"The navigational equations that are applied to the IMU output to obtain the complete set of navigation parameters is presented in the block diagram. It consists of the double integration of the measured acceleration to obtain the aircraft velocity and then the position. In a strapdown navigation implementation the acceleration is measured in the aircraft body axis and the position of the system is required in a local level coordinate system called the navigation frame.

To determine the aircraft acceleration in the navigation frame, it is necessary to determine the orientation of the aircraft body frame relative to this navigation frame and use this description of the relative orientation between the two axis systems to convert the acceleration measurement from the body frame to the navigation frame. This is where the gyroscopes come into play.

As presented in the block diagram, the gyro cluster measurement of the aircraft angular rate relative to the inertial frame is integrated to determine the system’s orientation (known as the attitude). The attitude can be presented in terms of Euler angles (roll, pitch and yaw), in terms of a direction cosine matrix or in terms of a quaternion representation (Titterton & Weston, 2004; Stevens & Lewis, 2003; Farrell,2008; Rogers 2007; Groves, 2008; Farrell & Bath, 1999). The attitude representation is used to convert the accelerations to the navigational frame. Some additional corrections for the effect of the Earth’s rotational rate on the gyros, changes in gravity as a function of position and altitude and the Coriolis effect resulting from the relative rotation between the two frames is also needed."