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.

翻译：Gaussian 混合物过滤器将高斯混合物模型的简单性和功率与粒子过滤器的可辨识的趋同性和功率结合起来。 共同高斯混合物过滤器的质量在很大程度上取决于每个高斯混合物的共变量矩阵的选择。 这项工作将共同高斯混合物过滤器扩展至根据样本共变量矩阵参数估计的适应性共变量选择。 通过使用预期最大化算法, 以在线方式计算出共变量矩阵参数的最佳选择。 Lorenz'63 等式的数值实验显示,拟议方法与在粒子过滤中已知的经典结果相融合。 更多共变量参数选择和中等规模Lorenz'96 等式的更先进的数字结果显示,拟议方法可以比标准 EnGMF 和其他经典数据同化算法要好得多。