论文标题
集合高斯混合物滤波器的自适应协方差参数化技术
An Adaptive Covariance Parameterization Technique for the Ensemble Gaussian Mixture Filter
论文作者
论文摘要
合奏高斯混合物滤光片将高斯混合模型的简单性和功率与可证明的粒子过滤器的可收敛性和功率相结合。集合高斯混合物滤光片的质量在很大程度上取决于每个高斯混合物中协方差矩阵的选择。这项工作将基于样品协方差矩阵的参数化估计值扩展到自适应的协方差。通过使用期望最大化算法，以在线方式计算协方差矩阵参数的最佳选择。 Lorenz '63方程式上的数值实验表明，所提出的方法会收敛到粒子过滤中已知的经典结果。进一步的数值结果具有更多的协方差参数化选择和中等大小的洛伦兹'96方程，这表明，所提出的方法的性能可以明显优于标准ENGMF，以及其他经典数据同化算法。
The ensemble Gaussian mixture filter combines the simplicity and power of Gaussian mixture models with the provable convergence and power of particle filters. The quality of the ensemble Gaussian mixture filter heavily depends on the choice of covariance matrix in each Gaussian mixture. This work extends the ensemble Gaussian mixture filter to an adaptive choice of covariance based on the parameterized estimates of the sample covariance matrix. Through the use of the expectation maximization algorithm, optimal choices of the covariance matrix parameters are computed in an online fashion. Numerical experiments on the Lorenz '63 equations show that the proposed methodology converges to classical results known in particle filtering. Further numerical results with more advances choices of covariance parameterization and the medium-size Lorenz '96 equations show that the proposed approach can perform significantly better than the standard EnGMF, and other classical data assimilation algorithms.
