# Experimental Validation of GNSS Interferometric Radio Occultation
## 4 Data Processing, Analysis and Discussion
### Interferometric RO Processing
#### 4.3.2 iRO Doppler Estimation with Removed Effect of PRN123  
The presence of two different PRNs within the main beam of the antenna results in a phase pattern that cannot be attributed to a single PRN. The presence of the geostationary SBAS satellite results in constant phase and amplitude which are estimated using two distinct methods.  
1. **Fixed estimation**: By assuming a constant amplitude, the contribution of PRN123 is estimated by averaging the correlation output in the period when PRN24 is out of the main beam of the antenna, i.e., after SoD51000. \[\overline{\mathbf{R}_{z}^{\text{PRN123}}}=\langle\mathbf{R}_{z}\rangle_{SoD>51000}\] (18)
2. **P2P correction:** By assuming a non-constant amplitude, the contribution of PRN123 is corrected point by point (p2p) by the amplitude of the waveform obtained with the clean replica method, and the contribution of PRN123 to the output of the iRO cross-correlation can be estimated by \[\mathbf{R}_{z_{\text{iRO}}}^{\text{PRN123}}\left(t_{1}\right)=\overline{ \mathbf{R}_{z_{\text{iRO}}}^{\text{PRN123}}}\frac{\left|\mathbf{R}_{z_{\text{ iCR}}}^{\text{PRN123}}\left(t_{1}\right)\right|^{2}-\left|\mathbf{R}_{z_{ \text{iNCR}}}^{\text{PRN123}}\left(t_{1}\right)\right|^{2}}{\left|\mathbf{R}_{ \text{CR}}^{\text{PRN123}}\right|^{2}-\left|\overline{\mathbf{R}_{z_{\text{ iNCR}}}^{\text{PRN123}}}\right|^{2}}\] (19) in which \(\overline{\mathbf{R}_{z_{\text{CR}}}^{\text{PRN123}}}\) is the clean-replica cross-correlation output averaged after SoD51000, \(\mathbf{R}_{z_{\text{CR}}}^{\text{PRN123}}\left(t_{1}\right)\) is the the clean-replica cross-correlation output at \(t_{1}\), the subscript N denotes the thermal noise component, and the noise components \(\left|\mathbf{R}_{z_{\text{iNCR}}}^{\text{PRN123}}\left(t_{1}\right)\right|\) and \(\left|\mathbf{R}_{z_{\text{iNCR}}}^{\text{PRN123}}\left(t_{1}\right)\right|\) are computed from the _signal free_ area, i.e., 2 chips before the peak of the waveform.  
The contribution of PRN123 estimated with both methods is then removed from the cross-correlation output, and the Doppler of the received signal can be estimated again.  
The Doppler estimations by applying both inter-satellite interference removing methods are presented in Figure 8. It can be seen that the Doppler observation with the iRO technique is consistent  
Figure 7: Doppler estimation of PRN24 with the iRO technique.  
with the predicted one by removing the contribution of PRN123. Table 1 shows the standard deviation of the estimated Doppler with respect the predicted one, for two periods of time. The corrected iRO method is unable to provide correct Doppler estimates towards the end of the experiment (SoD \(>50,600\)), when the SNR is lowest. But just before, it is when the correction works best.  
In this situation, the Doppler frequency of PRN24 is large, and the Doppler filtering caused by the phase-compensated autocorrelation in Equation (11) is very effective in removing any residual contribution of PRN123, who has a zero Doppler because it is a geo-stationary satellite. At the beginning of the experiment, when PRN24 is at higher elevation, its Doppler frequency is smaller, and the Doppler filtering of other PRNs with similar (or zero) Doppler is not so effective. In the case of a spaceborne RO receiver the Doppler dynamics are much larger than in a ground-based experiment as the one presented in this paper. This means that the phase-compensated autocorrelation will allow to provide better Doppler filtering in a spaceborne receiver than in a ground-based experiment.  
The results obtained with both correction methods are very similar, so the result from the _fixed_ correction method is used in the following analysis.