## 2 The CNES PPP-WIZARD Demonstrator
### Computation of the post-processed Phase Biases  
To overcome the different limitations of the real-time phase bias productions (lack of compatible stations, RTCM standard not up to date for some BDS-3 real-time observables), it has been decided to implement a routine production of post-processed phase biases besides the real-time ones. The idea is to compute the phase biases in addition to the already existing products at the IGS. GFZ rapid products were chosen because they support all the GNSS constellations and are of low latency (a few days). The process is described in Figure 5.  
It is first mandatory to collect all the necessary data (rinex files of a network of more than 260 IGS stations, SP3, CLK and YAW files, and auxiliary products such as the sinex file of the day, antex files, code biases, and broadcasts). The phase biases can then be computed following these steps:  
1. a first PPP pass (forward, backward) to compute the troposphere elongation of the stations;
2. the computation of the observed minus computed (OmC) values of all the code and phase observables;
3. the resolution of ambiguities on a chosen set of the OmC values combinations (the output of this process is the satellite fractional phase biases of the combinations) in the same way as the one done for the production of the real-time products;  
Figure 4: Number of E6-compatible stations at the IGS. Figure 5: Phase biases computation diagram. 4. the inversion of the combined fractional phase biases to recover individual phase biases. For step 1, the IF code and phase measurements are used for the correction part of the Kalman filter. Since the satellite code biases and clock offsets are known from the retrieved data, and since the stations receiver positions are known from the weekly combination of the IGS daily combined sinex solutions, the only unknowns that remain in the modeled observables are the wet zenithal troposphere delay, the receiver IF code and phase biases, as well as the IF float ambiguity: \[ \begin{split} C_{\text{IF},ij}+h_{\text{IF}}^{s}-\rho_{r,\text{ IF}}^{s}-b_{\text{IF},C_{\text{IF},ji}}^{s}&=m(E^{s})T_{Z}+\tilde{b}_{r, \text{IF},C_{\text{IF},ji}},\\ L_{\text{IF},ij}+h_{\text{IF}}^{s}-\rho_{r,\text{IF}}^{s}& =m(E^{s})T_{Z}+\tilde{b}_{r,\text{IF},L_{\text{IF},ij}}+\lambda_{IF,ij}N_{\text{IF},ij},\end{split} \] (32) with \(b_{\text{IF},C_{\text{IF},ji}}^{s}\), \(\tilde{b}_{r,\text{IF},C_{\text{IF},ji}}^{s}\), \(b_{\text{IF},L_{\text{IF},ji}}^{s}\), \(\tilde{b}_{r,\text{IF},L_{\text{IF},ji}}^{s}\), \(\lambda_{\text{IF},ij}\), and \(N_{\text{IF},ij}\) being the satellite/receiver code IF biases, the satellite/receiver phase IF biases, the IF wavelength, and the IF ambiguity, respectively. Since the IF ambiguity is defined by: \[N_{IF,ij}=\frac{\gamma_{j}\lambda_{i}N_{i}-\gamma_{i}\lambda_{j}N_{j}}{\gamma_ {i}-\gamma_{j}},\] (33) its integer property is not maintained. Therefore, it can be estimated along with the IF receiver phase bias. Defining \(\tilde{b}_{\text{IF},L_{\text{IF},ji}}=\tilde{b}_{r,\text{IF},L_{\text{IF},ji} }+\lambda_{IF,ij}N_{\text{IF},ij}\), the model of the code and phase measurements used to estimate the wet zenithal troposphere delay is: \[ \begin{split} C_{\text{IF},ij}+h_{\text{IF}}^{s}-\rho_{r,\text{ IF}}^{s}-b_{\text{IF},C_{\text{IF},ji}}^{s}&=m(E^{s})T_{Z}+\tilde{b}_{r, \text{IF},C_{\text{IF},ji}},\\ L_{\text{IF},ij}+h_{\text{IF}}^{s}-\rho_{r}^{s}&=m(E ^{s})T_{Z}+\tilde{b}_{r,\text{IF},L_{\text{IF},ji}}.\end{split} \] (34)  
The OmC values computed for step 2 consist of the difference between the raw code and phase measurements, from which are subtracted the geometric distance corrected by the phase center offset and the phase center variations, the Sagnac and Shapiro effects, the wind-up term for the phase measurement, the satellite clock offsets, the satellite code biases, and the previously computed wet zenithal troposphere. The process for the determination of the satellite phase biases at step 3 is the same as the one presented in Section 2.1 for the computation of the real-time phase biases.