# GNSS Timing Performance Assessment and Results Analysis
## 2 The Key Indicators and Assessment Method of GNSS Timing Performance  
### Principle of GNSS Timing  
Currently, UTC is the international standard timescale, which is obtained from an average of about 450 atomic clocks maintained in about 80 national timing laboratories around the world. The laboratories participate in the UTC calculation through sending clock data to BIPM and generate their real-time local estimates of UTC called UTC(k). UTC(k) estimates are contributions of UTC, where the \"k\" denotes the particular timing laboratory [18; 19]. For example, UTC(USNO) is a contribution of UTC generated at the US Naval Observatory (USNO). UTC(SU) is a contribution of UTC generated at the Russian Metrological Institute of Technical Physics and Radio Engineering. UTC(NTSC) is a con tribution of UTC generated at the National Time Service Center of China (NTSC). BIPM regularly publishes the difference between UTC and UTC(k) [20].  
Each GNSS has an independent time system that generates its internal reference timescale, which is called the system timescale. The system timescales of GPS, GLONASS, BDS, and Galileo (GNSST) correspond to GPST, GLONASST, GST, and BDT respectively. The system times of BDS, GPS, and Galileo are accumulated continuously according to the International System of Unit (SI) of seconds from their individual start epoch [21; 22; 23]. GLONASST is periodically corrected with leap seconds [24]. GNSST is necessarily steered to its time base, i.e., the national UTC(k). Consequently, the traceability of GNSST to UTC(k) is accomplished by a precise connection between the GNSS control center and national UTC(k) laboratories. GPST is steered closely to UTC(USNO) modulo 1 s. GLONASST is steered to UTC(SU). GST is steered to a reference UTC time provided by the Galileo Time Service Provider (GTSP) according to contributions from European UTC(k) laboratories. BDT is related to the UTC through UTC(NTSC). The time offset between GNSST and UTC/UTC(k) called the UTC Offset (UTCO) is determined by a time comparison between the GNSS control center and national UTC(k) laboratories. The prediction model parameter of UTCO based on the measurement processing is regularly broadcast to users by GNSS satellite.  
On the premise that the antenna coordinates of the GNSS monitoring receiver are known precisely, the time offset between the receiver time (t\({}_{\text{u}}\)) and system time (GNSST)) can be obtained from one visible satellite by subtracting various correction elements such as the geometric distance, satellite clock error, ionosphere delay, and troposphere delay from the pseudo-range observation. Furthermore, the time offset between receiver time and broadcast UTC, recorded as t\({}_{\text{u}}\)-UTC/UTC(k), is obtained using the broadcast UTCO model parameter. At this stage, GNSS timing is completed [25; 26; 27]. Usually, several satellites can be observed simultaneously at the receiver. Thus, the timing performance can be improved by weighted averaging of the receiver time offset from multiple satellites [27]. The principle of GNSS timing is illustrated in Figure 1.  
As shown in Figure 1, t\({}_{\text{u}}\)-UTC/UTC(k) can be calculated as follows:  
\[\text{t}_{\text{u}}\text{-UTC/UTC(k)}=[\text{t}_{\text{u}}-\text{t}^{(\text{s} )}]_{\text{Mon}}+[\text{t}^{(\text{s})}-\text{GNSST}]_{\text{Nav}}+[\text{UTCO }]_{\text{Nav}}, \tag{1}\]  
where the subscript Mon indicates that the time offset is obtained by receiving a SIS, and Nav indicates that the time offset is obtained from a navigation message.