In AS6969™, a vector is strictly a quantity with direction in ordinary space.

In the standard, a vector coordinate reference system (CRS) is a coordinate system (CS) that is anchored to a coordinate datum (CD). The CS has two forms. The first is a set of equations for true vectors. The second is a set of equations for the position vector and its time derivatives. Position is handled differently by the CS because it is an affine quantity. An affine quantity is one in which the sum of two values has no meaning. For example, it is not meaningful to add two geodetic positions. The difference between two position vectors, however, is meaningful – it is a displacement vector (a true vector). Time (versus time duration) and temperature (versus temperature difference) are also affine quantities.

The CD, to which the CS is anchored in a CRS, provides both a position datum, which is required for the position vector, and a direction datum, which is required for all vectors.

For true vectors, the CS is defined by equations for the generalized quantity q, where q may be substituted for any true vector such a force, velocity, momentum, electric field strength, and so on. The quantity vector differential is also defined (dq), which is important for metrological quantities such as quantity uncertainty.

As stated, the position vector r is a special case. For the position vector, the equations for its time derivatives of velocity and acceleration are provided, together with the time derivatives of important angle coordinates and components in the CS. For example, in the cylindrical CS angular velocity and angular acceleration are also defined.

The ellipsoidal CS (such as WGS84) is different in that it only addresses the position vector, noting that its derivative (dr) provides the axes of the local tangent plane (LTP). Thus an ellipsoidal CRS is mathematically tied to the earth-fixed LTP and vehicle-carried LTP.

The AS6969™ approach is important because multiple state quantities can be tied explicitly to the same CRS or to a mathematically connected set of CRS. To achieve this, the CRS does not specify the measurement units for each coordinate. Valid measurement units for each coordinate are selected according to the quantity.

In AS6969™, three kinds of angle are considered. These are plane angle (a scalar), vector angle, and Euler angle. Euler angles are used in coordinate operations to transform a coordinate tuple from one CRS to another. Some quantities are Euler angles, such as vehicle heading, pitch and roll. These are not tied to a CRS but to a coordinate operation (CO) between two CRS. Currently one CO is provided in AS6969™: the CO from the LTP (north east down) CRS to the vehicle body Cartesian CRS.