## 2 Set-Up and Hardware Description
### Receiver  
The used hardware to capture the data comprised a Septentrio (SSN) AsteRx-U dual antenna multi-frequency receiver in conjunction with the 2 pol multi-frequency antenna prototype developed by the Fraunhofer Institute for Integrated Circuits (see Figure 1). The receiver is a commercial L1/L2/E5/E6 receiver used in many industrial positioning and attitude applications. The RHCP output of the antenna was connected to the main input of the receiver, while the LHCP output was connected to the auxiliary input of the receiver. The default software of the AsteRx-U receiver independently acquires and tracks satellite signals from each antenna input. This is a suitable approach for the normal 2D attitude use case of the receiver. However, when used for 2 pol applications, the receiver would fail to permanently monitor the polarization of the signal, as the LHCP component could only be tracked if its carrier-to-noise ratio (CN0) is sufficiently high. It is for the above reason that the receiver software was modified.  
Rather than having an independent tracking of the LHCP and RHCP components, the receiver only tracks the RHCP component and replicates the local code and carrier timing of the RHCP tracking to correlators which connect to the LHCP signal, as shown in Figure 4. In this way, the receiver synchronously gathers RHCP and LHCP correlation values, ensuring a permanent polarization monitoring of the signal. Both correlations are integrated coherently over a programmable time \(\Delta T\), yielding the following correlation output for satellite signal \(k\) at epoch \(T\):  
\[\begin{split} P_{\text{R},k}(T)&\doteq\int_{T- \Delta T}^{T}\text{RHCP}(\tau)\text{PRN}_{k}(\tau)e^{-j(\omega_{0}\tau+\phi_{k} (\tau))}\widehat{D}_{k}(\tau)\text{d}\tau,\\ P_{\text{L},k}(T)&\doteq\int_{T-\Delta T}^{T} \text{LHCP}(\tau)\text{PRN}_{k}(\tau)e^{-j(\omega_{0}\tau+\phi_{k}(\tau))} \widehat{D}_{k}(\tau)\text{d}\tau.\end{split} \tag{1}\]  
The PRN-code and local carrier phase (i.e., \(\{\tau,\omega_{0},\phi_{k}\}\)) are estimated from the RHCP signal, as well as the navigation data bit \(\widehat{D}_{k}\). For pilotized signals, only the pilot component was used in the correlation process, making \(\widehat{D}_{k}\) irrelevant. The integration time \(\Delta T\) was set to 100 ms. This was done for all satellites in view from GPS (L1C/A-L2C), GALILEO (E1-E5b), GLONASS (L1C/A-L2C/A) and BeiDou (B1-B2). The resulting RHCP and LHCP correlations were logged on non-volatile memory in the receiver for post-processing, along with the usual raw GNSS data and differential corrections from a nearby reference station. At this point, it is interesting to analyze the LHCP SNR after the described processing. The relation between SNR and CN0 is given by \(\text{SNR}=\text{CN0}+10\log(\Delta T)\). So, for a RHCP CNO of 40 dB-Hz and RLR around 15 dB, which are typical values under nominal conditions, we get an LHCP SNR of 15 dB for \(\Delta T=100\) ms. If we extend the integration time to 1 s, we gain 10 dB, which is sufficient to handle extreme cases with LHCP CN0's of 10-15 dB-Hz. Lower values are not relevant, as they correspond to RHCP CNO's useless for precision receiver because of cycle slips.