An adaptive neurofuzzy Kalman filter

It is of great practical significance to merge the neural network identification technique and the Kalman filter to achieve adaptive and optimal filtering and prediction for unknown observable nonlinear processes. In this paper, an operating point dependent ARMA model is used to represent the nonlinear system, and a neurofuzzy network is used to approximate each AR parameter of such a model which can then be converted to its equivalent state-space representation. Using this state-space form, a Kalman filter can be applied to estimate the system state. The system modelling algorithm and the Kalman filter are combined in a bootstrap scheme, in which the error between the measured output and the filtered output is used to train the neural network, thus adaptive filtering for noisy nonlinear system is achieved. A simulated example is also given