## 3 Numerical Simulation  
To verify the effectiveness of this method, MATLAB 2021b is used as a simulation platform to carry out the verification. In the study of interference effects in satellite navigation systems, additive white Gaussian noise (AWGN) has emerged as the predominant interference mode due to its canonical statistical characteristics and ubiquitous presence. In the experiment, band-limited white noise was generated through equivalent low-pass filtering operations and utilized as the simulated navigation interference source. Figure 1 shows the results of the decoherence direction-finding scheme for the lateralization of the interference signal. The amplitude measured by the antenna is concentrated in the direction of the interference source of the satellite navigation signal. M is the number of antenna elements, and it can be seen that the larger M is, the more data is received, and the direction-finding amplitude becomes more stable. However, even M = 8 ensures better direction-finding accuracy. This is because the normalized amplitude of the angular antenna direction finding in other directions is minimal. In contrast, the amplitude in the direction of the interference source is very sharp, thus ensuring the accuracy of the AOA direction finding. When generating the simulation data, it is assumed that the position of the interference source is fixed, the interference transmitting antenna is an omnidirectional antenna, the transmitting power of the interference source is 120 W, and the distance between the interference source and each receiver is 0.2-0.5 km. The bandwidth \(B\) of the interference signal is 32.736 MHz. The simulation data are the data of the interference signals received from different interference monitoring base stations, and the receiver position error and ambient noise error should be added to the simulation data for the sake of making the simulation data closer to the real data, where the receiver position error is modeled as zero-mean \(\sigma_{pos}^{2}\)-variance Gaussian noise in each Cartesian coordinate and the ambient noise error is modeled as AWGN with noise power \(P_{noise}=k_{B}TB\), where \(k_{B}\) is the Boltzmann constant, \(T\) is the standard noise temperature, and B is the bandwidth of the interference signal. Figure 2 shows the joint AOA and TDOA localization results. TDOA localization based on least squares ([PERSON] estimated) and maximum likelihood estimation ([PERSON] estimated) are also illustrated in Figure 2.  
It can be seen that both algorithms for solving the position equation achieve good performance. In addition, it can be seen that the joint positioning algorithm achieves better positioning accuracy than the single interference positioning algorithm. The dashed lines in the figure indicate the AOA localization curves and the TDOA localization curves, with each set of curves indicating possible interference source localization locations. This is because both the AOA localization algorithm and the TDOA localization algorithm  
Figure 1: Decoherence-based direction finding algorithm vs. M.  
Figure 2: Joint interference localization results. require the cooperative localization of multiple base stations to achieve accurate localization of the interference source. The localization result of a single base station is a set of possible locations. Figure 3 compares the error of solving the system of position equations by least squares and maximum likelihood estimation, and it can be seen that, regardless of the size of the noise error, the least squares method for solving the system of position equations is better than the maximum likelihood estimation algorithm.