For the unknown but bounded noise discrete-time state space system, a state estimation method based on orthotope filtering is proposed. The bounded error method is first used to analyze the measurement noise and state prediction process, and the prediction state set uses orthotope after being wrapped, which is dispersed into constraints. Then due to the updated minimum edge, the zonotope is tightly wrapped by the orthotope before being dispersed into constraints, which forms a triple constraint with the measurement equation constraints. The upper and lower bounds of all states are obtained by solving linear programming problems. The bounds of this method are the most compact orthotope of the feasible set of wrapped states. Simulation examples illustrate the effectiveness and accuracy of the proposed method for estimating the state of discrete state space systems.