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We show that unconstrained Model Predictive Control (MPC) based on step response models is identical to linear quadratic optimal output feedback under a particular disturbance and measurement noise assumption. More specifically, MPC in its unconstrained form is equivalent to the optimal state observer (Kalman filter) designed for step disturbances at the output and in the absence of measurement noise, plus linear quadratic state feedback. Analytical results on the state estimation based on step response models allow us to generalize the conventional MPC (which is widely applied in industry) to processes with integrators and to cases with white measurement noise without introducing any additional complexity. For the case of an integrated white noise disturbance entering at the output through general first order dynamics (including integrator) and white measurement noise, the optimal state estimator is conveniently parametrized in terms of a real parameter vector whose dimension is equal to the number of outputs. This parametrization is independent of model complexity and eliminates the need for solving a Riccati equation of potentially very large order. It also provides natural on-line tuning parameters for closed-loop robustness and noise-filtering. Our analysis shows that the new state-estimation-based MPC is a direct extension of conventional MPC techniques such as Dynamic Matrix Control (DMC) and Internal Model Control (IMC).