The problem of system state estimation in the presence of an adversary is investigated for linear dynamic systems. It is assumed that the adversary injects additive false information into the sensor measurement. The impact of the false information on the Kalman filter's estimation performance is analyzed for a general dynamic system. To be concrete, a target tracking system has been used as an example. In such a system, if the false information is injected only once, the effect of the false information on the Kalman filter proves to be diminishing over time, even when the Kalman filter is unaware of the false information injection. The convergence rate as a function of the maneuvering index is analyzed. If the false information is repeatedly injected into the system, the induced estimation error proves to reach a finite steady state. Numerical examples are presented to support the theoretical results.