## Appendix A GNSS Basics  
The GNSS architecture contains three blocks: the acquisition sub-system, the tracking sub-system and the navigation sub-system. The roles of these sub-systems are the following. Acquisition:  
* to detect the GNSS signals which are present;
* to realize a first estimation of their frequency and delay characteristics. Tracking:
* to rest locked on the signals received from the acquisition sub-system;
* to decode the navigation message;
* to estimate the distance traveled by each signal to arrive at the receiver. Navigation:
* to calculate the position of the receiver;
* to determine the bias of the receiver's internal clock versus the reference system. The estimation of the position of the vehicle which carries the GNSS receiver is done by triangulation in the navigation sub-system. The distance between the receiver's carrier vehicle and each satellite available in the region where the vehicle is situated isestimated in the tracking sub-system, and based on these estimations, the localization is made. The position estimation accuracy depends on the number of satellites available, on their positions and on the quality of the signals received from these satellites. The distance towards the satellite (range) can be estimated by the tracking sub-system of the GNSS receiver with the aid of the delay, \(\tau\), between the emission of the incident wave and the reception of the reflected wave. The access to GPS satellites is provided by the Code Division Multiple Access (CDMA) principle. Each satellite has its own Pseudo Random Noise (PRN) code, which is a bipolar signal, \(C(t)\). It is multiplied with the data transmitted by the satellite for navigation purposes, \(D(t)\), obtaining a new bipolar signal, which represents the modulator for the Binary Phase Shift Keying (BPSK) modulation of the carrier. The power of the transmitted signal is denoted by \(E_{c}\). The expression of the signal generated is:  
\[c(t)=\sqrt{2}E_{c}D(t)C(t)e^{i(2\pi f_{p}t+\theta_{p})}. \tag{1}\]  
This is a very large bandwidth signal. The received signal is of the form:  
\[s(t)=bc(t-\tau_{0})e^{j2\pi\
u_{0}t}+\eta(t) \tag{2}\]  
where the delay (proportional to the target range) is denoted by \(\tau_{0}\), the Doppler frequency (related to the target velocity) by \(\
u_{0}\), \(\eta(t)\) represents a complex white Gaussian noise with power spectral density \(N_{0}\) and \(b\) is a random variable which describes the propagation. In modern implementations, such as for several GALILEO signals, the BPSK modulation is replaced by Binary Offset Carrier (BOC) modulation. This BOC modulation, along with their modified versions multiplexed BOC (MBOC) and composite BOC (CBOC), uses a sub-carrier to create separate spectra on each side of the transmitted carrier. It presents some advantages, such as a high degree of spectral separation from existing navigation signals, and leads to significant improvements in terms of tracking, interference and multipath mitigation. The GNSS signal is detected by the acquisition sub-system with the aid of a Maximum Likelihood (ML) detector, by correlation with a locally generated replica. The sampled version of the received signal, \(s[n]\), is multiplied with a sampled version of the signal \(c(t)\), locally generated, \(c[n]\), which is delayed with a delay \(\tau\), taken from a lookup table, and is multiplied with a complex exponential with argument \(\
u\) taken from the same lookup table. The \(N\) samples of the multiplication's result are added, obtaining a sufficient statistic, \(T(s)\) (proportional with the correlation of signals \(s[n]\) and \(c[n]\), computed in zero), whose value is compared with a detection threshold, \(\gamma^{\prime}\). If the value of \(T(s)\) is bigger than the threshold value, then the hypothesis H\({}_{1}\) which supposes that \(\tau_{0}=\tau\) and that \(\
u_{0}=\
u\) will be considered as true. Otherwise, other values for \(\tau\) and \(\
u\) will be selected from the lookup table and the computation procedure, already described, will be repeated.