A positioning system includes: a gyro sensor configured to detect an angular velocity of a moving body; a geomagnetic sensor configured to detect a direction in which the moving body is placed; an acceleration sensor configured to detect an acceleration of the moving body; and a gyro sensor output correction part configured to correct an output of the gyro sensor, wherein the gyro sensor output correction part is configured to convert output components of the gyro sensor into at least one of a rotation matrix and a quaternion based on output components of the geomagnetic sensor and output components of the acceleration sensor, and to calculate a posture of the moving body based on the rotation matrix or the quaternion.