# Detecting and Mitigating Attacks on GPS Devices
## 3 GNSS Overview
### GNSS Performance Expectations
If there are no errors and no propagation effects, the measured phase, \(\Phi\), will take the following form [31]:  
\[\Phi=\Phi_{R}(t_{R})-\Phi_{T}(t_{R})+N_{R}^{T} \tag{2}\]  
where  
\(\Phi_{R}\) is the phase of the receiver;  
\(\Phi_{T}\) is the phase of the received satellite signal;  
\(N_{R}^{T}\) is the ambuiguity between the satellite and receiver. However, as was the case in the previous pseudorange discussion, the measured phase will differ due to several degradation factors, and the carrier phase measurement model will take the form of Equation (3) [31]. \[\lambda\Phi=\rho(t_{R},t_{T})-c(\delta t_{R}-\delta t_{T})+\lambda N_{R}^{T}- \delta_{IONO}+\delta_{TROP}+\delta_{TIDE}+\delta_{PATH}+\delta_{REL}+\varepsilon \tag{3}\]  
where \(\lambda\) is the signal wavelength, and the remainder of the terms are similar to those in Equation (1). For a more thorough description of the various pseudorange and carrier phase measurement models and error components, the reader is referred to [32]. The formal GPS performance standard published by the United States Department of Defense (DoD) [33] states that \"[...] well-designed GPS receivers have been achieving horizontal accuracy of 3 m or better and vertical accuracy of 5 m or better 95% of the time\". This level of accuracy has been substantiated by numerous studies, several of which are summarized in Table 3; however, these studies established variation due to the factors mentioned above. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Authors** & **Reference** & **Type of Results** & \begin{tabular}{c} **Scenario/Conditions** \\ **Considered** \\ \end{tabular} & **Factors Considered** & \begin{tabular}{c} **General Conclusions of** \\ **Accuracy** \\ \end{tabular} \\ \hline [PERSON]. [PERSON] & [34] & Theoretical & Various & \begin{tabular}{c} Clock error, orbit error, \\ refraction, multipath, \\ code-tracking error \\ \end{tabular} & Position accuracy: \\ \hline [PERSON] et al. & [35] & Experimental & \begin{tabular}{c} Open stationary, \\ open mobile, urban \\ stationary \\ \end{tabular} & \begin{tabular}{c} Variability across \\ GPS receivers \\ \end{tabular} & \begin{tabular}{c} HDOP: 0.7–1.2 \\ VDOP: 0.9–1.6 \\ \end{tabular} \\ \hline [PERSON] and & [36] & Experimental & \begin{tabular}{c} Open stationary, \\ open mobile \\ \end{tabular} & \begin{tabular}{c} Variability across \\ GPS receivers \\ \end{tabular} & \begin{tabular}{c} Position accuracy: \\ 0–4 m \\ \end{tabular} \\ \hline [PERSON] et al. & [37] & Experimental & Urban stationery & \
\begin{tabular}{c} Variability across \\ GPS receivers \\ \end{tabular} &
\begin{tabular}{c} Position accuracy: \\ \textless{}28 m for 95\% of the time \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of GPS performance analysis. Multi-frequency GPS receivers processing both L1 and L2 carriers can obtain improved position accuracy with centimeter-level accuracy [41]; however, as previously noted, multi-frequency GPS receivers are larger, more expensive, not common in consumer or commercial applications, and are historically more prevalent in professional and military applications. There is also the concept of Differential GPS (D-GPS). D-GPS is based on the idea that two receivers near each other experience similar atmospheric errors. A network of GPS receivers at known locations is established, and they publish their signal measurement data for each visible satellite for public consumption. GPS receivers can then download this information, commonly referred to as GPS correction data, from the nearest fixed site and apply that data to correct any measurement errors in their data, improving the accuracy of their position estimation. This process can be done in real time if the GPS receiver can access the required connectivity. More commonly, differential correction is performed in non-real time by post-processing the published correction data.