Correlated noise filtering and invariant directions for the Riccati equation

The Riccati equation associated with a class of discrete-time correlated noise problems is examined, and the concept of invariant directions for this equation is introduced. For single-output systems the set of such directions is completely characterized. Deletion of these directions by an appropriate transformation of the Riccati equation results in a minimal order equation for computation. This transformation also reveals the underlying structure of the optimal filter for the correlated noise problem.