Wang Jiaolong, Zhang Dexin, Shao Xiaowei
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 800 Dongchuan Road, 200240 Shanghai, China.
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 800 Dongchuan Road, 200240 Shanghai, China.
ISA Trans. 2019 Aug;91:174-183. doi: 10.1016/j.isatra.2019.01.016. Epub 2019 Jan 23.
For nonlinear continuous-discrete systems, this paper elaborates a new accurate implementation of continuous-discrete cubature Kalman filter (CD-CKF). As the main contribution of this work, the new Kalman prediction stage begins by integrating the nonlinear continuous model for all the cubature sample vectors; the prior estimate state and covariance prediction are based on the weighted statistics of these integrated cubature sample vectors and the Gauss-Legendre approximation scheme. The new square root form CD-CKF is also derived and accurately implemented by combining with the modified variable stepsize NIRK. As the advantages of proposed approach, the complicated and error-prone processes of solving covariance differential equation or calculating derivatives are avoided, while the positive semi-definiteness of prior error covariance are numerically guaranteed. Simulations of traffic control scenarios further confirm the new approach's superior filtering performance in both reliability and accuracy.
针对非线性连续 - 离散系统，本文阐述了连续 - 离散容积卡尔曼滤波器（CD - CKF）的一种新的精确实现方法。作为这项工作的主要贡献，新的卡尔曼预测阶段首先对所有容积样本向量积分非线性连续模型；先验估计状态和协方差预测基于这些积分后的容积样本向量的加权统计以及高斯 - 勒让德近似方案。还通过与改进的变步长NIRK相结合，推导并精确实现了新的平方根形式的CD - CKF。该方法的优点在于，避免了求解协方差微分方程或计算导数等复杂且易出错的过程，同时在数值上保证了先验误差协方差的半正定性。交通控制场景的仿真进一步证实了新方法在可靠性和准确性方面具有卓越的滤波性能。
