# Localization of GNSS Spoofing Interference Source Based on a Moving Array Antenna
## 2 System Model and Signal Processing Methods
### Signal Acquisition and Tracking Methods  
After implementing the antenna model described in Section 2.1 for signal reception, this method devises a signal receiving and processing process, as depicted in Figure 3, to effectively handle all received genuine and spoofing GNSS signals at each antenna element, thereby the acquisition, tracking, and carrier phase measurement of all the signals can be accurately achieved. Each array element of the antenna array depicted in Figure 3 corresponds to a single radio frequency (RF) channel, enabling RF signal conditioning, down-conversion, intermediate frequency (IF) signal filtering and amplification, and analog-to-digital (AD) conversion to obtain the digital IF signal corresponding to each element. As shown in Figure 3, we have designed an efficient satellite signal acquisition method suitable for the scenario described in this paper. This method performs signal acquisition only on the signals received from array element 0 to obtain observation vectors \(\left[\tau_{0}^{1},\cdots\tau_{0}^{h},\cdots,\tau_{0}^{K}\right]\) and \(\left[f_{0}^{1},\cdots f_{0}^{h},\cdots,f_{0}^{K}\right]\), where \(\tau_{0}^{h}\) and \(f_{0}^{h}\) represent a coarse estimate of the code phase and carrier frequency measurement for satellite \(h\), respectively. Given that the inter-element spacing is within half of the carrier wavelength, this approach uses the acquisition observation vector of element 0 directly as input to track the signals from the other antenna elements, thereby circumventing the need for signal acquisition processes involving the remaining 6 elements. At the same time, the algorithm in reference [28] can be used to further reduce the implementation cost of the method. This algorithm is an  
Figure 2: The \(6+1\) antenna model. improved parallel code phase acquisition (PCA) algorithm that can speed up the acquisition process while slightly reducing the detection probability. The signal tracking process in Figure 3 involves assigning a tracking channel to each satellite signal received by each antenna element, where the tracking channel \(i\), \(h\) is the channel to satellite \(h\) received by element \(i\). The tracking process enables the measurement of the carrier phase and generates the observed vector \(\left[\phi_{0^{\prime}}^{1}\cdots\phi_{i}^{h},\cdots,\phi_{\phi}^{K}\right]\) of carrier phase, where \(\phi_{i}^{h}\) represents the measured value of satellite \(h\)'s carrier phase received by array element \(i\). The method described in this paper leverages the aforementioned carrier phase observations for efficient extraction and localization of GNSS spoofing interference. Figure 4 depicts the signal reception loop design employed for the tracking channel. In Figure 4, the loop consists of a code loop located at its upper part and a carrier loop located at its lower part. The signal tracking method employed in this paper follows the classical approach described in reference [29], which is widely adopted for GNSS receiver design. Figure 4: Structural diagram of the signal tracking loop. Figure 3: Schematic diagram of signal reception and processing. The correction parameters for the code phase and carrier phase, denoted as \(\Delta\tau\) and \(\Delta\phi\), respectively, in Figure 4, are calculated according to the method detailed in reference [30]. The proposed method, which can be implemented on a GNSS nulling antenna hardware platform, enables simultaneous spoofing interference detection and localization with anti-jamming. However, adaptive beamforming modifies the array pattern in real time, which has the potential to introduce phase-center bias into the antenna array. Since we need to maintain the accurate measurement of the carrier phase in the application scenario of this paper, these deviations must be compensated for to reduce the carrier phase measurement error of the GNSS receiver. Reference [30] gives the calculation method of the code phase and carrier phase correction amount to compensate for the above error.