A resilient state estimation scheme for uniformly observable nonlinear systems, based on a method for local identification of sensor attacks, is presented. The estimation problem is combinatorial in nature, and so many methods require substantial computational and storage resources as the number of sensors increases. To reduce the complexity, the proposed method performs the attack identification with local subsets of the measurements, not with the set of all measurements. A condition for nonlinear attack identification is introduced as a relaxed version of existing redundant observability condition. It is shown that an attack identification can be performed even when the entire state cannot be recovered from the measurements. As a result, although a portion of measurements are compromised, they can be locally identified and excluded from the state estimation, and thus, the true state can be recovered. Simulation results demonstrate the effectiveness of the proposed scheme.