# Analysis of Multi-Antenna GNSS Receiver Performance under Jamming Attacks
## 3 Simulation Results and Discussion
### Position Domain Analysis  
For the position domain analysis, the code and carrier phase measurements were processed using the RTKLib open source software [30]. The measurements generated using the reference antenna of the array without interference were used as the base observations for the RTK software. The remote observations were generated from the beamformed data affected by interference. This kind of processing acts like a zero-baseline and any distortion in the measurements affects the position solution. The open source software was used without any modifications. In the RTKLib, the continuous carrier phase ambiguity resolution mode was selected and forward-backward processing was performed.  
The east, north, and height position errors for PM and MPDR with chirp interference are shown in Figure 9. The RTK software outputs a quality flag for each solution update indicating a fixed or float solution. PM was not able to provide fixed solutions and position errors on the order of 10 cm occur. MPDR was able to provide fixed solutions and position errors were at the sub-millimetre level.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**PM**} & \multicolumn{2}{c}{**MPDR**} \\ \cline{2-5}
**PRN** & **Mean (mm)** & **Standard Deviation (mm)** & **Mean (mm)** & **Standard Deviation (mm)** \\ \hline PRN 3 & \(10.7\) & \(0.4\) & \(0.04\) & \(0.4\) \\ PRN 6 & \(3.4\) & \(0.2\) & \(-0.01\) & \(0.4\) \\ PRN 10 & \(30.5\) & \(1.8\) & \(0.07\) & \(0.7\) \\ PRN 16 & \(5.0\) & \(0.4\) & \(0.05\) & \(0.6\) \\ PRN 18 & \(7.6\) & \(0.3\) & \(-0.01\) & \(0.5\) \\ PRN 21 & \(1.4\) & \(0.2\) & \(-0.05\) & \(0.5\) \\ PRN 24 & \(-16.2\) & \(0.4\) & \(0.01\) & \(0.5\) \\ PRN 25 & \(23.3\) & \(0.4\) & \(-0.03\) & \(0.5\) \\ PRN 29 & \(-6.9\) & \(0.3\) & \(0.03\) & \(0.5\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Carrier phase measurement errors using PM and MPDR in the presence of chirp interference.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**PM**} & \multicolumn{2}{c}{**MPDR**} \\ \cline{2-5}
**PRN** & **Mean (m)** & **Standard Deviation (m)** & **Mean (m)** & **Standard Deviation (m)** \\ \hline PRN 3 & \(0.27\) & \(0.31\) & \(0.02\) & \(0.55\) \\ PRN 6 & \(0.33\) & \(0.27\) & \(0.02\) & \(0.59\) \\ PRN 10 & \(0.50\) & \(1.93\) & \(0.08\) & \(0.75\) \\ PRN 16 & \(0.31\) & \(0.36\) & \(0.01\) & \(0.59\) \\ PRN 18 & \(0.28\) & \(0.33\) & \(0.02\) & \(0.69\) \\ PRN 21 & \(0.31\) & \(0.30\) & \(-0.04\) & \(0.58\) \\ PRN 24 & \(0.35\) & \(0.49\) & \(0.02\) & \(0.65\) \\ PRN 25 & \(0.38\) & \(0.55\) & \(0.04\) & \(0.55\) \\ PRN 29 & \(0.31\) & \(0.40\) & \(-0.01\) & \(0.60\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Pseudorange measurement errors for PM and MPDR in the presence of chirp interference.  
The mean and standard deviations of the position errors observed for both beamformers are provided in Table 5. In the PM case, satellite directions are not considered in the optimization criterion and the antenna phase values are not added coherently. This will have adverse effect on the carrier phase measurements as discussed in the measurement analysis section. These biased measurements will affect carrier phase based positioning. It should be noted that with PM, different biases are observed for different PRNs and these bias values are a function of the interference and satellites AOA and cannot be calibrated beforehand.