The fast subsampled-updating fast Newton transversal filter (FSU FNTF) for adapting long FIR filters

The FNTF algorithm starts from the RLS algorithm for adapting FIR filters. The FNTF algorithm approximates the Kalman gain by replacing the sample covariance matrix inverse by a banded matrix: (AR(M) assumption for the input signal). The approximate Kalman gain can still be computed using an exact recursion that involves the prediction pads of two fast transversal filter (FTF) algorithms of order M. We introduce the subsampled updating (SU) approach in which the FNTF filter estimate and Kalman gain are provided at a subsampled rate, say every L samples. The low-complexity prediction part is kept and a Schur type algorithm is used to compute a priori filtering errors at the intermediate time instants, while some convolutions are carried out with the FFT. This leads to the FSU FNTF algorithm which has a low computational complexity for relatively long filters