Fast generalized sliding window RLS recursions for IIR recurrence related basis functions

This paper extends the existing fast recursive least-squares algorithms originally intended to exponentially weighted windows and general models, to a generalized sliding window RLS formulation (GSWRLS) with possible several breakpoints. The recursions hold regardless of the data structure induced. As a result, it allows known algorithms such as unwindowed RLS, sliding-window RLS, affine projection, and others to make use of the low displacement rank property of the Ricatti variable, achieving fast recursions irrespective of the displacement operator, assuming it is induced via recurrence related polynomial basis. Several updates and down-dates analogous to the ones encountered in the standard fast RLS theory are derived, along with the exact algorithm initialization. Simulations based on IIR orthonormal basis functions are presented.