False-data attacks in stochastic estimation problems with only partial prior model information

The security of state estimation in critical networked infrastructure such as the transportation and electricity (smart grid) networks is an increasingly important topic. Here, the problem of recursive estimation and model validation for linear discrete-time systems with partial prior information is examined. Further, detection of false-data attacks on robust recursive estimators of this type is considered. The framework considered in this work is stochastic. An underlying linear discrete-time system is considered where the statistics of the driving noise is assumed to be known only partially. A set-valued estimator is then derived and the conditional expectation is shown to belong to an ellipsoidal set consistent with the measurements and the underlying noise description. When the underlying noise is consistent with the underlying partial model and a sequence of realized measurements is given then the ellipsoidal, set-valued, estimate is computable using a Kalman filter-type algorithm. A group of attacking entities is then introduced with the goal of compromising the integrity of the state estimator by hijacking the sensor and distorting its output. It is shown that in order for the attack to go undetected, the distorted measurements need to be carefully designed.