UKF Based Nonlinear Filtering Using Minimum Entropy Criterion

A novel filter for nonlinear and non-Gaussian systems is proposed in this paper. The unscented Kalman filter is designed to give a preliminary estimation of the state. An additional RBF-network is added to the UKF innovation term to compensate for the non-Gaussianity of the whole system. The Renyi's entropy of the innovation is introduced and parameters of the RBF-network are updated using minimum entropy criterion at each time step. It has been shown that the proposed algorithm has a high accuracy in estimation because entropy can characterize all the randomness of the residual while UKF only cares for the mean and the covariance. It has been proved that with properly chosen bandwidth Σ, the minimum entropy problem of the innovation is convex. Therefore, the proposed adaptive nonlinear filter will be globally convergent and the misadjustment will be proportional to the step size μ. The effectiveness of the proposed method is shown by simulation.