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

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2 Author(s)
Jing Fei Jiang ; Dept. of Electron. Eng., Fudan Univ., Shanghai, China ; Jian Qiu Zhang

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.

Published in:

Antennas and Propagation, IEEE Transactions on  (Volume:58 ,  Issue: 12 )

Date of Publication:

Dec. 2010

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