Geometric methods for structured covariance estimation
- Resource Type
- Conference
- Authors
- Ning, Lipeng; Jiang, Xianhua; Georgiou, Tryphon
- Source
- 2012 American Control Conference (ACC) American Control Conference (ACC), 2012. :1877-1882 Jun, 2012
- Subject
- Robotics and Control Systems
Measurement
Transportation
Approximation methods
Covariance matrix
Vectors
Noise
Maximum likelihood estimation
- Language
- ISSN
- 0743-1619
2378-5861
The problem considered in this paper is that of approximating a sample covariance matrix by one with a Toeplitz structure. The importance stems from the apparent sensitivity of spectral analysis on the linear structure of covariance statistics in conjunction with the fact that estimation error destroys the Toepliz pattern. The approximation is based on appropriate distance measures. To this end, we overview some of the common metrics and divergence measures which have been used for this purpose as well as introduce certain alternatives. In particular, the metric induced by Monge-Kantorovich transportation of the respective probability measures leads to an efficient linear matrix inequality (LMI) formulation of the approximation problem and relates to approximation in the Hellinger metric. We compare these with the maximum likelihood and the Burg method on a representative case study from the literature.