Abstract: Techniques for estimating a current inclination and azimuth of a drill bit of a wellbore drilling system are described. The estimates for the current inclination and azimuth are generated using measurements obtained for one or more parameters associated with the drilling process performed by the drill bit and taken over a range of the wellbore falling within a sliding window having a predefined distance D extending along the wellbore.

Abstract: One or more sensors are positioned downhole in a wellbore of a geological formation. One or more survey directional measurements associated with the wellbore are performed and one or more continuous directional measurements associated with the wellbore are performed. A wellbore trajectory model projects a trajectory of the wellbore to respective measured depths where at least one of the one or more survey directional measurements and one or more continuous directional measurements were performed to predict one or more directional measurements of the wellbore at the respective measured depths. One or more errors are determined based on the predicted one or more directional measurements, the one or more survey directional measurements, and the one or more continuous directional measurements. The wellbore trajectory model is calibrated based on the one or more errors.

Abstract: One or more wellbore trajectories and respective control inputs are determined which meet a wellbore trajectory model, a constraint, and a wellbore length. A wellbore trajectory and respective control input from the one or more wellbore trajectories and respective control inputs are then identified which minimize a cost function associated with the performance objective. The control input associated with this wellbore trajectory are output to a drilling system for drilling a wellbore.