This manuscript develops an algorithm that fuses Carleman moving horizon estimation (CMHE) and Carleman model predictive control (CMPC) together, to design an output feedback receding horizon controller. CMHE identifies the system states as the initial condition for CMPC to make optimal control decisions. The control decisions made by CMPC update the dynamic models used in CMHE to make more precise estimations. Modeling the nonlinear system with Carleman approximation, we estimate the system evolution for both CMHE and CMPC analytically. The Gradient vectors and Hessian matrices are then provided to facilitate the optimizations. To further reduce real-time computation, we adapt the advanced-step NMHE and advanced-step NMPC concepts to our CMHE/CMPC pair to develop an asCMHE/asCMPC pair. It pre-estimates the states and pre-designs the manipulated input sequence one step in advance with analytical models, and then it updates the estimation and control decisions almost in the real-time with pre-calculated analytical sensitivities. A nonlinear CSTR is studied as the illustration example. With CMHE/CMPC pair, the computational time is decreased to one order of magnitude smaller than standard nonlinear MHE and nonlinear MPC. With asCMHE/asCMPC pair, the real-time estimation and control decisions takes a negligible amount of wall-clock time. (C) 2018 Elsevier Ltd. All rights reserved.