# Localization of GNSS Spoofing Interference Source Based on a Moving Array Antenna
## 4 Simulations and Results
### Experiment 2: Spoofing Localization Effects at Different Carrier Phase Measurement Errors  
This experiment tests the effectiveness of different GNSS spoofing interference source localization methods under different carrier phase measurement errors along the above five paths. The experimental comparison methods include the method proposed in this article, the global search method for the cost function of Equation (16), and two typical two-step methods. In the two-step comparison methods, the measurements of the arrival angle of deceptive interference signal by array antennas are both implemented using the approach described in reference [38]. Two-step Method 1 employs the Beamsum Criterion principle from reference [39] to locate the spoofing interference source, while Two-step Method 2 utilizes the least squares principle from reference [39] for locating the deceptive source.  
To comprehensively evaluate the performance of the proposed method, Experiment 2 tests the effects of the proposed method under different spoofing interference source location settings and performs statistics on the location results. The spoofing source locations  
Figure 9: Comparison of the double-difference carrier phase observables with the set threshold. (a) Double-difference results with channel 1; (b) Double-difference results with channel 2.  
setup are shown in Figure 8. According to references [40; 41], while ensuring effective tracking, the setting range for the standard deviation of carrier phase measurements in this experiment is \(0.005\times 2\pi\) rad \(-20\times 0.005\times 2\pi\) rad, with a mean value set at 0 and measured in radians. The standard deviation of the self-positioning error of the array antennas is set to 1 with a mean value of 0 and units are meters.  
The second experiment involves conducting 100 tests for each carrier measurement error setting, wherein all 10 interference sampling points in the interference path shown in Figure 8 are located for each test. Subsequently, the root mean square errors (RMSEs) of the aforementioned 1000 location results are calculated. In each test, we conducted 10 carrier phase single-difference observations and constructed matrix \(W\) using Equations (20) and (22). The experimental results are presented in Figure 10, where Figure 10a-e illustrates the comparative outcomes among different methodologies across five paths. The horizontal axis of the figure represents the standard deviation of the carrier phase measurement error, measured in 0.005\(\pi\) rad, while the vertical axis represents the localization RMSE, measured in meters. Simulation results demonstrate that as the carrier phase measurement error increases, the proposed method exhibits significantly superior location accuracy compared to the two-step methods, and it closely approximates the CRB and the global search method. This demonstrates that the proposed method is more adaptable to carrier measurement errors and is more suitable for spoofing interference monitoring applications in the dynamic scenario of this paper. Figure 10f compares the location performance of our method under five monitoring paths, among which straight paths 1, 2, and 5 are better than circular paths 3 and 4. Path 5 has the best performance among the straight paths due to its displacement in both horizontal and vertical directions. Therefore, we choose path 5 as the recommended path for our method.  
Figure 10: _Cont._  
In this experiment, we recorded the number of iterations of the method and the normalized value of the cost function Equation (16) while the method was running and statistically analyzed the mean value of the normalized cost function for 1000 experiments. Figure 11 shows the relationship between the number of iterations and the mean value of the normalized cost function under the five test paths of this experiment. The results show that the five test paths can converge after six iterations. To ensure the effectiveness of the algorithm, the number of iterations in this paper is set to eight.