A compact algorithm for the intersection and approximation of N-dimensional polytopes

In a very general sense, estimation problems are concerned with relating measurements to a (hopefully small) region containing the unknown state or parameters. Polytopes present a natural candidate for the representation and manipulation of such regions. In fact, assuming the existence of a suitable model, many problems may be reduced to one of efficiently representing N-dimensional polytopes and forming their intersections. The algorithm described in this paper provides a solution to the above problem which is reasonably efficient and requires very little computer code. Although originally developed for use in tracking, it can easily be implemented to perform system identification and has potential application to any problem requiring a versatile representation for N-dimensional convex sets.