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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.


Performance of LUCJD, LQCJD, PARAFAC, UWEDGE, FAJD, JTJD versus the noise covariance level. SNR is 2 dB and the number of snapshots is 1,000. (a) The overall RMSAE curves of DOA estimates. (b) The overall RMSE curves of polarization amplitude angle estimates. (c) The overall RMSE curves of polarization phase difference angle estimates.
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f5-sensors-12-03394: Performance of LUCJD, LQCJD, PARAFAC, UWEDGE, FAJD, JTJD versus the noise covariance level. SNR is 2 dB and the number of snapshots is 1,000. (a) The overall RMSAE curves of DOA estimates. (b) The overall RMSE curves of polarization amplitude angle estimates. (c) The overall RMSE curves of polarization phase difference angle estimates.

Mentions: Secondly, we fix SNR and the number of snapshots to 2 dB and 1,000, respectively, and let the noise covariance levels ρ1 = ρ2 vary from 0∼0.9. The results from 100 independent runs are demonstrated in Figure 5. We can see quite diverse behaviors for CNJD and PARAFAC based strategies with the noise covariance changing, which clearly demonstrate the pros and cons of both strategies. More exactly, we note that the increase in noise covariance would generally improve the performance of CNJD based methods. In particular, the proposed LUCJD and LQCJD provide the best performance among all the CNJD algorithms with regards to the accuracy of joint DOA and polarization estimation. In addition, FAJD and JTJD provide almost equal performance as LUCJD and LQCJD for low noise covariance levels, yet become unsteady for ρ1 = ρ2 ≥ 0.8 and ρ1 = ρ2 ≥ 0.9, respectively. This is because the CNJD methods, especially the proposed LUCJD and LQCJD, are usually very robust to noise with structured covariance, which would yield additional contribution to the joint diagonalizable structures other than sources. Moreover, we note that PARAFAC, on the other hand, behaves inversely to the CNJD ones, as the increase in noise covariance results in a dramatic rise in the its curves. This is because the PARAFAC algorithms are usually sensitive to underfactoring (the number of parallel factors in the tensor model is greater than the number of sources) [58] and noise with high covariance levels would result in such underfactoring (when noise covariance increases, noise becomes interference, and thus contributes an additional factor to the PARAFAC model). The above observations are in accordance with our analysis in Remark 4, Section 3, that CNJD performs better than PARAFAC with regards to the robustness to color noise, yet the latter has stronger ability in suppressing white noise.


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)

Performance of LUCJD, LQCJD, PARAFAC, UWEDGE, FAJD, JTJD versus the noise covariance level. SNR is 2 dB and the number of snapshots is 1,000. (a) The overall RMSAE curves of DOA estimates. (b) The overall RMSE curves of polarization amplitude angle estimates. (c) The overall RMSE curves of polarization phase difference angle estimates.
© Copyright Policy
Related In: Results  -  Collection

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

f5-sensors-12-03394: Performance of LUCJD, LQCJD, PARAFAC, UWEDGE, FAJD, JTJD versus the noise covariance level. SNR is 2 dB and the number of snapshots is 1,000. (a) The overall RMSAE curves of DOA estimates. (b) The overall RMSE curves of polarization amplitude angle estimates. (c) The overall RMSE curves of polarization phase difference angle estimates.
Mentions: Secondly, we fix SNR and the number of snapshots to 2 dB and 1,000, respectively, and let the noise covariance levels ρ1 = ρ2 vary from 0∼0.9. The results from 100 independent runs are demonstrated in Figure 5. We can see quite diverse behaviors for CNJD and PARAFAC based strategies with the noise covariance changing, which clearly demonstrate the pros and cons of both strategies. More exactly, we note that the increase in noise covariance would generally improve the performance of CNJD based methods. In particular, the proposed LUCJD and LQCJD provide the best performance among all the CNJD algorithms with regards to the accuracy of joint DOA and polarization estimation. In addition, FAJD and JTJD provide almost equal performance as LUCJD and LQCJD for low noise covariance levels, yet become unsteady for ρ1 = ρ2 ≥ 0.8 and ρ1 = ρ2 ≥ 0.9, respectively. This is because the CNJD methods, especially the proposed LUCJD and LQCJD, are usually very robust to noise with structured covariance, which would yield additional contribution to the joint diagonalizable structures other than sources. Moreover, we note that PARAFAC, on the other hand, behaves inversely to the CNJD ones, as the increase in noise covariance results in a dramatic rise in the its curves. This is because the PARAFAC algorithms are usually sensitive to underfactoring (the number of parallel factors in the tensor model is greater than the number of sources) [58] and noise with high covariance levels would result in such underfactoring (when noise covariance increases, noise becomes interference, and thus contributes an additional factor to the PARAFAC model). The above observations are in accordance with our analysis in Remark 4, Section 3, that CNJD performs better than PARAFAC with regards to the robustness to color noise, yet the latter has stronger ability in suppressing white noise.

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.