [11], orbit determination [12; 13; 14], differential code bias (DCB) [15; 16], orbit and clock analysis [17], and time and frequency transfer [18]. In actuality, for a navigation satellite system, positioning is one of the core functions and basic services. GNSS-based PPP is an absolute positioning technology, which employs the GNSS observations collected by a single receiver as well as the precise products of satellite clocks and orbits from international GNSS service (IGS) [19; 20].