N-vector

n-vector is a three parameter non-singular horizontal position representation well-suited for replacing latitude and longitude in mathematical calculations and computer algorithms. Geometrically, it is a unit vector that is normal to the reference ellipsoid. The vector is decomposed in an Earth centered earth fixed coordinate system. It behaves the same at all Earth positions, and it holds the mathematical one-to-one property.

A normal vector to a strictly convex surface can be used to uniquely define a surface position. n-vector is an outward-pointing normal vector with unit length used as a position representation.

For most applications the surface is the reference ellipsoid of the Earth, and thus n-vector is used to represent a horizontal position. Hence, the angle between n-vector and the equatorial plane corresponds to geodetic latitude, as shown in the figure.

A surface position has two degrees of freedom, and thus two parameters are sufficient to represent any position on the surface. On the reference ellipsoid, latitude and longitude are common parameters for this purpose, but as all two-parameter representations, they have singularities. This is similar to orientation, which has three degrees of freedom, but all three-parameter representations have singularities. In both cases the singularities are avoided by adding an extra parameter, i.e. to use n-vector (three parameters) to represent horizontal position and a unit quaternion (four parameters) to represent orientation.

...
Wikipedia