MUSIC Algorithm for Vector-Sensors Array Using Biquaternions

Abstract

International audienceIn this paper, we use a biquaternion formalism to model vector-sensor signals carrying polarization information. This allows a concise and elegant way of handling signals with eight-dimensional (8-D) vector-valued samples. Using this model, we derive a biquaternionic version of the well-known array processing MUSIC algorithm, and we show its superiority to classically used long-vector approach. New results on biquaternion valued matrix spectral analysis are presented. Of particular interest for the biquaternion MUSIC (BQ-MUSIC) algorithm is the decomposition of the spectral matrix of the data into orthogonal subspaces. We propose an effective algorithm to compute such an orthogonal decomposition of the observation space via the eigenvalue decomposition (EVD) of a Hermitian biquaternionic matrix by means of a newly defined quantity, the quaternion adjoint matrix. The BQ-MUSIC estimator is derived and simulation results illustrate its performances compared with two other approaches in polarized antenna processing (LV-MUSIC and PSA-MUSIC). The proposed algorithm is shown to be superior in several aspects to the existing approaches. Compared with LV-MUSIC, the BQ-MUSIC algorithm is more robust to modelization errors and coherent noise while it can detect less sources. In comparaison with PSA-MUSIC, our approach exhibits more accurate estimation of direction of arrival (DOA) for a small number of sources, while keeping the polarization information accessible

DOA estimation for conformal vector-sensor array using geometric algebra

“…(17). For e xyz is isomorphic to complex imaginary unit j [9], ψ(A)can be regarded as a complex matrix. Then, all the operation rules of the complex matrix are applicable to ψ(A).…”

“…However, the orthogonality of the signal components was lost in this case. In view of this, a hypercomplex model for multicomponent signals impinging on vector sensors was presented in [9]. This model was based on biquaternions (quaternions with complex coefficients).…”

DOA Estimation of Noncircular Signals Using Quaternions

“…However, most existing algorithms are based on the conjugate augmented output vector. Recently, a few methods for direction-of-arrival (DOA) estimation were presented based on the hypercomplex framework [6][7][8]. In [9,10], Gou et al used biquaternion-based algorithms to estimate the DOAs of noncircular signals.…”

Filtering and tracking with trinion-valued adaptive algorithms

“…Multidimensional (m-D) signal processing has a variety of applications and the modeling of multiple variables is carried out traditionally within the real-valued matrix algebra, while in recent years we have observed the successful exploitation of hypercomplex numbers in areas including colour image processing (Pei and Cheng, 1999;Pei et al, 2004;Sangwine and Ell, 2000;Parfieniuk and Petrovsky, 2010;Ell et al, 2014;Liu et al, 2014), vector-sensor array processing (Le Bihan and Mars, 2004;Miron et al, 2006;Le Bihan et al, 2007;Tao, 2013;Tao and Chang, 2014;Zhang et al, 2014;Hawes and Liu, 2015;Jiang et al, 2016a,b), and quaternion-valued wireless communications (Zetterberg and Brandstrom, 1977;Isaeva and Sarytchev, 1995;Liu, 2014). The most widely used hypercomplex numbers are quaternions, with rigorous physical interpretation for 3-D and 4-D rotational problems (Kantor et al, 1989;Ward, 1997).…”