# Preliminary Results of an Astri/UWM EGNSS Receiver Antenna Calibration Facility
## 4 Algorithm and Strategies of Data Processing  
Two main steps can be distinguished in PCC modeling. The first is the data preparation step, where data are corrected, i.e., other error and bias sources are reduced or eliminated. The second is the solution step, in which corrections are modeled. Several known factors and biases must be addressed to prepare raw carrier phase data for PCC estimation. Undifferenced phase observation of \(\Phi_{f_{A}}^{j}\) [m] is used in this case for the frequency \(f\) from station A to satellite \(j\). \[\Phi_{f_{A}}^{j}=\rho_{A}^{j}+c\Big{(}\delta t_{A}-\delta t^{j}\Big{)}+\lambda_{ f}N_{f_{A}}+\Big{(}\delta\varphi_{f_{A}}-\delta\varphi_{f}^{j}\Big{)}+T_{f_{A}}^{ j}-I_{f_{A}}^{j}+MP_{f_{A}}^{j}+PCV_{fA}+\varepsilon_{f_{A}}^{j} \tag{2}\]  
The equation considers the geometric distance \(\rho_{A}^{j}\), the speed of light \(c\), the receiver and satellite clock errors \(\delta t_{A}\) and \(\delta t^{j}\), respectively, the tropospheric \(T_{f_{A}}^{j}\) delay and ionospheric \(I_{f_{A}}^{j}\) delay, the ambiguity term \(N_{f_{A}}\), the hardware delays in the receiver (\(\delta\varphi_{f_{A}}\)) and satellite (\(\delta\varphi_{f}^{j}\)), the phase multipath term \(MP_{f_{A}}^{j}\), the phase center variations \(PCV_{fA}\), and measurement noise \(\varepsilon_{f_{A}}^{j}\). Figure 3: The hardware part of the GNSS antenna calibration system. By forming single differences \(SD_{A,B}^{j}(t_{i})\) on a short baseline of approximate 5 m between stations A and B at epoch \(t_{i}\), the effects introduced by the satellite and by distance-dependent factors are nearly eliminated. \[SD_{A,B}^{j}(t_{i})=\Phi_{f_{A}}^{j}-\Phi_{f_{B}}^{j} \tag{3}\]  
One may apply time differences (Figure 4) to single differences from Equation (3). \[\Delta SD_{f_{A,B}}^{j}(t_{i})=SD_{f_{A,B}}^{j}(t_{i+1})-SD_{f_{A,B}}^{j}(t_{i}) \tag{4}\]  
We can obtain access to the observation equation for any given frequency:  
\[ \begin{array}{c}\Delta SD=c\Delta\delta_{A,B}(t_{i},t_{i+1})+\Delta PCV_{A}^{ j}(t_{i},t_{i+1})+\Delta MP_{A,B}^{j}(t_{i},t_{i+1})+\Delta d_{A,B}^{j}(t_{i},t_{i+1 })+\\ \Delta T_{A,B}^{j}(t_{i},t_{i+1})-\Delta I_{A,B}^{j}(t_{i},t_{i+1})+\Delta p_{ A,B}^{j}(t_{i},t_{i+1})+PWU_{A,B}^{j}(t_{i},t_{i+1}),\end{array}  \tag{5}\]  
The equation includes the differential receiver clock error \(c\Delta\delta_{A,B}(t_{i},t_{i+1})\), topography of the PCV pattern \(\Delta PCV_{A}^{j}(t_{i},t_{i+1})\), and additional differential error terms. As the time offset between consecutive epochs is very short (within 5 s), and the station baseline is also very short (within 10 m), the terms \(\Delta T_{A,B}^{j}(t_{i},t_{i+1})\) and \(\Delta I_{A,B}^{j}(t_{i},t_{i+1})\) are neglected. The ambiguity term and the PCV are eliminated, as well as a multipath term at station B. The methodology also significantly reduces multipath effects at station A. As the PCVs of the calibrated antenna are determined by changing the orientation between subsequent epochs, the phase wind up correction \(PWU_{A,B}^{j}(t_{i},t_{i+1})\) has to be introduced to Equation (5). In the solution step, corrections are evaluated in two stages, namely, MPC modeling followed by PCVs modeling. The input data are TDSDs after error and bias cleaning. The MPC is determined using the assumption that \(\sum\ (PCV)^{2}=min\). As a result, \(\Delta\)N, \(\Delta\)E, and \(\Delta\)U of MPC will be obtained. In the next step, the input data are PCV residuals obtained after MPC determination. PCVs are modeled using spherical harmonics. At least three independent solutions are provided, and then PCVs in an elevation-only function are compared and finally the most similar solutions are selected to calculate the final mean solution. The final step is achieved by converting the achieved results to the ANTEX format. In standard analysis, PCVs are parametrized with spherical harmonic expansion (SHE) using an expansion of degree of n = 8 and an order m = 5.