# Comprehensive Analysis of PPP-B2b Service and Its Impact on BDS-3/GPS Real-Time PPP Time Transfer
## 2 Methods
### Assessment Methods of PPP-B2b Corrections  
Currently, the PPP-B2b contains only the first four message types, as shown in Table 1. The IOD SSR represents the issue number of state space representation, which should remain consistent with each other for different message types. The IODP included in message types one and four denotes the satellite mask's data issue number. Users can use it to determine if the data in the two message types match. The ephemeris and clock offset corrections broadcast by the GNSS downlink signal are identified by the issue number IODN, and the users could determine whether the broadcast ephemeris matches the orbit corrections in message types two, six, and seven by the IODN. For shared satellites, they can be used to recover real-time orbits and clock offsets only if the clock offset's IOD Corr and the orbit's IOD Corr contained in message types two and four, respectively, are the same. The update periods of the two IOD Corrs are 48 s and 6 s. Note that when the clock offset's IOD Corr at the current moment is different from that at the previous moment, the orbit's IOD Corr does not change, which may lead to outliers in PPP. To eliminate the mismatching problem, when the two IOD Corrs are different, it is an efficient method to use the clock offset's IOD Corr that previously matched the orbit's IOD Corr, which will reduce the impact on the PPP performance [25]. Since the broadcast ephemeris provides the orbit corrections in the X/Y/Z components under the ECEF framework, and the PPP-B2b provides the orbit corrections in the radial (R), along-track (A), and cross-track (C) components, PPP-B2b satellite orbit corrections in the R/A/C directions should be converted to the corrections in the X/Y/Z directions under the ECEF coordinate system. The precise satellite orbit \(\mathbf{X}_{prec}\) and clock offset \(t_{prec}\) can be expressed by using Equations (1)-(3) [22]. \[\mathbf{\delta X}= \begin{bmatrix}\mathbf{e}_{r}&\mathbf{e}_{a}&\mathbf{e}_{c} \end{bmatrix} \cdot\mathbf{\delta O} \tag{1}\]  
\[\mathbf{X}_{prec}=\mathbf{X}_{brdc}-\mathbf{\delta X} \tag{2}\]  
\[t_{prec}=t_{brdc}-\frac{C_{0}}{c} \tag{3}\]  
where \(\mathbf{\delta O}= \begin{bmatrix}\mathbf{\delta}O_{r}&\mathbf{\delta}O_{a}& \mathbf{\delta}O_{c}\end{bmatrix} ^{\text{T}}\) is the vector of orbit parameters provided by PPP-B2b; \( \begin{bmatrix}\mathbf{e}_{r}&\mathbf{e}_{a}&\mathbf{e}_{c}\end{bmatrix} \) is an orthogonal matrix consisting of three unit vectors; \(\mathbf{\delta X}\) is the converted vector of the orbit parameters; \(\mathbf{X}_{brdc}\) and \(t_{brdc}\) indicate the satellite coordinates and clock offsets obtained from the broadcast ephemeris, respectively; \(C_{0}\) is the PPP-B2b clock parameters; and \(c\) is the speed of light in the vacuum. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Information Content** & **Message Type** & **IODs** & **Nominal Validity(s)** \\ \hline Clock correction & 4, 6, 7 & IOD SSR, IODP, IOD Corr & 12 \\ DCB correction & 3 & IOD SSR & 86,400 \\ Orbit correction & 2, 6, 7 & IOD SSR, IODN, IOD Corr & 96 \\ URAI & 2, 5, 6, 7 & - & 96 \\ Satellite mask & 1 & IOD SSR, IODP & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Information of PPP-B2b messages. In addition, the DCB caused by the hardware delay difference of the satellites between different frequencies could affect the PPP performance. The PPP-B2b provides the DCB products to eliminate the hardware delay and enable synchronous processing of different signals by using the Equation (4) [22]. \[\widetilde{P}_{sig}=P_{sig}-DCB_{sig} \tag{4}\]  
where \(P_{sig}\) is the initial observations; \(DCB_{sig}\) denotes the differential code bias of the corresponding signal; and \(\widetilde{P}_{sig}\) denotes the corrected observations.