A fully Kalman-trained radial basis function network for nonlinear speech modeling

This paper presents a radial basis function neural network which is trained to learn the dynamics of nonlinear autonomous systems. Contrary to conventional approaches, not only the output layer weights, but also the other parameters of the RBF network are trained using the extended Kalman filter algorithm. The advantages over conventional methods are that centers and variances of the hidden layer nodes need not be calculated before the optimum output weight matrix is determined, and that on-line training is possible. Due to a suitable factorization of the Riccati divergence equation as contained in the Kalman filter, the algorithm can be implemented local to the nodes in the network, and a matrix inversion replaced by simple divisions, thereby significantly reducing the computational complexity. Finally, the network is applied to the task of learning the dynamics of speech signals obtained from sustained vowels, and subsequently used to re-synthesize these vowels autonomously.