Attacks on Sensor Network Parameter Estimation with Quantization: Performance and Asymptotically Optimum Processing

Byzantine attacks on sensor systems estimating the value of an unknown deterministic parameter based on quantized observations are studied. Initially, asymptotically optimum processing is investigated for the family of attacks that would pass bad data detectors at the sensors. Bad data detectors check that the sensor data fits the models employed by the estimation approach when it assumes no attack is present. It is then shown that it is possible to identify the attacked sensors, under stated assumptions, with perfect accuracy as the number of observations K from each sensor tends to infinity. If the number of sensors tends to infinity while having a finite K, it is shown that the attacked sensors can be identified with a given accuracy that can be set by K, allowing considerable design flexibility. Next, the performance of any estimation approach employed by the sensor system under any general attack is described for cases where any number of observations and sensors are employed. A classification for these general attacks which categorizes them according to the information available to the attacking entity is introduced. Solving optimization problems over these attack classes leads to expressions which describe the performance of any specific estimation algorithm under the most devastating attacks with full information and the generally less effective information free attacks. Constraints are considered to account for some attack detection performed by the sensor system.