# Evaluating the Vulnerability of Several Geodetic GNSS Receivers under Chirp Signal L1/E1 Jamming
## 2 GNSS Use in Geodesy and Jamming
The code and carrier-phase observations are acquired from the same (at least four) satellites \(i\) at two locations \(A\) and \(B\), respectively [36]:  
\[ \begin{array}{l}P_{A}^{i}=Z_{A}^{i}+\Delta\rho_{A}^{i}=\mathrm{r}_{A}^{i}+c \Big{(}\delta t_{A}+\delta t^{i}\Big{)}+O^{i}+T_{A}^{i}+I_{A}^{i}+M_{A}^{i}+ \delta P_{A}^{i}+\cdots,\\ \Phi_{A}^{i}=\lambda\cdot\mathrm{N}_{A}^{i(0)}+\Delta\varphi_{A}^{i}=\mathrm{r }_{A}^{i}+c\Big{(}\delta t_{A}+\delta t^{i}\Big{)}+O^{i}+T_{A}^{i}-I_{A}^{i}+M _{A}^{i}+\delta\Phi_{A}^{i}+\cdots,\\ P_{B}^{i}=Z_{B}^{i}+\Delta\rho_{B}^{i}=\mathrm{r}_{B}^{i}+\delta\big{(}\delta t _{B}+\delta t^{i}\big{)}+O^{i}+T_{B}^{i}+I_{B}^{i}+M_{B}^{i}+\delta P_{B}^{i}+ \cdots,\\ \[PERSON]_{B}^{i}=\lambda\cdot\mathrm{N}_{B}^{i(0)}+\Delta\varphi_{B}^{i}=\mathrm{ r}_{B}^{i}+c\Big{(}\delta t_{B}+\delta t^{i}\Big{)}+O^{i}+T_{B}^{i}-I_{B}^{i}+M _{B}^{i}+\delta\Phi_{B}^{i}+\cdots,\end{array}  \tag{3}\]  
\(P_{A}^{i}\) and \(P_{B}^{i}\) are code and \(\Phi_{A}^{i}\) and \(\Phi_{B}^{i}\) are carrier-phase observations at locations \(A\) (base) and \(B\) (rover) from satellite \(i\), expressed in metres; \(\Delta\varphi_{A}^{i}\) and \(\Delta\varphi_{B}^{i}\) are carrier-phase measurements that are unambiguous in the fixed number of wavelengths; and ambiguity numbers \(\mathrm{N}_{A}\) and \(\mathrm{N}_{B}\) have to be resolved using algorithms. The satellite clock error \(\delta t^{i}\), as well as the orbital error \(O^{i}\), are the same for the base station and rover receiver, while other errors are receiver or location dependent. For the base receiver (at point \(A\)) for which coordinates are known, most of the effects in Equation (3) can be defined numerically. Estimated errors at the base can be used in the computation process of correcting ambiguity, provided that the location of the rover is close to that of the base receiver. However, some errors (mostly multipath, or in the worst-case, intentional degradation of the signal) remain, which can significantly affect the positioning. Methods that allow for the resolution of ambiguities in relative positioning are based on double differences because they do not contain changing clock errors. The goal of algorithms is to find ambiguity numbers, which minimise the residuals of double differences of carrier-phase observations (\(\
abla\Delta\)), given as [36]:  
\[\sum_{i=1}^{n-1}\
abla\Delta v^{i}=\sum_{i=1}^{n-1}\
abla\Delta r^{i}-\
abla \Delta\Phi^{i}-\lambda\cdot\
abla\Delta\mathrm{N}^{i}-\
abla\Delta\delta\Phi^ {i}. \tag{4}\]  
In Equation (4), \(\Delta\) and \(\
abla\) present single and double difference operators, respectively. RTK algorithms must satisfy the condition \(\
abla\Delta v^{i}\to 0\). Several algorithms can be used for ambiguity fixing. The least squares ambiguity decorrelation adjustment algorithm (LAMBDA) [37] and modified LAMBDA (MLAMBDA) algorithm [38] have been proven to theoretically be the most efficient integer ambiguity algorithms. LAMBDA reduces the computational complexity, thus allowing for significant development of the RTK method. The algorithms of RTK are based on the continuous tracked measurements to perform the initialisation of the carrier-phase ambiguities. Interruption of a signal at one of the receivers (either \(A\), \(B\), or both) requires a new initialisation process (ambiguity fixing). In the event of interruptions at a rover's location, only the user is affected. Interruptions at the location of a base receiver, from which (usually) many users acquire observations for positioning, are far more severe. Therefore, CORS networks address issues, such as the high reliability of real-time distribution and quality control of the data they collect. The occurrence of the disruption of jammers should be another aspect to consider. The problem for RTK users is that they often only produce coordinates without storing raw observations for additional observation quality checks.