基于Unscented变换的包围卡尔曼滤波
Ensemble Kalman filter with the unscented transform
摘要：
基于无迹变换的概念引入了对集合卡尔曼滤波器（EnKF）的修改方案（Julier等人，2000年; Julier和Uhlmann，2004年），因此在这项工作中将其称为集合无迹卡尔曼滤波器（EnUKF）。当分析的误差分布是对称的（不一定是高斯分布）时，可以表明，与普通的EnKF相比，通过逐项检查多维泰勒级数展开，EnUKF具有对背景的总体均值和协方差的更准确的估计。这意味着，在与真实状态的偏差更小的意义上，EnUKF可以在状态估计中具有比普通EnKF更好的性能。为了验证，我们在Lorenz和Emanuel（Lorenz and Emanuel，1998）的40维系统上进行了一些数值实验。仿真结果支持我们的论点。
英文摘要：
A modification scheme to the ensemble Kalman filter (EnKF) is introduced based on the concept of the unscented transform (Julier et al., 2000; Julier and Uhlmann, 2004), which therefore will be called the ensemble unscented Kalman filter (EnUKF) in this work. When the error distribution of the analysis is symmetric (not necessarily Gaussian), it can be shown that, compared to the ordinary EnKF, the EnUKF has more accurate estimations of the ensemble mean and covariance of the background by examining the multidimensional Taylor series expansion term by term. This implies that, the EnUKF may have better performance in state estimation than the ordinary EnKF in the sense that the deviations from the true states are smaller. For verification, some numerical experiments are conducted on a 40-dimensional system due to Lorenz and Emanuel (Lorenz and Emanuel, 1998). Simulation results support our argument.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
