INERTIAL PLATFORM EQUATIONS

INERTIAL NAVIGATION EMPLOYS AN INERTIAL INPUT, OUTPUT SYSTEM COMPOSED OF A COMPUTER AND A GIMBALLED PLATFORM CONTAINING GYROS AND ACCELEROMETERS MOUNTED ALONG THE AXES OF THE MEASUREMENT SYSTEM. The accelerometers constantly measure acceleration in this system of axes, which is required to have a known orientation with respect to inertial space. The computer is usually referenced to earths longitude and latitude, or to some other reference frame having known space and time orientation with respect to measurement axes system. Mathematical expressions for each of nine platforms are derived for the acceleration components, angular rates, and linear and ground velocities. The most important problem in inertial navigation is the establshment of the level plane through a point above the Earth, which is represented approximately by an Earth reference ellipsoid. Platform level is defined by the choice of the normal or vertical, which may be geocentric, running through the center of the reference ellipsoid or non-geocentric, intercepting the polar axis out of center. The directional coincidence of the normal with the mass attraction is called the mass attraction vertical. The vertical taken normal to the surface of the reference ellipsoid is called the geodetic vertical.