Preprint
Sensing with Optimal Matrices
ArXiv.org
06/01/2012
Abstract
We consider the problem of designing optimal M×N (M≤N) sensing matrices which minimize the maximum condition number of all the submatrices of K columns. Such matrices minimize the worst-case estimation errors when only K sensors out of N sensors are available for sensing at a given time. For M=2 and matrices with unit-normed columns, this problem is equivalent to the problem of maximizing the minimum singular value among all the submatrices of K columns. For M=2, we are able to give a closed form formula for the condition number of the submatrices. When M=2 and K=3, for an arbitrary N≥3, we derive the optimal matrices which minimize the maximum condition number of all the submatrices of K columns. Surprisingly, a uniformly distributed design is often \emph{not} the optimal design minimizing the maximum condition number.
Details
- Title: Subtitle
- Sensing with Optimal Matrices
- Creators
- Hema Kumari AchantaSoura DasguptaWeiyu Xu
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- ISSN
- 2331-8422
- Language
- English
- Date posted
- 06/01/2012
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984198000002771
Metrics
53 Record Views