基于极大似然准则和最大期望算法的自适应UKF 算法

针对噪声先验统计特性未知情况下的非线性系统状态估计问题,提出了基于极大似然准则和 最大期望算法的自适应无迹卡尔曼滤波(Unscented Kalman filter, UKF) 算法.利用极大似然准则构造含有噪声统计特性的对数似然函数,通 过最大期望算法将噪声估计问题转化为对数似然函数数学期望极大化问题,最终得到带次优递 推噪声统计估计器的自适应UKF算法.仿真分析表明,与传统UKF算法相比,提出的自适应UKF算法 有效克服了传统UKF算法在系统噪声统计特性未知情况下滤波精度下降的问题,并实现了系统噪 声统计特性的在线估计.

An Adaptive UKF Algorithm Based on Maximum Likelihood Principle and Expectation Maximization Algorithm

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.