Higher Order Neural Networks Learning by Extended Kalman Filter

The Extended Kalman filter (EKF) is well known as a state estimation method for a nonlinear system and has been used to train a multilayered neural network (MNN) by augmenting the state with unknown connecting weights. The EKF Neural networks training algorithm is superior to standard back-propagation algorithm, but it is also known that Higher Order Neural Networks (HONN) have better performance than a standard multilayer perceptron networks. In this paper, more robust new learning algorithm for a Higher Order Neural Networks (HONN) based on EKF is proposed. The algorithm is an EKF coupled with HONN model, and has a new algorithm used to approximate the uncertainty of the system extreme nonlinearities. HONN consists of Generalized mean Neuron model (GMN).The GMN consists of an aggregation function which is based on generalized mean of all the inputs applied to it. EKF-HONN model is used for non linear state estimation, and to determine the weights and error covariance, the one step ahead prediction. Simulation results show that the proposed new algorithm is quite effective and can be implemented in the field of adaptive filtering nonlinear state estimation and predictions in place of traditional methods.