# Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products
## 1 Introduction  
Satellite time in the GNSS system is established and maintained by satellite onboard clocks, and the performance of satellite clocks directly determines the accuracy of navigation, positioning, and timing services. Therefore, the performance evaluation of satellite onboard clocks is of great significance to GNSS system construction and user service [1]. China's BeiDou-2 Navigation Satellite System (BDS-2) has officially provided services to the Asia-Pacific region since 2012 [2]. Its satellite constellation consists of seven inclined geosynchronous orbit (IGSO), five geostationary (GEO), and three medium Earth orbit (MEO) satellites [3]. All of the BDS-2 satellites are manufactured by the China Academy of Space Technology (CAST). Each satellite is equipped with four high-quality rubidium (Rb) clocks [4]. Performance of BDS-2 onboard clocks has been widely studied. The clock model fitting accuracy is about 0.4 ns [5], which is worse than that of GPS satellites [6]. The clock drift rate is about \(1\times 10^{-13}\) s/day [7]. Daily frequency stability can reach a level of \(10^{-14}\)[8]. From 2013 to 2018, an atomic clock switch was detected on all BDS-2 satellites, which indicated that BDS satellites needed further improvements in clock quality [5]. To improve the service performance of atomic clocks, new generation high-precision Rb clocks and passive hydrogen masers (PHM) have been equipped on BDS-3 experimental (BDS-3e) satellites and subsequent BDS-3 satellites [9, 10, 11]. The BDS-3 constellationconsists of three GEO, twenty-four MEO, and three IGSO satellites, which were developed and manufactured by CAST and the Shanghai Engineering Centre for Microsatellites (SECM) [9; 10]. With construction of the BDS-3 system, some initial studies were carried out on the performance of the BDS-3e and BDS-3 MEO satellite onboard clocks [12; 13; 14; 15; 16; 17]. The drift rate of Rb clocks on the BDS-3 MEO satellite is about \(1.15\times 10^{-18}\) s/s and that of the PHMs is \(3.15\times 10^{-19}\) s/s, which are \(7.5\%\) and \(73\%\) less than that of BDS-2 Rb clocks, respectively [14]. The noise level of BDS-3 MEO clocks evaluated by the daily fitting residuals is about 0.2 ns [15]. Moreover, the 2-hour, 10-hour, and 7-day prediction precisions of BDS-3 PHMs are about 0.3, 0.4, and 2.2 ns, respectively [16]. The daily stability of BDS-3 MEO satellites is about 2-\(5\times 10^{-15}\) s/s [14]. The stability level of the BDS-3 PHMs is comparable to that of the PHMs of the Galileo as well as to the Rb clocks of the GPS Block IIF; meanwhile, the improved BDS-3 Rb clock is comparable to that of the Galileo Rb clock [17]. With the improved stability of BDS-3 satellite clocks, about 70% level positioning accuracy for BDS-3 is better than 0.65 m at 10 min, which is much better than the positioning accuracy of BDS-2 [18]. Although many pieces of research focus on BDS-3 onboard clocks, these studies concentrated on the performance of the clocks equipped in the BDS-3 experimental satellites and the 18 BDS-3 MEO satellites. By the end of 2021, the complete BDS-3 system was officially in operation for more than one year, but few studies analyzed the performance of the three types of BDS-3 satellites' (including IGSOs, MEOs, and GEOs) onboard clocks. In this paper, the precision clock offset products with an interval of 30 s from day-of-year (DOY) 1, 2021 to DOY 300, 2021 provided by GeoForschungsZentrum (GFZ) are used to evaluate the onboard clock performance of 29 BDS-3 satellites, including IGSOs, MEOs, and GEOs. Performance of BDS-2 clocks is also evaluated for comparison with BDS-3 clocks. Firstly, the long-term clock bias, frequency, drift, and noise are compared and evaluated based on the clock offset data. Then, the fitting residuals of satellite clocks are computed to reflect the noise level of onboard clocks. Furthermore, frequency stability is analyzed, since frequency stability is an important index for evaluating onboard clock characteristics.