Fast RLS algorithm for a second-order Volterra filter

The authors present a fast recursive least-squares (RLS) algorithm for general filters (e.g. a second-order Volterra filter) that can be represented by a linear regression model. The fast RLS algorithm is based on an algebraic approach which makes use of the interrelations between forward and backward linear prediction filters and reduces the computational complexity to O(MN) multiplications, where N is the number of filter coefficients and M is the number of the input elements to be replaced at every time instant. An initial condition and the modifications of previous algorithms with which one can avoid numerical instability are discussed