Systems and methods for navigation of a vehicle use a processing system. The systems and methods can allow an aircraft to take-off in low visibility conditions. The processing system includes a cross tracker, an error processor and an error estimator. The cross tracker is configured to determine a cross track deviation using a hybrid positon and runway heading data. The error processor is configured to determine the hybrid positon from inertial reference system data and corrected error data, and the error estimator is configured to provide the corrected error data using estimates derived from delta range data from a global navigation satellite system receiver.