A real-time high accuracy position and orientation system (RT-HAPOS) system for a vehicle, such as an aircraft, comprises a global navigation satellite system (GNSS) receiver disposed on the vehicle and an integrated inertial navigation (IIN) module disposed on the vehicle. The GNSS receiver generates GNSS position data indicating approximate positions of the vehicle during a data acquisition period in which the vehicle is moving. The IIN module executes a real-time kinematic (RTK) algorithm during the data acquisition period to generate output position data indicating positions of the vehicle at a greater precision than the GNSS position data, based on the GNSS position data, inertial measurement data acquired on the vehicle during the data acquisition period, and a set of virtual reference station (VRS) observables received during the data acquisition period from a remote source external to the vehicle, where the VRS observables are based on the GNSS position data.