Sebastian Miron

Quaternion-MUSIC for vector-sensor array processing

This paper considers the problem of direction of arrival (DOA) and polarization parameters estimation in the case of multiple polarized sources impinging on a vector-sensor array. The quaternion model is used, and a data covariance model is proposed using quaternion formalism. A comparison between long vector orthogonality and quaternion vector orthogonality is also performed, and its implications for signal subspace estimation are discussed. Consequently, a MUSIC-like algorithm is presented, allowing estimation of waves DOAs and polarization parameters. The algorithm is tested in numerical simulations, and performance analysis is conducted. When compared with other MUSIC-like algorithms for vector-sensor array, the newly proposed algorithm results in a reduction by half of memory requirements for representation of data covariance model and reduces the computational effort, for equivalent performance. This paper also illustrates a compact and elegant way of dealing with multicomponent complex-valued data.

MUSIC Algorithm for Vector-Sensors Array Using Biquaternions

In 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.

Vector-sensor MUSIC for polarized seismic sources localization

This paper addresses the problem of high-resolution polarized source detection and introduces a new eigenstructure-based algorithm that yields direction of arrival (DOA) and polarization estimates using a vector-sensor (or multicomponent-sensor) array. This method is based on separation of the observation space into signal and noise subspaces using fourth-order tensor decomposition. In geophysics, in particular for reservoir acquisition and monitoring, a set of-multicomponent sensors is laid on the ground with constant distance between them. Such a data acquisition scheme has intrinsically three modes: time, distance, and components. The proposed method needs multilinear algebra in order to preserve data structure and avoid reorganization. The data is thus stored in tridimensional arrays rather than matrices. Higher-order eigenvalue decomposition (HOEVD) for fourth-order tensors is considered to achieve subspaces estimation and to compute the eigenelements. We propose a tensorial version of the MUSIC algorithm for a vector-sensor array allowing a joint estimation of DOA and signal polarization estimation. Performances of the proposed algorithm are evaluated.

A CANDECOMP/PARAFAC Perspective on Uniqueness of DOA Estimation Using a Vector Sensor Array

We address the uniqueness problem in estimating the directions-of-arrival (DOAs) of multiple narrowband and fully polarized signals impinging on a passive sensor array composed of identical vector sensors. The data recorded on such an array present the so-called “multiple invariances,” which can be linked to the CANDECOMP/PARAFAC (CP) model. CP refers to a family of low-rank decompositions of three-way or higher way (mutidimensional) data arrays, where each dimension is termed as a “mode.” A sufficient condition is derived for uniqueness of the CP decomposition of a three-way (three mode) array in the particular case where one of the three loading matrices, each associated to one mode, involved in the decomposition has full column rank. Based on this, upper bounds on the maximal number of identifiable DOAs are deduced for the two typical cases, i.e., the general case of uncorrelated or partially correlated sources and the case where the sources are coherent.

Uni-mode and Partial Uniqueness Conditions for CANDECOMP/PARAFAC of Three-Way Arrays with Linearly Dependent Loadings

In this paper, three sufficient conditions are derived for the three-way CANDECOMP/PARAFAC (CP) model, which ensure uniqueness in one of the three modes (“uni-mode-uniqueness”). Based on these conditions, a partial uniqueness condition is proposed which allows collinear loadings in only one mode. We prove that if there is uniqueness in one mode, then the initial CP model can be uniquely decomposed in a sum of lower-rank tensors for which identifiability can be independently assessed. This condition is simpler and easier to check than other similar conditions existing in the specialized literature. These theoretical results are illustrated by numerical examples.

High resolution vector-sensor array processing using quaternions

The aim of this paper is to introduce a novel MUSIC-like algorithm for polarized sources characterization based on a quaternion model for two-component sensor-array signal. The associated data covariance matrix is described and a comparison with the classical long-vector approach is made. We show that the use of quaternions improves the signal subspace estimation accuracy and reduces the computational burden. Additionally, the proposed algorithm presents a better resolution power for direction of arrival (DOA) estimation than the long-vector approach, for equivalent statistical performances

Approximate joint diagonalization by nonorthogonal nonparametric Jacobi transformations

We propose a novel algorithm for the problem of nonorthogonal joint diagonalization of a set of structured matrices based on successive Jacobi-like transformations. Though the elementary transformation matrices we use are not optimal in the sense of the global criterion, they are ensured to be nonsingular, and can be computed in closed form. The algorithm is efficient in virtue of its low computational complexity and fast convergence. The performance of the new algorithm is compared in simulations to the similar algorithms of the recent literature.

High Resolution Vector-Sensor Array Processing Based on Biquaternions

This paper presents a version of MUSIC algorithm for linear vector-sensor arrays based on a complexified quaternionic (biquaternionic) modelization of the output three-components vector-signals. A way of computing the eigenvalue decomposition of a biquaternion valued matrix is introduced and the subspace decomposition of the biquaternionic spectral matrix of the observations is used to define the biquaternionic MUSIC estimator (BQ-MUSIC). Performances of the BQ-MUSIC are compared with classical long-vector technique

Identifiability of the parafac model for polarized source mixture on a vector sensor array

By means of the parallel factor (PARAFAC) decomposition, we present a novel method working on a vector-sensor array for blind separation of polarized sources in virtue of their distinct spatial and temporal signatures. Identifiability is studied, and explicit constraints on the sources are derived to ensure the data model identifiable. We show, by numerical simulations, that the estimation performance can approach that of non-blind estimation by optimally designing the source polarizations.

Multilinear direction finding for sensor-array with multiple scales of invariance

In this paper, we introduce a novel direction-finding algorithm for a multiscale sensor array, that is, an array presenting multiple scales of spatial invariance.We show that the collected data can be represented as a Candecomp/Parafac model for which we analyze the identifiability properties. A two-stage algorithm for direction-of-arrival estimation with such an array is also proposed. This approach generalizes the results given in [1] to an array that presents an arbitrary number of spatial invariances.We illustrate, on two particular array geometries, that our method outperforms, in some difficult scenarios, the ESPRIT-based approach introduced in [2], the ESPRIT-MUSIC of [3], and the tensor-ESPRIT of [4].