Maximum Likelihood Principle Based Adaptive UKF Algorithm

In this paper, we investigate the state estimation problem of nonlinear systems under the condition that the prior statistical characteristic of noise is unknown. An adaptive unscented Kalman filter (UKF) is proposed. In this algorithm, the maximum likelihood principle is applied to establish the log likelihood function with the unknown noise statistical characteristics. Then, the noise property estimation problem is transformed into the maximization of the mean of the log likelihood function, which can be achieved by using the expectation maximization algorithm. Finally, a suboptimal adaptive UKF can be obtained. Simulations show that the proposed adaptive UKF algorithm can deal with the problem of filtering accuracy declination of the traditional UKF when the prior noise statistical characteristic is unknown. The proposed algorithm can estimate the statistical parameters online.