An Adaptive UKF Algorithm Based on Maximum Likelihood Principle and Expectation Maximization Algorithm
基于极大似然准则和最大期望算法的自适应UKF算法

In order to solve the state estimation problem of nonlinear systems without knowing prior noise statistical characteristics, an adaptive unscented Kalman filter (UKF) based on the maximum likelihood principle and expectation maximization algorithm is proposed in this paper. In our algorithm, the maximum likelihood principle is used to find a log likelihood function with noise statistical characteristics. Then, the problem of noise estimation turns out to be maximizing the mean of the log likelihood function, which can be achieved by using the expectation maximization algorithm. Finally, the adaptive UKF algorithm with a suboptimal and recurred noise statistical estimator can be obtained. The simulation analysis shows that the proposed adaptive UKF algorithm can overcome the problem of filtering accuracy declination of traditional UKF used in nonlinear filtering without knowing prior noise statistical characteristics and that the algorithm can estimate the noise statistical parameters online.