A system determines three-dimensional attitude of a stationary or moving platform using signals from a Global Navigation Satellite System (GNSS) antenna that undergoes deliberate translation, which may be occasional. The system uses single GNSS receiver, a single GNSS antenna, and inertial acceleration and/or rotation rate sensors. In one implementation, the GNSS antenna and inertial sensing components are rigidly connected and mounted to a pallet that is intentionally translated along a track as needed. In a second implementation, the GNSS antenna is mounted to a pallet, and the inertial sensing components are fixed in position. To maximize effectiveness, the track is oriented along a geometrical direction of the platform that is predominantly in a lateral direction from the gravity vector. The system achieves three-dimensional attitude accuracy that rivals interferometric GNSS systems.