Geometric Algebra of Euclidean 3-Space for Electromagnetic Vector-Sensor Array Processing, Part I: Modeling

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 m...

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Veröffentlicht in:IEEE transactions on antennas and propagation Jg. 58; H. 12; S. 3961 - 3973
Hauptverfasser: Jiang, Jing Fei, Zhang, Jian Qiu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.12.2010
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algebra
Antennas
Applied classical electromagnetism
Arrays
Computational modeling
Covariance matrix
Data covariance matrix
Data models
electromagnetic vector-sensor array
Electromagnetic wave propagation, radiowave propagation
Electromagnetism; electron and ion optics
Euclidean 3-space
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
geometric algebra
Mathematical analysis
Mathematical model
Mathematical models
multivector
Noise
Physics
Multiplication
Electromagnetism
Array signal processing
Quaternion
Euclidean 3-space
Data covariance matrix
Covariance matrices
Geometrical model
electromagnetic vector-sensor array
Cross correlations
geometric algebra
Magnetic devices
Analytical method
Euclidean space
Modelling
Sensor array
multivector
Signal detection
ISSN:0018-926X, 1558-2221
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Zusammenfassung: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.
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ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2010.2078468