Low-rank multi-parametric covariance identification

Author: 

Musolas, A
Massart, E
Hendrickx, J
Absil, P
Marzouk, Y

Publication Date: 

5 May 2021

Journal: 

BIT Numerical Mathematics

Last Updated: 

2021-10-19T13:24:15.353+01:00

DOI: 

10.1007/s10543-021-00867-y

abstract: 

We propose a differential geometric approach for building 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 interpolation, for instance over a grid of relevant conditions describing the underlying stochastic process. The interpolation is computationally tractable in high dimensions, as it only involves manipulations of low-rank matrix factors. We also consider the problem of covariance identification, i.e., 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 utility of these differential geometric families for interpolation and identification in a practical application: wind field covariance approximation for unmanned aerial vehicle navigation.

Symplectic id: 

1178367

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article