A self-contained system that can automatically determine the position, velocity, and attitude of a moving vehicle for the purpose of directing its future course. Based on prior knowledge of time, gravitational field, initial position, initial velocity, and initial orientation relative to a known reference frame (coordinate system), an inertial navigation system (INS) is capable of determining its present position, velocity, and orientation without the aid of external information. The generated navigational data are used to determine the future course for a vehicle to follow in order to bring it to its destination. Such systems have found application in the guidance and control of submarines, ships, aircraft, missiles, and spacecraft. The sensors making these measurements, based on one of the basic properties of mass—inertia, are gyroscopes (gyros) and accelerometers.