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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 distribution of DOA and polarization estimates from 50 independent runs, SNR is 30dB, the number of snapshots is 1,000. The noise is with covariance levels (ρ1, ρ2) = (0.5, 0.5). (a) Distribution of DOA estimates. (b) Distribution of polarization estimates.
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f3-sensors-12-03394: The distribution of DOA and polarization estimates from 50 independent runs, SNR is 30dB, the number of snapshots is 1,000. The noise is with covariance levels (ρ1, ρ2) = (0.5, 0.5). (a) Distribution of DOA estimates. (b) Distribution of polarization estimates.

Mentions: In the first simulation, we consider the scenario that six sources are impinging on an array of two EMVS’s, to verify our identification analysis in Remark 6, Section 3. We note that in this case the number of sources reaches the upper-bound, while the EMVS number reaches the lower-bound according to Remark 6, and thus this is the most difficult case to the identifiability for the proposed strategy. The source DOA’s are (θ1, φ1) = (47°, 15°), (θ2, φ2) = (12°, 84°), (θ3, φ3) = (40°, 60°), (θ4, φ4) = (30°, 20°), (θ5, φ5) = (60°, 13°), and (θ6, φ6) = (80°, 65°). The source polarizations are (γ1, η1) = (72°, 74°), (γ2, η2) = (60°, 43°), (γ3, η3) = (10°, 33°), (γ4, η4) = (65°, 23°), (γ5, η5) = (45°, 40°), and (γ6, η6) = (34°, 78°). In addition, we fix the SNR to 30 dB, fix the number of snapshots to 1000, set the noise covariance levels in Equations (18a)∼(18c) as (ρ1, ρ2) = (0.5, 0.5), and perform 50 independent runs for both LUCJD and LQCJD based algorithms. We here note that SNR in this scenario is set to a high level so that the impact of noise on the result could be ignored, and thus enabling a clearer illustration of the identifiability property of the proposed strategy. The distributions of DOA and polarization estimates are plotted in Figure 3. We note from the figure that the results from 50 independent runs assemble around the true values of the source DOA’s and polarizations denoted by crossed dashed lines, and this verifies our identifiability analysis in Remark 6 that our proposed strategy could successfully identify at most six sources with at least two EMVS’s.


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 distribution of DOA and polarization estimates from 50 independent runs, SNR is 30dB, the number of snapshots is 1,000. The noise is with covariance levels (ρ1, ρ2) = (0.5, 0.5). (a) Distribution of DOA estimates. (b) Distribution of polarization estimates.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3376564&req=5

f3-sensors-12-03394: The distribution of DOA and polarization estimates from 50 independent runs, SNR is 30dB, the number of snapshots is 1,000. The noise is with covariance levels (ρ1, ρ2) = (0.5, 0.5). (a) Distribution of DOA estimates. (b) Distribution of polarization estimates.
Mentions: In the first simulation, we consider the scenario that six sources are impinging on an array of two EMVS’s, to verify our identification analysis in Remark 6, Section 3. We note that in this case the number of sources reaches the upper-bound, while the EMVS number reaches the lower-bound according to Remark 6, and thus this is the most difficult case to the identifiability for the proposed strategy. The source DOA’s are (θ1, φ1) = (47°, 15°), (θ2, φ2) = (12°, 84°), (θ3, φ3) = (40°, 60°), (θ4, φ4) = (30°, 20°), (θ5, φ5) = (60°, 13°), and (θ6, φ6) = (80°, 65°). The source polarizations are (γ1, η1) = (72°, 74°), (γ2, η2) = (60°, 43°), (γ3, η3) = (10°, 33°), (γ4, η4) = (65°, 23°), (γ5, η5) = (45°, 40°), and (γ6, η6) = (34°, 78°). In addition, we fix the SNR to 30 dB, fix the number of snapshots to 1000, set the noise covariance levels in Equations (18a)∼(18c) as (ρ1, ρ2) = (0.5, 0.5), and perform 50 independent runs for both LUCJD and LQCJD based algorithms. We here note that SNR in this scenario is set to a high level so that the impact of noise on the result could be ignored, and thus enabling a clearer illustration of the identifiability property of the proposed strategy. The distributions of DOA and polarization estimates are plotted in Figure 3. We note from the figure that the results from 50 independent runs assemble around the true values of the source DOA’s and polarizations denoted by crossed dashed lines, and this verifies our identifiability analysis in Remark 6 that our proposed strategy could successfully identify at most six sources with at least two EMVS’s.

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.