Low-rank multi-parametric covariance identification

We propose a differential geometric approach for building families of low-rank covariance matrices, via interpolation on matrix manifolds. In contrast with standard parametric classes, these offer significant flexibility problem-specific tailoring the choice “anchor” matrices interpolation, instance over grid relevant conditions describing underlying stochastic process. The is computationally tractable in high dimensions, as it only involves manipulations factors. also consider problem identification, i.e., selecting most representative member family given data set. this setting, procedures such maximum likelihood estimation are nontrivial because rank-deficient; we resolve issue by casting identification distance minimization. demonstrate utility and practical application: wind field approximation unmanned aerial vehicle navigation.