Abstract : This research is devoted to vector-sensor array processing methods. The signals recorded on a vector-sensor array allow the estimation of the direction of arrival and polarization for multiple waves impinging on the antenna. We show how the correct use of polarization information improves the performance of algorithms. The novelty of the presented work consists in the use of mathematical models well-adapted to the intrinsic nature of vectorial signals.
The first approach is based on a multilinear model of polarization that preserves the intrinsic structure of multicomponent acquisition. In this case, the data covariance model is represented by a cross-spectral tensor. We propose two algorithms (Vector-MUSIC and Higher-Order MUSIC) based on orthogonal decompositions of the cross-spectral tensor. We show in simulations that the use of this model and of the multilinear orthogonal decompositions improve the performance of the proposed methods compared to classical techniques based on linear algebra.
A second approach uses hypercomplex algebras. Quaternion and biquaternion vectors are used to model the polarized signals recorded on two, three or four-component sensor arrays. Quaternion-MUSIC and Biquaternion-MUSIC algorithms, based on the diagonalization of quaternion and biquaternion matrices are introduced. We show that the use of hypercomplex numbers reduces the computational burden and increases the resolution power of the methods.