## 1 Introduction  
GPS is susceptible to a variety of interferences due to the low signal power. For GPS receivers, there are two major types of interferences at present: jamming and spoofing. Strong interferences are used in jamming, usually resulting in loss of lock and positioning failure of the target receiver. Hence the concealment of this interference is poor. On the other hand, spoofing is a structural interference, the counterfeit signals rebroadcasted by spoofers are very similar to the authentic signals from satellites and can gradually induce the positioning results of the target receiver to a false location [1; 2; 3; 4]. Compared with jamming, spoofing is less likely to be found by the target receiver and hence is more sinister. The early spoofing is simplistic. Specifically, one simply attaches a power amplifier and a transmitting antenna to a satellite signal simulator and broadcasts the counterfeit signals toward the target receiver. However, the simplistic spoofing usually needs the cooperation of jamming to bring the target receiver into the reacquisition first. In 2008, [PERSON] et al. successfully developed a repeater based on a software receiver, which can directly deceive the target receiver at the tracking stage. It reminds people of the threat of spoofing once again [1]. Correspondingly, research on anti-spoofing began to develop rapidly. In 2012, [PERSON] et al. made a comprehensive study of spoofing threats and briefly introduced different techniques for two main categories, namely spoofing detection and spoofing mitigation [5]. According to the description of related papers, common spoofing countermeasures can be categorized to four groups: signal power anomaly detection [2; 3], time-of-arrival anomaly detection [6; 7; 8], space processing [9; 10; 11; 12], and correlation peak distortion detection [13; 14; 15; 16; 17]. [PERSON] [12] proposed adaptive antenna array beamforming null steering method, which can directly shield the counterfeit signals from a single interference source. However, it is difficult in deploying multiple antennas. In view of the diversity of spoofing, [PERSON] used multiple anti-spoofing methods simultaneously on the receiver and achieved the mitigation of simplistic spoofing [18]. However, on the whole, most of the current anti-spoofing techniques are merely able to detect the spoofing. This means that the target receiver can ensure that the positioning results are not affected by closing the corresponding channels after detecting the spoofing only when the number of the authentic signals spoofed with the counterfeit signals is small. Based on the discussions above, the spoofing mitigation needs to be further researched in anti-spoofing. Multipath and spoofing share the similarity that they distort the correlation peaks of the composite signals. In particular, if the carrier frequency of the counterfeit signal deviates from that of its corresponding authentic signal, the distortion of the correlation peak of the composite signal will be serious. Instead, if the carrier frequency of the counterfeit signal is consistent with that of its corresponding authentic signal, the correlation peak of the composite signal of spoofing will be similar to that of multipath, which is the most difficult situation to detect and handle. Hence, the carrier frequencies of the counterfeit signal and its corresponding authentic signal are set to be the same (frequency lock mode) [19]. As a result, multipath mitigation approaches can be applied to anti-spoofing [20]. However, the counterfeit signals rebroadcasted by spoofers and the multipath signals are significantly different. The major differences are as follows [21]:  
1. Except for the special case that the direct signal is blocked, multipath signals from a satellite are typically weaker than its direct signal, while the counterfeit signals for spoofing are usually slightly higher in power than the authentic signals. 2. The correlation peaks of multipath signals lag behind the correlation peak of the corresponding direct signal.