# Fault-Free Protection Level Equation for CLAS PPP-RTK and Experimental Evaluations
## 2 Overview of the CLAS Broadcast Messages  
CLAS receives the GNSS observation data from approximately 1200 GEONET stations and processes the data to generate the correction and integrity messages in a Compact SSR format. The Compact SSR messages are broadcast through the L6 band by the QZSS and are defined as RTCM 3 compatible proprietary message type 4073 [13]. The Compact SSR messages have 12 subtypes consisting of correction and integrity information, and the message types are listed in Table 1[21]. The correction messages for the orbit, clock, code bias, and phase bias are called common corrections. The zenith tropospheric delay and slant ionospheric delay for each GNSS are referred to as local corrections.  
Among the message subtype IDs, the quality messages are included in subtype IDs 7, 8, 9, and 12. Subtype ID 7 provides a quality indicator for the user range accuracy (URA) of each satellite, and others provide a troposphere quality indicator as well as an SSR slant total electron content (STEC) quality indicator. The quality indicator is represented by a combination of CLASS and VALUE, the values of which range from 0 to 7, as seen in Equation (1). The SSR URA and tropospheric quality indicators were converted to a physical quantity using the following Equation [21]:  
\[\text{Quality Indicator }[\text{mm}]\leq 3^{\text{CLASS}}\left(1+\frac{\text{ VALUE}}{4}\right)-1\ [\text{mm}] \tag{1}\]  
The SSR STEC physical quantity was read from a table relating the SSR STEC quality indicators to the SSR STEC correction uncertainty.  
The total ranging error for \(i\)th satellite can be estimated by the following equation  
\[\sigma_{i}=\sqrt{\left(\sigma_{i,user}\right)^{2}+\left(\sigma_{i,vis}/10 \right)^{2}+\left(\frac{40.3\times 10^{16}}{f^{2}}\sigma_{i,\text{ iono }}\times 100\right)^{2}+\left(\left(\sigma_{i,\text{ trop }}/10\right)/\sin E_{i}\right)^{2}}, \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Message Name**} & **Message Type ID** & \multirow{2}{*}{**Nominal Validity Period [s]**} & \multirow{2}{*}{**Nominal Update Interval [s]**} \\  & **Subtype ID** & & \\ \hline Compact SSR Mask & MT4073,1 & 1 & 30 \\ Compact SSR GNSS Orbit Correction & MT4073,2 & 60 & 30 \\ Compact SSR GNSS Clock Correction & MT4073,3 & 10 & 5 \\ Compact SSR GNSS Satellite Code Bias & MT4073,4 & 60 & 30 \\ Compact SSR GNSS Satellite Phase Bias & MT4073,5 & 60 & 30 \\ Compact SSR GNSS Satellite Code and & MT4073,6 & 60 & 30 \\ Phase Bias & MT4073,7 & 60 & 30 \\ Compact SSR GNSS URA & MT4073,7 & 60 & 30 \\ Compact SSR STEC Correction & MT4073,8 & 60 & 30 \\ Compact SSR Gridded Correction & MT4073,9 & 60 & 30 \\ Compact SSR Service Information & MT4073,10 & (N/A) & (N/A) \\ Compact SSR GNSS Combined & MT4073,11 & 10 or 60 & 5 or 30 \\ Correction & MT4073,12 & 60 & 30 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Compact SSR message type, nominal validity period, and nominal update interval.  
where \(\sigma_{i,user}\) is a user-specific local error, such as multipath errors. \(\sigma_{i,sis}\) is a signal in space error representing the correction message uncertainty of the orbit, clock, code, and carrier biases. \(\sigma_{i,\text{ iono}}\) is the ionospheric delay correction uncertainty provided from the STEC correction quality indicator in total electron content unit (TECU). \(\sigma_{i,\text{ topo}}\) represent the troposphere delay correction uncertainty. \(f\) is the frequency of the GNSS signal and \(E_{i}\) is the satellite elevation angle. The total ranging error is calculated in centimeters, which is why both \(\sigma_{i,sis}\) and \(\sigma_{i,\text{ topo}}\) divided by 10 is used, and the same applies for \(\sigma_{i,\text{ iono}}\). Some examples of the CLAS broadcast quality indicators are presented in Section 4.