Adaptive Recursive Least Squares Algorithm based on Echo State Neural Network

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In order to model time-varying dynamical systems with more accuracy, and to further exploit the potential capacities of recurrent neural networks, we propose a novel recursive least square (RLS) algorithm based on echo state network (ESN), and note it as RLSESN in this paper. ESN is a new paradigm for using recurrent neural networks (RNN) with a simpler training method. RLSESN 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.