A system for determining orientation or position of a movable supporting structure, such as a vehicle, includes a special inertial sensor unit. This unit includes a single gyroscope hereinafter referred to as a "gyro", with its spin axis mounted in alignment with the sensitive axis of an accelerometer. The gyro and accelerometer are mounted pendulously to rotate only about a single axis which is aligned with a direction of travel of the vehicle or with a projectile launching assembly. In additon to being pendulously mounted as mentioned above, the gyro and accelerometer combination may be rotated relative to their pendulous support, to certain fixed positions, in order to facilitate rapid initial alignment and orientation and pre-mission calibration of the inertial instruments. The pendulously mounted unit is also provided with an optical encoder to indicate the roll angle of the vehicle to which the inertial unit is secured.In an initial rapid alignment sequence after the unit is energized, the rotation of the earth is sensed and the information stored with the unit in two or three different orientations, and, using this stored information, and the stored accelerometer outputs, the azimuth of the pendulous axis relative to true north and its pitch or elevation angle may be accurately determined.When mounted in a vehicle and used in combination with the output from the vehicle odometer, an accurate indication of the movement of the vehicle may be obtained, and when combined with initial position and orientation data, the position of the vehicle may be continuously determined.