An Augmented Extended Kalman Filter Algorithm for Complex-Valued Recurrent Neural Networks

An augmented complex-valued Extended Kalman Filter (ACEKF) algorithm for the class of nonlinear adaptive filters realised as fully connected recurrent neural networks (FCRNNs) is introduced. The algorithm is derived based on the recent developments in augmented complex statistics, and the Jacobian matrix within the ACEKF algorithm is computed using a general fully complex real time recurrent learning (CRTRL) algorithm. This makes ACEKF suitable for processing general complex-valued nonlinear and nonstationary signals and bivariate signals with strong component correlations. Simulations on benchmark and real-world complexvalued signals support the approach.