Distributed estimation in the presence of attacks for large scale sensor networks

Distributed estimation using quantized data in the presence of Byzantine attacks is considered. Several subsets of sensors are assumed to be tampered with by different adversaries. Under the control of adversaries, the compromised sensors transmit fictitious data to the fusion center (FC) in order to undermine the estimation performance of the sensor network. First, we show that it is possible to asymptotically identify the attacked sensors and categorize them into different groups corresponding to different attacks, provided it is known that the set of unattacked sensors is larger than any set of attacked sensors taken over by one attack. Next, we consider joint estimation of the statistical description of the attacks and the parameter to be estimated. It can be shown that the corresponding Fisher Information Matrix (FIM) is singular. To overcome this, a modified quantization approach is proposed, which will provide a nonsingular FIM. Thus, the statistical properties of the attacks and the parameter to be estimated can be accurately estimated with sufficient data, provided that the number of time samples at each sensor is not less than 2. Furthermore, the FIM is employed to provide necessary and sufficient conditions under which utilizing the compromised sensors in the proposed fashion will lead better estimation performance when compared to approaches where the compromised sensors are ignored. Finally, numerical results imply that for some cases, significant estimation performance gain can be achieved by taking advantage of compromised sensors.