  Cyber-physical systems are found in many applications such as power networks,
manufacturing processes, and air and ground transportation systems. Maintaining
security of these systems under cyber attacks is an important and challenging
task, since these attacks can be erratic and thus difficult to model. Secure
estimation problems study how to estimate the true system states when
measurements are corrupted and/or control inputs are compromised by attackers.
The authors in [1] proposed a secure estimation method when the set of attacked
nodes (sensors, controllers) is fixed. In this paper, we extend these results
to scenarios in which the set of attacked nodes can change over time. We
formulate this secure estimation problem into the classical error correction
problem [2] and we show that accurate decoding can be guaranteed under a
certain condition. Furthermore, we propose a combined secure estimation method
with our proposed secure estimator and the Kalman Filter for improved practical
performance. Finally, we demonstrate the performance of our method through
simulations of two scenarios where an unmanned aerial vehicle is under
adversarial attack.
