Summary: An adaptive Unscented Kalman filtering (UKF) algorithm with noise statistic estimator is designed to solve the problem that the conventional UKF declines in accuracy and further diverges when the prior noise statistic is unknown and time-varying. Firstly, a constant noise statistic estimator which is suboptimal and unbiased is deduced based on Maximum A-posteriori (MAP) estimation. Then, the recursive equations of time-varying noise statistic estimator are given through exponential weighting of the constant noise statistic estimator. Finally, performance analysis of the adaptive UKF algorithm is done. Under the condition of unknown and time-varying noise statistic, the proposed adaptive UKF algorithm still converges, moreover its filtering precision and stability are better than those of the conventional UKF. An adaptive capability to deal with variable noise statistic is performed by the presented UKF. The simulation examples show its effectiveness.