基于期望最大化算法和求容积卡尔曼平滑器的气动参数辨识算法
Aircraft System Identification via Cubature Kalman Smoother with Expectation Maximization Algorithm

针对初值和噪声统计特性未知情形下的飞行器系统辨识的问题，提出了基于期望最大化（expectation maximization，EM）和求容积卡尔曼平滑器（cubature Kalman smoother，CKS）的辨识算法。该算法用期望最大化算法对初值和噪声的统计特性进行估计；用求容积卡尔曼平滑器估计状态向量和未知参数。在期望最大化算法的求期望步骤中，所求的期望值通过求容积规则获得，用较少的采样点保证了估计精度；在期望最大化算法的最大化步骤中，未知量的最优值以解析解形式给出，减小了计算量。仿真结果说明，该算法在飞行器气动参数辨识问题中，能给出较好的辨识结果。与其他方法的对比验证说明新算法具有辨识精度高、收敛速度快等优点。
This paper developed a novel system identification algorithm to estimate parameter of aircraft dynamics modeled in state space. The developed method utilizes the cubature Kalman smoother to estimate the state and unknown parameters, combined with expectation-maximization algorithm, which estimates the statistics-unknown parameters, i.e., the mean and covariance of an initial state, and the covariance of both process noise and measurement noise. To reduce the computational cost with considerable accuracy decline, the cubature Kalman smoother is employed to approximate the expectation values in the expectation maximization. Further, the analytical forms of unknown statistics parameters are given in the maximization step, which makes the nonconvex numerical optimization unnecessary. Its effectiveness is demonstrated through one problem of estimating aircraft aerodynamic parameters. The result shows that the proposed algorithm is of high accuracy as well as converge faster compared with other algorithms