# On the Use of a Feedback Tracking Architecture for Satellite Navigation Spoofing Detection
## 3 The ECADLL
Amplitude values, \(\hat{a}_{n,i}\) and \(\hat{a}_{n,q}\), are estimated using the in-phase and quadrature results of the prompt correlation \(I_{P}\) and \(Q_{P}\), as:  
\[\hat{a}_{n,i} = \frac{I_{P}}{\lambda} \tag{6}\] \[\hat{a}_{n,q} = \frac{Q_{P}}{\lambda} \tag{7}\]  
where \(\lambda\) is a damping factor, slightly smaller than one, used to adjust the estimation accuracy. The PLL structure in Figure 1 does not use the same correlation output as other units. It uses the correlation values between the total incoming signal (\(s(t)\)) and the Unit0 local code (\(c(t-\tau_{0})\)). Thus, in the presence of impairments, the local carrier phase will not be completely aligned with the carrier phase of the satellite signal. Nonetheless, the carrier phase error will be estimated by the couple of ALLs inside each unit. Actually, recovering the relative phase shift for any single signal component will be necessary, in order to produce the correct replica and add it to the feedback signal. As an example, in Figure 2, the basic working procedure of the ECADLL algorithm is shown when the spoofing and satellite signals are aligned in phase. On the left side of the picture, an estimated correlation function of a generic received signal affected by spoofing is shown. On the right part, we observe the results for the first iteration and for the iterations after the architecture reaches the steady state. At the beginning of the tracking procedure, the architecture starts tracking the residual of the operation \(s(t)-\hat{s}_{0}\) inside Unit1. At the following iteration, the feedback Switch B is closed, and after a transition time, the two units' estimations will be locked at values very close to the originals, such that \(\hat{s}_{0}\approx s_{0}\) and \(\hat{s}_{1}\approx s_{1}\). A monitoring block, shown in Figure 3, receives as inputs the estimations of \(\hat{\tau}_{n},\hat{a}_{n}\) and \(\hat{\theta}_{n}\), for all of the units, and it is in charge of turning on and off each of them. We worked under the assumption that a spoofing attack will happen after some time that the receiver is turned on, so the monitoring block is in charge of deciding the moment when each unit is to be introduced by closing Switch A. If the spoofer is not present, Unit1 will be tracking noise, so its amplitude \(\hat{a}_{1}\) will be small, and its delay \(\hat{\tau}_{1}\) will wander randomly. Once the spoofer signal appears on the satellite signal correlation  
Figure 2: ECADLL basic working procedure when the satellite signal and the spoofing signal are aligned in phase. On the left, the incoming signal is shown, and on the right, the solution after N iterations. Only the in-phase channel is shown in this image for simplicity. space, Unit1 will quickly track the interference signal, thus increasing its value of amplitude and locking the DLL around a value of \(\tau_{1}\). At this moment, the monitoring block will close Switch B, starting the feedback loop and obtaining a better estimation of the parameters. The thresholds used by the monitoring block are defined based on the product of front-end bandwidth (\(B\)) and the time of chip (\(T_{c}\)). The product \(B\cdot T_{c}\) affects the shape of the correlation function, rounding the peak of the correlation when the product is small. This effect causes a degradation on the detection capabilities, for impairments that are close to the peak. Section 4 discusses the spoofing detection algorithm, which uses as inputs the estimations of each unit, i.e., \(\hat{\tau}_{n}\), \(\hat{\mu}_{n}\) and \(\hat{\theta}_{n}\), and takes the decision of whether an impairment is present in the incoming signal or not.