A fast M-D Chandrasekhar algorithm for second order Volterra adaptive filtering

This paper presents a fast method for nonlinear filtering based on multichannel Chandrasekhar equations. By assuming that the adaptive second order Volterra filter may be transformed in a multichannel input linear filter, we present a new form of the second order Volterra filtering based a the fast multichannel Chandrasekhar algorithm. This method has a computational complexity of 3.N³ multiplications per time instant, where N represents the memory span in number of samples of the nonlinear system model. This compares with 7.N³ multiplications required for application of the fast Kalman filter with the same approach. A direct implementation of the RLS algorithm has a computational complexity of N⁶. The adaptive filter is successfully used in a second order Volterra system identification in a stationary environment