# A Tri-Satellite Interference Source Localization Method for Eliminating Mirrored Location
## 1 Introduction  
With the rapid growth of satellite communication services, the interference signals received are also increasing. Satellite interference source localization technology [1; 2], which can receive electromagnetic signals passively to locate the interference source, is the principal method of satellite anti-interference technologies. Aiming at the complex interference environment of satellite communication, several advanced technologies have been proposed to suppress the satellite interference [3; 4; 5] in recent years. Meanwhile, several satellite interference systems have been developed [6; 7], represented by a \"NOSS\" series of a marine surveillance satellite developed by the US Navy, the Transmitter Location System (TLS) model 2000 developed by the Interferometric Inc., the SatID developed and operated by Defence Research Agency (DRA) of the UK, and the State Space Satellite Monitoring System (SSSMS) developed by the State Radio Regulation of China. The satellite interference source localization technology has the advantages of wide coverage, long operating distance, concealed reception, and strong survivability. Using the passive location, the satellite localization technology has strong survivability and concealed reception. The localization technology is based on the long baseline interferometry method for the satellites to realize wide area coverage. In addition, the detection of very weak signals isachieved through correlation techniques. It can locate interference source targets quickly and accurately, and has an important role and broad application prospects in both civil and military fields. The current satellite interference source localization methods mainly use the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA) measured by the signals received from the main satellite and the adjacent satellites to determine the location. The localization methods can be classified into analytical methods [8; 9; 10; 11; 12; 13; 14], optimized solutions [15; 16; 17; 18; 19; 20], and intelligent algorithms [21; 22; 23] in recent years. The analytical methods derive the closed-form solution of the nonlinear localization equation set based on mathematical approximation and the intermediate variable. The nonlinear equations of localization are transformed into a set of linear equations, in which the closed-form solution can be derived. In the optimization techniques, the localization problem is reformulated as a convex optimization problem and can be solved based on the convex optimization algorithm. However, the local convergence may be produced in the optimization procedure. Considering the nonlinear characteristics of the location equations, the intelligent methods are proposed in recent years to deal with the grid search problem. Compared with the exhaustive method, the intelligent search algorithm has a higher search efficiency. However, when the need for the location accuracy increases, the complexity of the algorithm increases exponentially. Compared with TDOA measurement, the FDOA measurement requires more reference stations for satellite ephemeris calibration. Therefore, the tri-satellite TDOA localization system has lower cost and more reliable location results. The tri-satellite TDOA localization method is based on two TDOA lines of position (LOP) for intersection positioning. Affected by the ephemeris of the satellite and the location of the interference source, the TDOA LOP have two intersection points at a certain moment, and it is difficult to distinguish the correct location from the mirrored location of the interference source. The research in the existing literature mainly focuses on the optimization of TDOA measurement [24; 25] and the solution of localization equations [26; 27]. For the mirrored location that appears in the location process, the correct location can only be obtained based on the prior knowledge of the interference location in the conventional methods. When the prior knowledge is missed, the mirrored location cannot be eliminated.