# A Tri-Satellite Interference Source Localization Method for Eliminating Mirrored Location
## 5 Results
### Real Data Result Analysis  
In this section, the satellite real data processing results are presented to validate the effectiveness of the proposed algorithm. A signal from a cooperative interfering transmitter is illuminating the main satellite in synchronous orbit. The location of the interfering transmitter is [108.79\({}^{\circ}\) E, 32.32\({}^{\circ}\) N]. The two adjacent satellites can receive and relay the sidelobe signal of the interfering transmitter to the ground. This signal relayed from the three satellites is received by three C-band antennas, respectively. The CAF processing is used to measure the TDOA and FDOA of the main satellite and the adjacent satellites. The CAF processing results at a single moment are shown in Figure 7.  
Figure 5: Localization errors versus the error of the initial location error. Figure 6: Localization errors versus the TDOA measure errors. Figure 7: Results of the CAF processing using the real data in actual tests. (**a**) The CAF processing result in TDOA-FDOA plane; (**b**) the mesh of the CAF processing results in TDOA-FDOA; (**c**) the FDOA slice of maximum CAF amplitude; (**d**) the TDOA slice of maximum CAF amplitude. After measuring the TDOA and FDOA of the received data from the satellite, the multi-moment localization and the proposed method are used to solve the location of the interference transmitter. It can be seen from the change of the cost function in the iterative process that the required results can be obtained by iterating 2-3 in Figure 8a. From the intersection of the time difference lines in Figure 8b, it can be seen that, due to the error in the time difference measurement, the time difference lines at the real point position at multiple times cannot completely intersect at one point. Compared with the real point position, the time difference line at the mirrored point is more divergent, so the method based on multi-time measurement can be used to remove the mirrored point. The location results and location errors of the multiple-moment localization method and the proposed method in four moments are shown in Table 1. It can be found that the location errors vary with the location time, which is caused by the motion of the satellite. Meanwhile, the performance of localization of the proposed method is better than the multiple-moment location method with smaller location errors. The multi-time localization algorithm can locate near the real position of the radiation source target, but the accuracy is affected by the time difference measurement error, and it is difficult to obtain high localization accuracy. The proposed method can greatly improve the localization accuracy at multiple moments on the basis of removing mirrored points through subsequent point-by-point localization. \begin{table}
\begin{tabular}{c c c c} \hline
**Localization Method** & **Location Time** & **Location Result** & **Location Error** \\ \hline \multirow{4}{*}{Multiple moment method} & 20 December 2020 14:29:54 & 108.7986\({}^{\circ}\) E 32.4250\({}^{\circ}\) N & 11.66 km \\  & 20 December 2020 15:29:54 & 108.7949\({}^{\circ}\) E 32.3725\({}^{\circ}\) N & 5.84 km \\  & 20 December 2020 16:29:54 & 108.8000\({}^{\circ}\) E 31.9776\({}^{\circ}\) N & 37.93 km \\  & 20 December 2020 17:29:54 & 108.8281\({}^{\circ}\) E 31.7897\({}^{\circ}\) N & 58.86 km \\ \hline \multirow{4}{*}{Proposed method} & 20 December 2020 14:29:54 & 108.7899\({}^{\circ}\) E 32.2679\({}^{\circ}\) N & 5.80 km \\  & 20 December 2020 15:29:54 & 108.7937\({}^{\circ}\) E 32.3174\({}^{\circ}\) N & 0.48 km \\ \cline{1-1}  & 20 December 2020 16:29:54 & 108.7938\({}^{\circ}\) E 32.2880\({}^{\circ}\) N & 3.57 km \\ \cline{1-1}  & 20 December 2020 17:29:54 & 108.7938\({}^{\circ}\) E 32.3015\({}^{\circ}\) N & 2.08 km \\ \hline \end{tabular}
\end{table} 
Table 1: Location results and location errors of the multiple time method and the proposed method. Figure 8: Results of the localization using the real data in actual test.