Advanced PRNN based nonlinear prediction/system identification

Insight into the core of the pipelined recurrent neural network (PRNN) in prediction applications is provided. It is shown that modules of the PRNN contribute to the final predicted value at the output of the PRNN in two ways, namely through the process of nesting, and through the process of learning. A measure of the influence of the output of a distant module to the amplitude at the output of the PRNN is analytically found, and the upper bound for it is derived. Furthermore, an analysis of the influence of the forgetting factor in the cost function of the PRNN to the process of learning is undertaken, and it is found that for the PRNN, the forgetting factor can even exceed unity in order to obtain the best predictor. Simulations on three speech signals support that approach, and outperform the other stochastic gradient based schemes