The "Extended" preferred ordering theorem for precision acquisition tracking and pointing

In radar tracking, the Preferred Ordering Theorem for updating the state vector in rectangular coordinates using an Extended Kalman Filter states that the measurement components of a detection should be used sequentially in the order azimuth first, then elevation, and range last. Such is counterintuitive to a common belief that the most accurate measurement should be used first, since that is usually range. However, it is shown here that the theorem loses its efficacy as a track converges. An extension is therefore given to remedy that, which is dubbed the DKF after Desargues, since it is based on an analysis involving projective geometry. With this approach a track in rectangular coordinates can be updated using a range or angle observation, separately or sequentially in either order, with less error. In this presentation the basic issues are illustrated, and the DFK is defined and contrasted with the EKF.