Quaternion Valued Neural Networks and Nonlinear Adaptive Filters

A class of locally analytic transcendental functions suitable for nonlinear adaptive filtering and neural network filtering is proposed. Since the stringent standard analyticity conditions prevent full exploitation of nonlinear quaternionic models, we make use of local analyticity conditions to provide a framework for a generic extension of nonlinear learning algorithms from the real and complex domain. In addition, it is shown that the use of the proposed class of locally analytic transcendental functions in conjunction with widely linear modelling allows to fully exploit the second-order information in the data. Simulations over a range of noncircular synthetic, chaotic and real world three dimensional wind signals support the approach.