# Localization of GNSS Spoofing Interference Source Based on a Moving Array Antenna
## 3 Proposed Methods
### Extraction of Spoofing Interference Based on the Double-Differenced Carrier Phase
The software-defined radio (SDR) platform proposed in reference [26] implements the above equal-length conditions, which can be used for the implementation and testing of the method in this paper. In practical applications, the GNSS signal source can be used to calibrate multiple hardware channels (including antenna feeders), and the calibration diagram is shown in Figure 5.  
In this method, the seven channels corresponding to the 6 + 1 array antenna track the same navigation satellite signal output by the GNSS signal source and output the carrier phase measurement differences between the hardware channels of element 1 to element 6 and the hardware channel of element 0 as the correction values. In practice, these correction values are used to achieve a consistent correction for each channel. In this paper, the GNSS spoofing interference extraction is performed using double-difference carrier phase measurements. For satellite signals \(k\) and \(h\), the carrier phase double-difference equation for array element i is defined as follows. \[\Delta\varphi_{i}^{k,h}=\varphi_{i}^{k}-\varphi_{i}^{h}=\frac{2\pi}{\lambda} \left(\rho_{i}^{k}-\rho_{0}^{k}\right)+\varepsilon_{i}^{k}-\varepsilon_{0}^{h }-\frac{2\pi}{\lambda}\left(\rho_{i}^{h}-\rho_{0}^{h}\right)-\varepsilon_{i}^ {h}+\varepsilon_{0}^{h} \tag{4}\]  
If the signals from satellites \(k\) and \(h\) originate from the same spoofing source, then the propagation paths of both satellite signals from transmitter to receiver are identical. Therefore, the carrier phase double-difference \(\Delta\varphi_{i}^{kh}\) can be simplified as follows. \[\Delta\varphi_{i}^{k,h}=(\varepsilon_{i}^{k}-\varepsilon_{0}^{h})-(\varepsilon _{i}^{h}-\varepsilon_{0}^{h}) \tag{5}\]  
Figure 5: Calibration diagram of multiple hardware channels. The tracking error of the carrier phase is typically less than 1% of the carrier wavelength [33], that is, \(|\varepsilon|\leq 0.005\times 2\pi\) rad, thus we set the maximum value of \(8|\varepsilon|\) as the threshold for identifying and extracting spoofing interference, that is, \(Th=0.04\times 2\pi\) rad. If the double-differenced carrier phase observation between the satellite signal \(k\) and the satellite signal \(h\) is less than the threshold value \(Th\), then it is possible that both the satellite signals originate from the same spoofing interference. In practical application scenarios, considering the method's accuracy and real-time nature, we establish that signals from two satellites originate from the same spoofing interference source when there are continuous five-carrier phase double-difference observation values below a certain threshold. Considering that the carrier phase may fluctuate in dynamic scenarios, we use the statistical method for carrier phase measurement errors in reference [34]. When implementing the proposed method in this paper, we can set up two hardware channels for carrier phase measurement on the same antenna element and can monitor and compile statistics on the carrier phase measurement error \(\varepsilon\), in real-time. Then, \(8|\varepsilon|\), corresponding to the measured \(\varepsilon\), is used as the interference extraction threshold to improve the effectiveness of the spoofing interference extraction and confirmation in this paper.