Secure state-estimation for dynamical systems under active adversaries

We consider the problem of state-estimation of a linear dynamical system when some of the sensor measurements are corrupted by an adversarial attacker. The errors injected by the attacker in the sensor measurements can be arbitrary and are not assumed to follow a specific model (in particular they can be of arbitrary magnitude). We first characterize the number of attacked sensors that can be tolerated so that the state of the system can still be correctly recovered by any decoding algorithm. We then propose a specific computationally feasible decoding algorithm and we give a characterization of the number of errors this decoder can correct. For this we use ideas from compressed sensing and error correction over the reals and we exploit the dynamical nature of the problem. We show using numerical simulations that this decoder performs very well in practice and allows to correct a large number of errors.