A Derivative-Free Kalman Filter for Parameter Estimation of Recurrent Neural Networks and Its Applications to Nonlinear Channel Equalization

Recurrent neural networks (RNNs) trained with gradient-based algorithms such as real-time recurrent learning or back-propagation through time have a drawback of slow convergence rate. These algorithms also need the derivative calculation through the error back-propagation process. In this paper, a derivative-free Kalman filter, so called the unscented Kalman filter (UKF), for training a fully connected RNN is presented in a state-space formulation of the system. The UKF algorithm makes the RNN have fast convergence speed and good tracking performance without the derivative computation. Through experiments of nonlinear channel equalization, the performance of the RNN with the UKF is evaluated.