论文标题
低级多参数协方差识别
Low-rank multi-parametric covariance identification
论文作者
论文摘要
我们通过低级矩阵歧管上的插值为低级别协方差矩阵的家族提出了一种差异几何结构。与标准参数协方差类别相反，这些家族通过选择插值的“锚定”矩阵为特定问题的裁缝提供了显着的灵活性。此外，它们的低级别有助于在高维度和有限的数据方面的计算障碍。我们采用这些协方差族来进行插值和识别，其中后一个问题包括选择数据集的协方差家庭中最具代表性的成员。在这种情况下，诸如最大似然估计之类的标准程序是不平凡的，因为协方差家族是排名不足的。我们通过将识别问题置于距离最小化来解决此问题。我们在实际应用中证明了这些差异几何家族在插值和识别中的功能：无人驾驶航空车导航的风场协方差近似。
We propose a differential geometric construction for families of low-rank covariance matrices, via interpolation on low-rank matrix manifolds. In contrast with standard parametric covariance classes, these families offer significant flexibility for problem-specific tailoring via the choice of "anchor" matrices for the interpolation. Moreover, their low-rank facilitates computational tractability in high dimensions and with limited data. We employ these covariance families for both interpolation and identification, where the latter problem comprises selecting the most representative member of the covariance family given a data set. In this setting, standard procedures such as maximum likelihood estimation are nontrivial because the covariance family is rank-deficient; we resolve this issue by casting the identification problem as distance minimization. We demonstrate the power of these differential geometric families for interpolation and identification in a practical application: wind field covariance approximation for unmanned aerial vehicle navigation.
