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Geometric Algebra of Euclidean 3-Space for Electromagnetic Vector-Sensor Array Processing, Part I: Modeling.
- Source :
-
IEEE Transactions on Antennas & Propagation . 12/01/2010, Vol. 58 Issue 12, p3961-3973. 13p. - Publication Year :
- 2010
-
Abstract
- A new mathematical tool, the geometric algebra of Euclidean 3-space (G3), is introduced for electromagnetic vector-sensor array processing herein. This paper focuses on modeling the six-component outputs of a vector-sensor holistically by an entry called as a multivector in G3. A compact polarized model for the array, termed as a geometric algebra model (G-MODEL), is then presented. Using the G-MODEL, a novel data covariance matrix model is defined by the geometric products in G3 and then analyzed. The analytical results show that the six-component measurement noise of a vector-sensor can naturally be whitened if the noise cross-correlations between the different axial electric and magnetic components are equal to one another. Compared with the known best quad-quaternion model, the new covariance matrix model results in a reduction of half memory requirements while the amount of divisions is reduced to 1/2, multiplications and additions reduced to almost 1/7. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0018926X
- Volume :
- 58
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Antennas & Propagation
- Publication Type :
- Academic Journal
- Accession number :
- 57254711
- Full Text :
- https://doi.org/10.1109/TAP.2010.2078468