# A Method of Detections' Fusion for GNSS Anti-Spoofing
###### Abstract  
The spoofing attack is one of the security threats of systems depending on the Global Navigation Satellite System (GNSS). There have been many GNSS spoofing detection methods, and each of them focuses on a characteristic of the GNSS signal or a measurement that the receiver has obtained. The method based on a single detector is insufficient against spoofing attacks in some scenarios. How to fuse multiple detections together is a problem that concerns the performance of GNSS anti-spoofing. Scholars have put forward a model to fuse different detection results based on the Dempster-Shafer theory (DST) of evidence combination. However, there are some problems in the application. The main challenge is the valuation of the belief function, which is a key issue in DST. This paper proposes a practical method of detections' fusion based on an approach to assign the belief function for spoofing detections. The frame of discernment is simplified, and the hard decision of hypothesis testing is replaced by the soft decision; then, the belief functions for some detections can be evaluated. The method is discussed in detail, and a performance evaluation is provided, as well. Detections' fusion reduces false alarms of detection and makes the result more reliable. Experimental results based on public test datasets demonstrate the performance of the proposed method. GNSS; spoofing; detection; fusion; Dempster-Shafer theory; belief function 1  
[PERSON], [PERSON], [PERSON], M.  
monitoring [9; 10], vestigial signal detection, receiver autonomous integrity monitoring (RAIM) [4] and the extended method [11], etc. In addition, some crossing methods are proposed; for example, the authors of [12] propose a method based on machine learning and signal processing to monitor the interference of GNSS. However, there are shortcomings in these methods, and some of them are complementary in anti-spoofing. The cooperation of multiple spoofing detections is necessary to improve the performance of GNSS anti-spoofing. Information fusion is a key issue of the cooperation of multiple spoofing detections. There are many methods to fuse the information of different detectors, such as Bayesian data fusion, the Kalman filtering method, Dempster-Shafer theory (DST), etc. However, there are some obstacles in the applications. For example, a priori knowledge of the detectors is needed for Bayesian data fusion. The statistical properties of most detectors are known in the case of authentic GNSS signals, but uncertain in the case of spoofing signals, i.e., a priori information of the GNSS spoofing detectors is partially unknown. The uncertainty makes it impossible to apply Bayesian inference to calculate the posterior probabilities of the possible results. For the Kalman filtering method, the precise estimate of the noise covariances, including the covariances of process noise and observation noise, is very important in applications. However, a precise estimate is hard to obtain in the case of spoofing, because the style of spoofing is varied and unknown. DST [13] is a general framework for reasoning with uncertainty, and it provides a solution to combine evidence from different sources. It is suitable for use in situations where a priori information of detectors is partially unknown. The authors of [14] propose the framework of a mathematic model for conjunct GNSS spoofing detection. The model is based on the DST. However, it does not give the way to valuate the basic probability assignment (BPA) or belief function for each possible result of detection. Thus, the method cannot be implemented in practice. This paper focuses on this problem of DST and proposes a method to overcome this difficulty. Each spoofing detection makes a decision according to the anomaly of the signal. Usually, it is a hard decision to discern the authenticity of the received signals. A hard decision is easy to implement, but it loses some information of measurement. Thus, false decision cannot be rectified.