An adaptive amplitude learning algorithm for nonlinear adaptive IIR filters

A variant of the real time recurrent learning (RTRL) algorithm for a class of nonlinear adaptive infinite impulse response (IIR) filters, realised as a recurrent perceptron, with an adaptive amplitude in the nonlinearity is proposed. The amplitude of the nonlinear activation function of a neuron is made gradient adaptive to give the adaptive amplitude real time recurrent learning (AARTRL) algorithm. This makes the AARTRL suitable for processing nonlinear and nonstationary signals with a large and unknown dynamical range, and removes the unwanted effect of saturation nonlinearities within this class of filters. For rigour, sensitivity analysis is performed and the performance of the AARTRL algorithm is tested on prediction of signals with various complexity and dynamics. Experimental results show the gradient adaptive amplitude, AARTRL, outperform the standard RTRL on both the coloured and nonlinear, real-world and synthetic signals.