Geometric Algebra of Euclidean 3-Space for Electromagnetic Vector-Sensor Array Processing, Part I: Modeling

Jiang, Jialing; Zhang, Jian Qiu

doi:10.1109/tap.2010.2078468

Cited by 20 publications

(22 citation statements)

References 16 publications

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“…(3) Since three dipole-loop pairs are spatially separated, the noises on three dipole-loop pairs are uncorrelated to one another. Thus, the additive noise exists only in the real part of the covariance matrix, whereas no additive noise exists in the real part of the covariance matrix (Jiang & Zhang, 2010). Because only information in the imaginary part of the covariance matrix is exploited in the proposed algorithm, it is guaranteed to remove the effect of the additive noise.…”

Section: 1029/2019rs006796mentioning

confidence: 99%

Estimation Algorithm of Incident Sources' Stokes Parameters and 2‐D DOAs Based on Reduced Mutual Coupling Vector Sensor

Tao

Yang

2019

Radio Science

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To estimate Stokes parameters and two-dimensional (2-D) direction-of-arrival (DOA) of incident sources, a computational efficient algorithm is proposed based on reduced mutual coupling vector sensor. The biquaternion-based output model of reduced mutual coupling vector sensor is presented. The contribution in this paper is mainly on the estimation of Stokes parameters. By exploiting the information in both the covariance matrix and the pseudo-covariance matrix of the biquaternion-based sensor's output, the Stokes parameters and 2-D DOAs of partially polarized source can be extracted in closed form. Comparing with the Jone's formulation, the Stokes' formulation can characterize both completely polarized waves and partially polarized waves. Thus, the proposed algorithm is also applicable to completely polarized source. Because the proposed algorithm presents in closed form and does not require the search or iterative process, it is computationally more efficient. Simulations are used to verify the performance of the proposed algorithm.

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Section: 1029/2019rs006796mentioning

confidence: 99%

Estimation Algorithm of Incident Sources' Stokes Parameters and 2‐D DOAs Based on Reduced Mutual Coupling Vector Sensor

Tao

Yang

2019

Radio Science

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“…In addition, the signal has an elevation angle θ and an azimuth angle φ. The derivation of (23) is omitted here and the interested reader will find more material in [10]. Considering the polarization information, the aforementioned complex envelope, S E , can be written as where h is the signal polarization vector [16] and can be described by the auxiliary polarization angle (γ) and the polarization phase difference (η), that is, h ¼ cosγ sinγe…”

Section: Manifold Modeling Of Vector Sensors In the Conformal Arraymentioning

confidence: 99%

“…This model was based on biquaternions (quaternions with complex coefficients). Subsequently, Jiang et al introduced geometric algebra into the electromagnetic vector-sensor processing field [10]. However, the model cannot be applied to the conformal array since the pattern is assumed to be a scalar and the same for each element.…”

Section: Introductionmentioning

confidence: 99%

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DOA estimation for conformal vector-sensor array using geometric algebra

Tao

Yuan

2017

EURASIP J. Adv. Signal Process.

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In this paper, the problem of direction of arrival (DOA) estimation is considered in the case of multiple polarized signals impinging on the conformal electromagnetic vector-sensor array (CVA). We focus on modeling the manifold holistically by a new mathematical tool called geometric algebra. Compared with existing methods, the presented one has two main advantages. Firstly, it acquires higher resolution by preserving the orthogonality of the signal components. Secondly, it avoids the cumbersome matrix operations while performing the coordinate transformations, and therefore, has a much lower computational complexity. Simulation results are provided to demonstrate the effectiveness of the proposed algorithm.

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“…A vector-sensor comprises two or more collocated different types of scalar-sensors and is generally advantageous over a scalar-sensor, eg, for an electromagnetic vectorsensor, it can additionally exploit the polarization difference among the received signals [19]. Traditionally the output of a vector-sensor array is preprocessed to be a long-vector [19][20][21][22][23][24][25][26][27], while several recent approaches utilize hypercomplex (eg, quaternion [18], bicomplex [28], biquaternion [29,30], quad-quaternion [31], Euclidean 3-space [32]) or tensorial (eg, fourth-order interspectral tensor [33]) models. The use of hypercomplex algebra provides a compact way of handling of the recorded data, and demonstrates its unique characteristics in reduced memory consumption and improved robustness to model errors [18].…”

Section: Introductionmentioning

confidence: 99%

User–Parameter–Free Robust Adaptive Beamforming Algorithm for Vector–Sensor Arrayswithin the Hypercomplex Framework

Gou¹,

Liu²,

Ma³

et al. 2013

Journal of Electrical Engineering

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The major flaw of the conventional diagonal loading (DL) method is that it is unclear to choose appropriate DL levels or user-parameters (UPs), though several remarkable contributions have been made to regularize model errors without UPs. An UP-free algorithm for two-component vector-sensor arrays, which is robust to steering vector errors, is considered. The algorithm is within the hypercomplex framework using quaternions, and the optimal solution is found at the maximal correlation between the quaternionic and complex outputs. The performance of the proposed beamformer is illustrated via numerical simulations and is compared with several other UP-free adaptive beamformers.K e y w o r d s: array signal processing, robust adaptive beamforming, vector-sensor, user-parameter-free, quaternion

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Geometric Algebra of Euclidean 3-Space for Electromagnetic Vector-Sensor Array Processing, Part I: Modeling

Cited by 20 publications

References 16 publications

Estimation Algorithm of Incident Sources' Stokes Parameters and 2‐D DOAs Based on Reduced Mutual Coupling Vector Sensor

Estimation Algorithm of Incident Sources' Stokes Parameters and 2‐D DOAs Based on Reduced Mutual Coupling Vector Sensor

DOA estimation for conformal vector-sensor array using geometric algebra

User–Parameter–Free Robust Adaptive Beamforming Algorithm for Vector–Sensor Arrayswithin the Hypercomplex Framework

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