# Considering Inter-Frequency Clock Bias for BDS Triple-Frequency Precise Point Positioning
## 1 Introduction  
In a quest for independence, China has pursued the build-up of a proprietary national navigation satellite system for many years. According to the deployment timeline of the BeiDou navigation satellite system (BDS), its implementation has been carried out in three steps: BeiDou navigation demonstration system by 2000, regional BDS (BDS-2) by 2012 and global BDS (BDS-3) by 2020. So far, the first two steps have been realized. The deployment and operation of the demonstration system was successful. With the successful launch of the first BDS-2 satellite M1 into the Medium Earth Orbit (MEO) in 2007, the BDS-2 was initiated. A preliminary start of navigation and position services was declared on 27 December 2011. Along with the launch of the last Geostationary Earth Orbit (GEO)satellite G6 on 25 October 2012, the BDS-2 was successfully established. The official declaration of navigation and position services covering the Asia-Pacific region was made on 27 December 2012 with a BDS-2 constellation of 14 operational satellites. In 2015, China started to build up the BDS-3. So far, 5 BDS-3 In-Orbit Validation (IOV) satellites have been launched, which marks the BDS expansion from the regional to global scale. The fully deployed BDS-3 constellation will consist of 5 GEO satellites, 27 MEO satellites and 3 Inclined Geosynchronous Orbit (IGSO) satellites [1]. The Chinese BDS, the European Galileo system, the Japanese Quasi-Zenith Satellite System (QZSS), the Global Positioning System (GPS) Block IIF satellites, the GLONASS-K satellites and partial GLONASS-M satellites provide signals on three or more frequencies. The available triple-frequency signals open new prospects for integrity monitoring [2], for fast ambiguity resolution (AR) in precise relative positioning [3], for precise point positioning (PPP) [4; 5] and for ionospheric refraction analysis [6]. With the availability of more satellites from GLONASS, BDS and Galileo, many researchers focus on multi-constellation integration [7; 8; 9; 10; 11; 12]. The newly emerging situation is that the integration of multi-frequency signals has also become a trend in Global Navigation Satellite System (GNSS) development. In spite of the benefits from triple-frequency integration, an apparent inconsistency of up to 10 cm between the L1, L2 and L5 carriers was identified [13]. The L1/L2/L5 inconsistency, termed inter-frequency clock bias (IFCB), was defined as the difference between the precise satellite clock products calculated by two different ionospheric-free linear combinations of L1/L2 and L1/L5 carrier phase observations, and most likely attributed to the temperature-dependent and frequency-dependent phase bias [14]. On the contrary, the QZSS exhibited a good L1/L2/L5 consistency and no significant bias variations were observed [15; 16]. For Galileo, full consistency of three carriers could also be ensured [17]. There were small bias variations with respect to B1, B2 and B3 carriers for BDS-2 satellites, but the relevant IFCB variations were generally confined to the amplitude limits of about 2 cm [18; 19]. Since the amplitudes of single-day IFCB time series vary with time [20], their results, which were obtained based on a fairly limited amount of data, need to be further validated. The BDS-3 satellites transmit several new navigation signals, which provide more choices to form the ionospheric-free linear combination utilized for PPP. A further characterization and understanding of IFCB for BDS-2 and BDS-3 satellites is required. In addition, most of scientific studies on IFCB have focused on its characteristics and modeling, but rarely involve its effects on position determination. Actually, the high-precision IFCB estimates enable the consistent use of B1/B2 satellite clock products in B1/B3-based precise positioning. The main work includes the analysis of IFCB characteristics for BDS-2 and BDS-3 satellites and IFCB effects on BDS triple-frequency PPP.