  In this paper, the impact of false information injection is investigated for
linear dynamic systems with multiple sensors. It is assumed that the system is
unsuspecting the existence of false information and the adversary is trying to
maximize the negative effect of the false information on Kalman filter's
estimation performance. The false information attack under different conditions
is mathematically characterized. For the adversary, many closed-form results
for the optimal attack strategies that maximize Kalman filter's estimation
error are theoretically derived. It is shown that by choosing the optimal
correlation coefficients among the bias noises and allocating power optimally
among sensors, the adversary could significantly increase Kalman filter's
estimation errors. To be concrete, a target tracking system is used as an
example in the paper. From the adversary's point of view, the best attack
strategies are obtained under different scenarios, including a single-sensor
system with both position and velocity measurements, and a multi-sensor system
with position and velocity measurements. Under a constraint on the total power
of the injected bias noises, the optimal solutions are solved from two
perspectives: trace and determinant. Numerical results are also provided in
order to illustrate the effectiveness of the proposed attack strategies.
