Recursive least squares algorithm with adaptive forgetting factor based on echo state network

Echo state network (ESN) is a new paradigm for using recurrent neural networks (RNN) with a simpler training method. Based on ESN, we propose a novel recursive least square (RLS) algorithm and note it as λ-ESN in this paper. It consists of three main components: an ESN, a recursive least square (RLS) algorithm with adaptive forgetting factor, and a change detection module. At first, the change detection module modifies the forgetting factor online according to ESN output errors. And then, the RLS algorithm regulates the ESN output connection weights. The simulation experiment results show that the proposed ESN-based filters can model nonlinear time-varying dynamical systems very well; the modeling performances are significantly better than those autoregressive moving average (ARMA) model based filters.