Precise estimation of position, velocity, and orientation is crucial for robust control in airborne applications such as the fast maneuvering power kites for airborne wind energy generators. In this paper we present a sensor fusion approach for the measurements of a global navigation satellite system receiver and an inertial measurement unit, using methods from direct optimal control. The resulting optimization problem is based on the minimization of the weighted squared residuals between model predictions and measurements and solved using a direct collocation discretization strategy. The framework allows the formulation of a batch and filter estimator which include beside the estimation of the navigational states the identification of sensor parameters such as biases of the inertial measurement unit. The results of the algorithms are evaluated against a reference trajectory of a maneuvering single propeller aircraft and achieve root mean squared errors below 1 m in position, 0.4 ms-1 in velocity, and 0.5 deg in orientation for the batch estimator. The contribution in this paper is a first step towards the required robustness of state estimation for airborne applications.