基于EKF和UKF算法非均匀介质热物性参数重建

将无迹卡尔曼滤波技术(unscented Kalman filter, UKF)用于求解一维介质热物性参数反演问题；也对利用扩展卡尔曼滤波技术(extended Kalman filter, EKF)反演一维介质中热导率问题进行了研究。首先给出了正问题模型，然后详细介绍了EKF算法和UKF算法的基本原理。最后为了验证当前算法的可行性，采用UKF算法重建了介质内部随位置变化的热导率，并采用EKF算法重建了介质内部随时间变化的热导率。计算结果表明，UKF算法和EKF算法均能较为准确地反演介质的热导率。为了减小重建结果的时间滞后，建议使用较小的测量误差协方差R。

Reconstruction of thermophysical parameters in inhomogeneous media using extended Kalman filter and unscented Kalman filter

In this paper, the unscented Kalman filter (UKF) is used for the first time to solve the inverse problem of one-dimensional dielectric thermophysical properties. In addition, this paper also studies the inversion of thermal conductivity in one-dimensional media using extended Kalman filter (EKF). The forward model is introduced firstly. Basic principles of the EKF and UKF technique are also introduced in detail. In order to examine the feasibility of the proposed algorithms, the space-dependent and time-dependent thermal conductivities in media are reconstructed by the UKF and EKF techniques, respectively. All the reconstruction results indicate that thermal conductivities of media can be retrieved effectively by the EKF and UKF techniques. Moreover, the small measurement error covariance R should be selected to decrease the time lag of the reconstructed results.