A transformation of unit vectors to simplify derivations between Earth-centered and local North-East-and-up on an ellipsoid Earth

A transformation of unit vectors between Cartesian earth centered and local north, east, and up coordinates is presented to simplify derivations on an ellipsoid Earth. The unit vector relationships an used to simplify the derivation of a transformation for sending track files from a sensor platform (latitude, longitude) with local Cartesian coordinates (Xs-East, Ys-North, Zs-Up) to a receiving platform (latitude', longitude') with local Cartesian coordinates (Xr-East, Yr-North, Zr-Up). Zero altitude for both coordinate systems is taken to be sea level. Tracks may be ballistic, air, surface and/or subsurface.