In this paper, the conventional estimation-based receding horizon control paradigm is enhanced by using functional approximation, the adaptive modifications on state estimation and convex projection notion from optimization theory. The mathematical formalism of parameter adaptation and uncertainty estimation procedure are based on the redesign of optimal state estimation in discrete-time. By using Lyapunov stability theory, it is shown that the online approximation of uncertainties acting on both physical system and state estimator can be obtained. Moreover, the convergence criteria for online parameter adaptation with fully matched and partially matched cases are presented and shown. In addition, it is shown that the uniform boundedness of tracking and adaptation errors can be maintained by projection-based parameter update laws in discrete-time with adequate sampling times. Finally, the proposed method is implemented to quadrotor case study and the gradual recovery of feasible sub-optimal solutions are presented despite actuation, modeling and measurement errors. By using the proposed method, the uncertainty estimates are successfully converged to their prescribed values and both state prediction and command tracking of model predictive controller are corrected within the convergence bounds.