We address the problem of attack detection and isolation for a class of discrete-time nonlinear systems under (potentially unbounded) sensor attacks and measurement noise. We consider the case when a subset of sensors is subject to additive false data injection attacks. Using a bank of observers, each observer leading to an Input-to-State Stable (ISS) estimation error, we propose two algorithms for detecting and isolating sensor attacks. These algorithms make use of the ISS property of the observers to check whether the trajectories of observers are "consistent" with the attack-free trajectories of the system. Simulations results are presented to illustrate the performance of the proposed algorithms.for all e(0) ∈ R n and k ≥ 0. Note that, because λ S ∈ (0, 1), there always exist k * S such that c S λ k S |e(0)| ≤ ǫ, for any ǫ > 0 and k ≥ k * S . Definek * := max J,S {k * J , k * S } . For each subset J with card(J) = p − q, define π J (k) asSince there are at most q sensors under attack, we know there exist at least oneĪ ⊂ {1, . . . , p} with card(Ī) = p − q such that aĪ = 0 and (14) is satisfied. DefineFrom (14) and (16), we obtain πĪ (k) ≤ 2(ǫ + γ ′Ī ||mĪ || k ), for all k ≥k * , whereHowever, if the subset J of sensors is under attack, i.e., a J = 0, thenx J (k) andx S (k) in π J (k) are more inconsistent and might produce larger π J (k). Definēthen,z J can be used as a threshold to isolate attacked sensors. For all k ≥k * , we select out all the subsets J ⊂ {1, . . . , p} with card(J) = p − q that satisfyDenote asW (k) the set of sensors that we regard as attackfree at time k. Then,W (k) is given as the union of all subsets J such that (20) holds: W (k) := J⊂{1,...,p}:card(J)=p−q,πJ (k)≤zJ