# Evaluating the Vulnerability of Several Geodetic GNSS Receivers under Chirp Signal L1/E1 Jamming
## 2 GNSS Use in Geodesy and Jamming  
Several methods can be used to achieve high accuracy positioning in geodesy. Since static positioning can be time-consuming, kinematic positioning, especially the RTK method, is the most popular method used in most everyday geodetic applications. Its greatest advantage is the ability to acquire quality positioning in real time. Moreover, it enables immediate determination of coordinates in the national coordinate system, which is indispensable in the land cadastre. The typical nominal accuracy of RTK is 1 cm \(\pm\) 2 ppm in a horizontal plane and 2 cm \(\pm\) 2 ppm vertically or better. The basic concept is based on relative positioning to reduce and remove errors common to a base station and rover pair. This implies the fact that difficulties in positioning due to the presence of a jammer can occur in two situations: (a) at a base receiver or (b) at the location of a rover. GNSS relative positioning follows the scenario in which a priori coordinates are defined from absolute code positioning first. Single-point positioning, which is also known as a navigation solution, is based on a single receiver measuring satellites simultaneously. In this, the pseudoranges \(P_{A}^{i}\) from code measurement between the satellite \(i\) and the receiver \(A\) are used [36]:  
\[P_{A}^{i}=Z_{A}^{i}+\Delta\rho_{A}^{i}=\dot{r}_{A}^{i}+c\Big{(}\delta t_{A}+ \delta t^{i}\Big{)}+O^{i}+T_{A}^{i}+I_{A}^{i}+M_{A}^{i}+\delta P_{A}^{i}+\cdots \tag{1}\]  
In the above equation \(Z_{A}^{i}\) is an unambiguous time measurement from the navigation message and \(\Delta\rho_{A}^{i}\) stands for the code measurement, which is unambiguous beyond the code length. The right-hand side of the Equation (1) shows that code measurements, apart from the distance to the satellite \(\mathbf{r}_{A}^{i}\), contain the \(\delta t_{A}\) and \(\delta t^{i}\) receiver and satellite clock errors, respectively, \(O^{i}\), \(T_{A}^{i}\), \(I_{A}^{i}\) and \(M_{A}^{i}\) are the orbital, tropospheric, ionospheric and multipath errors, respectively, and \(\delta P_{A}^{i}\) is the code noise. Measurements from at least four satellites must be available to compute the unknown position and time. Besides the code, carrier-phase (or shorter phase) measurements \(\Phi_{A}^{i}\) can be used to obtain the distance between the satellite \(i\) and the receiver \(A\)[36]:  
\[\Phi_{A}^{i}=\lambda\cdot\mathrm{N}_{A}^{i(0)}+\Delta\varphi_{A}^{i}=\dot{r }_{A}^{i}+c\Big{(}\delta t_{A}+\delta t^{i}\Big{)}+O^{i}+T_{A}^{i}-I_{A}^{i}+ M_{A}^{i}+\delta\Phi_{A}^{i}+\cdots \tag{2}\]  
In Equation (2), the additional unknown \(\mathrm{N}_{A}^{i(0)}\) of the carrier-phase ambiguity number exists. As before, \(\delta t_{A}\) and \(\delta t^{i}\) stand for the receiver and satellite clock errors, respectively; \(O^{i}\), \(T_{A}^{i}\), \(I_{A}^{i}\) and \(M_{A}^{i}\) are the orbital, tropospheric, ionospheric and multipath errors, respectively; and \(\delta\Phi_{A}^{i}\) is the carrier-phase noise. The ionospheric term \(I_{A}^{i}\) has opposite signs for the code and carrier phase, which is due to the fact that the ionosphere produces an advance in the carrier-phase measurements equal to the delay on the code measurements. A positioning technique from the carrier-phase measurements that removes or models GNSS system errors to provide a high level of position accuracy from a single receiver is known as precise point positioning (PPP) [5; 6; 7]. In geodesy, the method is used mostly in post-processing since the time necessary to move from a float to a fixed solution is extended and the convergence can take several tens of minutes. Currently, relative carrier-phase-based methods, especially RTK, are still the most used geodetic positioning techniques. Relative GNSS carrier-phase positioning is based on the use of two receivers at two locations and on forming single, double and triple differences to reduce common errors for both (base and rover) receivers.