A general adaptive normalised nonlinear-gradient descent algorithm for nonlinear adaptive filters

An algorithm for training nonlinear adaptive finite impulse response (FIR) filters employed for nonlinear prediction and system identification is introduced. This general adaptive normalised nonlinear gradient descent (ANNGD) algorithm is fully gradient adaptive, unlike previously proposed algorithms of this kind. It is derived based upon the Taylor series expansion of the instantaneous output error of the filter. For rigour, the remainder of the Taylor series expansion in the derivation of the algorithm is made adaptive thus providing an adaptive learning rate. Experiments on coloured and nonlinear signals confirm that the ANNGD outperforms the other algorithms of this kind.