  This paper focuses on securely estimating the state of a nonlinear dynamical
system from a set of corrupted measurements. In particular, we consider two
broad classes of nonlinear systems, and propose a technique which enables us to
perform secure state estimation for such nonlinear systems. We then provide
guarantees on the achievable state estimation error against arbitrary
corruptions, and analytically characterize the number of errors that can be
perfectly corrected by a decoder. To illustrate how the proposed nonlinear
estimation approach can be applied to practical systems, we focus on secure
estimation for the wide area control of an interconnected power system under
cyber-physical attacks and communication failures, and propose a secure
estimator for the power system. Finally, we numerically show that the proposed
secure estimation algorithm enables us to reconstruct the attack signals
accurately.
