In this paper, an attack-resilient estimation algorithm is developed for linear discrete-time stochastic systems with inequality constraints on the actuator attacks and states. The proposed algorithm consists of optimal estimation and information aggregation. The optimal estimation provides minimum-variance unbiased (MVU) estimates, and then they are projected onto the constrained space in the information aggregation step. It is shown that the estimation errors and their covariances from the proposed algorithm are less than those from the unconstrained algorithm. Moreover, we proved that the state estimation errors of the proposed estimation algorithm are practically exponentially stable. A simulation on mobile robots demonstrates the effectiveness of the proposed algorithm compared to an existing algorithm.