An adaptive UKF with noise statistic estimator

The normal unscented Kalman filter (UKF) suffers from performance degradation and even divergence while mismatch between the noise distribution assumed to be known as a priori by UKF and the true ones in a real system. In order to improve the performance of the UKF with uncertain or time-varying noise statistic, a novel adaptive UKF with noise statistic estimator is developed and applied to nonlinear joint estimation of both the states and time-varying noise statistic. This noise statistic estimator, based on maximum a posterior (MAP), makes use of the output measurement information to online update the mean and the covariance of the noise. The updated mean and covariance are further fed back into the normal UKF. As a result of using such an adaptive mechanism the robustness of conventional UKF is substantially improved with respect to the uncertain or time-varying noise statistic in the real system. Finally, the proposed adaptive UKF is demonstrated to be superior to the normal UKF through comparing the simulation results with and without the adaptive mechanism.