# Consensus-Based Distributed Target Tracking with False Data Injection Attacks over Radar Network  
[PERSON]  
1 Harbin Institute of Technology, Harbin 150001, China; [EMAIL_ADDRESS] (Y.S. ); [PERSON]AIL_ADDRESS] (N.C.); [EMAIL_ADDRESS] (B.P.) [PERSON]  
1 Harbin Institute of Technology, Harbin 150001, China; [EMAIL_ADDRESS] (Y.S. ); [PERSON]AIL_ADDRESS] (N.C.); [EMAIL_ADDRESS] (B.P.) [PERSON]  
2 Beijing Aerospace Technology Institute, Beijing 100000, China; yuli,[EMAIL_ADDRESS] 2  
[PERSON]  
3 Harbin Jiancheng Group Co. Ltd., Harbin 150001, China; syz_hit@163.  
performance. Different from the cyberattacks mentioned before, false data injection (FDI) is a specific type of deception attack [19] which can deteriorate the estimation accuracy of the radar network by modifying the measurements of the attacked radars with unknown and time-varying attack variables. Most existing works about FDI attacks concentrate on the detector's design. Several effective detectors, such as \(\mathcal{O}^{2}\) detectors, summation detectors [22] and cumulative sum-based detectors [23], have been proposed to detect this kind of attack. The easiest way to deal with the attacked measurements is to discard them so that they will not affect the radar tracking system. Obviously, discarding the measurements leads to information loss, and it will suffer from filter divergence when the attack lasts for a long time. An alternative is to estimate the attack parameter and eliminate its effect. For attack parameter estimation, an augmented state Kalman filter (ASKF) may be used to produce the optimal state estimate, in which the stack vector technique is used by augmenting the attack parameter into the state. However, the computational burden of the ASKF increases dramatically with the augmented state dimension, especially in a large-scale network. Several studies considered distributed state estimation (DSE) with FDI attacks. In [24], a trust-based combination strategy was developed to classify sensors in a network into two clusters: the trusted one and the untrusted one. The sensor measurements in the untrusted cluster are discarded, which is obviously a waste of information. Moreover, the method can only deal with a case where less than half of the sensors are under attack. In [17], a confident covariance intersection-based fusion method was proposed, where the confidence factor is used to weight the estimate confidences of all radars, thus reducing the fusion weights of the injected data. The weight of the injected data is decreased, but the effect of it is not eliminated. The second challenge in target tracking using radar networks is how to achieve global consistency over the radar network. For DSE, consensus estimation is an effective tool for state estimation in sensor networks that are not fully connected to achieve global consistency. Consensus-based methods can be categorized based on the exchanged quantities among neighboring sensors. For example, sensors can exchange local state estimates (consensus on estimates method (CE)) [11; 14], local measurements and innovation covariances (consensus on measurements method (CM)) [10; 16] and information vectors and matrices (consensus on information method (CI)) [9; 15]. The CE does not exchange error covariance matrices, which makes it suffer from poor performance [12]. The CM can achieve the same accuracy as the centralized method only when the number of consensus steps trends toward infinity. The CI guarantees stability for any number of consensus steps, but its performance can be hampered because of the assumption that the correlations between the estimates from different sensors are completely unknown. Recently, a consensus method named Hybrid CMCI (HCMCI) [12; 13] has been proposed, which has the advantages of both the CM and CI methods. The stability analysis of the HCMCI in the case of linear systems has been given, and the effectiveness of the HCMCI has been shown in [12]. For the nonlinear case, Taylor expansion is used.