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Simultaneous source localization and polarization estimation via non-orthogonal joint diagonalization with vector-sensors.

Gong XF, Wang K, Lin QH, Liu ZW, Xu YG - Sensors (Basel) (2012)

Bottom Line: Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme.Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation.Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods.

View Article: PubMed Central - PubMed

Affiliation: School of Information and Communication Engineering, Dalian University of Technology, Dalian 116024, China. xfgong@dlut.edu.cn

ABSTRACT
Joint estimation of direction-of-arrival (DOA) and polarization with electromagnetic vector-sensors (EMVS) is considered in the framework of complex-valued non-orthogonal joint diagonalization (CNJD). Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme. Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation. Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods.

No MeSH data available.


The angle and polarization definitions. (a) The angle definition. (b) Polarization ellipse. (c) Poincare sphere.
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f2-sensors-12-03394: The angle and polarization definitions. (a) The angle definition. (b) Polarization ellipse. (c) Poincare sphere.

Mentions: Let (θ,φ) be the azimuth-elevation 2D DOA of a narrow-band planar EM signal (see Figure 2(a) for the angle definition). The induced electric field vector of this signal moves along the polarization ellipse which could be characterized by the ellipse angle α and orientation angle β, and the polarization state could further be represented by (γ,η) that are linked to (α,β) in the Poincare sphere [1] (see Figure 2(b,c) to visualize the polarization ellipse and the relationship between(γ,η) and (α,β)), 0 < θ < 2π, /φ/ ≤ π/2, 0 < γ < π/2, /η/ ≤ π. The output of an EMVS is written as [2]:(1)pθ,φ,γ,η≜[eθ,φ,γ,ηhθ,φ,γ,η]=[v(θ+π/2,0)−v(θ,φ+π/2)v(θ,φ+π/2)v(θ+π/2,0)] [cos γsin γeiη]where eθ,φ,γ,η ∈ C3 and hθ,φ,γ,η ∈ C3 are the collected electric and magnetic field vectors, respectively. v(θ, φ) ≜ [cos θ cos φ, sin θ cos φ, sin φ]T denotes the Poynting vector containing the three coordinates associated with orientation (θ,φ). Therefore, v(θ,φ), v(θ+π/2,0) and v(θ,φ+π/2,0) constitute a mutually orthogonal triad as shown in Figure 2(a). We herein label pθ,φ,γ,η as the angular-polarization steering vector as it reflects the amplitude-phase relationship among the received EM fields, which depends on both DOA and polarization.


Simultaneous source localization and polarization estimation via non-orthogonal joint diagonalization with vector-sensors.

Gong XF, Wang K, Lin QH, Liu ZW, Xu YG - Sensors (Basel) (2012)

The angle and polarization definitions. (a) The angle definition. (b) Polarization ellipse. (c) Poincare sphere.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3376564&req=5

f2-sensors-12-03394: The angle and polarization definitions. (a) The angle definition. (b) Polarization ellipse. (c) Poincare sphere.
Mentions: Let (θ,φ) be the azimuth-elevation 2D DOA of a narrow-band planar EM signal (see Figure 2(a) for the angle definition). The induced electric field vector of this signal moves along the polarization ellipse which could be characterized by the ellipse angle α and orientation angle β, and the polarization state could further be represented by (γ,η) that are linked to (α,β) in the Poincare sphere [1] (see Figure 2(b,c) to visualize the polarization ellipse and the relationship between(γ,η) and (α,β)), 0 < θ < 2π, /φ/ ≤ π/2, 0 < γ < π/2, /η/ ≤ π. The output of an EMVS is written as [2]:(1)pθ,φ,γ,η≜[eθ,φ,γ,ηhθ,φ,γ,η]=[v(θ+π/2,0)−v(θ,φ+π/2)v(θ,φ+π/2)v(θ+π/2,0)] [cos γsin γeiη]where eθ,φ,γ,η ∈ C3 and hθ,φ,γ,η ∈ C3 are the collected electric and magnetic field vectors, respectively. v(θ, φ) ≜ [cos θ cos φ, sin θ cos φ, sin φ]T denotes the Poynting vector containing the three coordinates associated with orientation (θ,φ). Therefore, v(θ,φ), v(θ+π/2,0) and v(θ,φ+π/2,0) constitute a mutually orthogonal triad as shown in Figure 2(a). We herein label pθ,φ,γ,η as the angular-polarization steering vector as it reflects the amplitude-phase relationship among the received EM fields, which depends on both DOA and polarization.

Bottom Line: Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme.Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation.Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods.

View Article: PubMed Central - PubMed

Affiliation: School of Information and Communication Engineering, Dalian University of Technology, Dalian 116024, China. xfgong@dlut.edu.cn

ABSTRACT
Joint estimation of direction-of-arrival (DOA) and polarization with electromagnetic vector-sensors (EMVS) is considered in the framework of complex-valued non-orthogonal joint diagonalization (CNJD). Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme. Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation. Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods.

No MeSH data available.