Electromagnetic Vector Sensor Research Articles

DOA estimation for coprime EMVS arrays via minimum distance criterion based on PARAFAC analysis

This study presents a minimum distance-based direction-of-arrival (DOA) estimation algorithm for coprime electromagnetic vector sensor (EMVS) arrays. The idea is to split-up the coprime array into two uniform linear arrays (ULAs) of vector sensors and arrange the received ULA data in the form of a three-way array suitable for parallel factor (PARAFAC) analysis, which fits least-square models to the received source signal mixtures of ULAs and thus enables to retrieve the model matrices corresponding to each ULA. Nevertheless, because of the array splitting the estimated DOAs from these matrices are not unique. To uniquely determine the DOA, the authors state and prove a theorem which is fundamental to the proposed algorithm and provides a means to find an estimate based on the minimum distance criterion. Efficacy of the proposed algorithm is demonstrated through performance comparison with other existing algorithms such as Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), long vector MUltiple SIgnal Classification (MUSIC), conventional PARAFAC and the propagator method being simulated for an equivalent element ULA of EMVS and spaced half a wavelength apart. Numerical simulations reveal that the proposed algorithm outperforms the others.

A Computationally Economic Location Algorithm for Bistatic EVMS-MIMO Radar

In this paper, we investigated into the problem of target location in a bistatic multiple-input multiple-output (MIMO), whose transmit antennas and receive antennas are electromagnetic vector sensors (EMVS). Unlike the traditional linear scaler-sensor array, a linear EMVS array can offer two-diemensional (2D) direction estimation, thus a bistatic EMVS-MIMO radar provides (2D) direction-of-arrival and 2D direction-of-departure estimation. Besides, it is able to estimate 2D transmit/receive polarization angles of the targets. An propagator method (PM)-based estimator is proposed. Firstly, it estimate the propagator from the covariance matrix. The parameters are achieved via utilizing the estimation method of signal parameters via rotational invariance technique (ESPRIT) and the vector cross-product technique. The proposed estimator is computationally friendly since it does not involving eigendecomposition of high-dimensional data. Also, it may has similar (or even better) parameter estimation accuracy than the current EPSRIT-Like algorithm. Simulation results verify the effectiveness of the proposed PM estimator.

Angle-Polarization-Range Estimation Using Sparse Polarization Sensitive FDA-MIMO Radar With Co-Prime Frequency Offsets

Polarization sensitive MIMO radar with frequency diverse array (PSFDA-MIMO) can provide additional target polarization information. It has a better target localization, tracking, classification, and recognition performance, compared with FDA-MIMO radar. In this paper, a sparse polarization sensitive FDA-MIMO radar with co-prime frequency offsets (SPS-CopFDA-MIMO radar) is proposed and a fast parameter estimation algorithm based on propagator method is developed. In receiver, the SPS-CopFDA-MIMO radar introduces full component electromagnetic vector sensor (EMVS) spaced much farther apart than a half-wavelength to achieve aperture extension, therefore provides high accuracy and unambiguous estimates of angle and polarization. In transmitter, the SPS-CopFDA-MIMO radar utilizes co-prime frequency offsets to enhance range resolution without decreasing the maximum unambiguous range. In the proposed algorithm, the angle, polarization, and range are estimated successively. First, polarization diversity is utilized to resolve the phase ambiguity induced by the sparse receiving array. Then, the polarization parameters are estimated based on these estimated angle parameters. Finally, a two-step phase unwrapping processing is proposed to get the high resolution and unambiguous range estimates. The Cramer-Rao bounds for angle, polarization and range are derived. The performance of the proposed SPS-CopFDA-MIMO radar technique is also validated by computer simulation results.

Joint DOA and Polarization Estimation via Canonical Polyadic Decomposition With Constant Modulus Constraints

We consider the joint estimation of direction-of-arrival (DOA) and polarization of constant modulus (CM) signals based on an electromagnetic vector-sensor (EMVS) array. Two algebraic algorithms for canonical polyadic decomposition (CPD) with CM constraint are proposed in two scenarios, in which the source signals are fully and partially CM, respectively. The proposed algorithms use the analytic CM algorithm in the first step to calculate the source matrix, and then exploit the CPD structure of the data tensor to compute the remaining factor matrices, from which the DOA and polarization parameters can finally be obtained. Due to the algebraic nature, the proposed algorithms are faster and more stable than the optimization based algorithms, and can be used to effectively initialize the latter. We have shown that the proposed algorithms have more relaxed uniqueness conditions than unconstrained CPD, and thus can be applied in highly underdetermined cases where the number of source signals greatly exceeds that of the EMVSs. Simulation results are provided to illustrate the performance of the proposed algorithms.

A Novel Power Inversion Antenna Array for the Beidou Navigation Satellite System

Power inversion (PI) arrays have been employed to suppress interference in satellite navigation systems. When the incident direction of a satellite signal is near that of the interference, there will be a significant degradation in the signal to noise ratio (SNR). To reduce this degradation, a PI antenna array composed of a right-hand circular polarized (RHCP) antenna and a spatially-spread electromagnetic vector sensor (SS-EMVS) subarray is proposed, which can suppress interference and acquire satellite signals in both the polarized and spatial domains. Even when the satellite signal is incident from the same direction as the interference, the SNR degradation can be reduced by exploiting the difference in polarization states. It is shown that the filtering is improved in the polarization domain compared with an RHCP PI array, and the SNR loss is lower than with an SS-EMVS PI array while the computational complexity is not increased. Furthermore, the proposed PI array is effective for all Beidou satellite system public service signals.

Joint DOA and Polarization Estimation with Two Parallel Sparse Dipole Arrays

Electromagnetic vector sensors (EMVS) have attracted growing attention in recent years. However, the mutual coupling effects in practical EMVS arrays may seriously degrade the parameter estimation performance. In order to solve this problem, a novel array configuration consisting of two parallel sparse dipole arrays is proposed. Based on the spatially rotational invariance property between the two parallel arrays and the interdipole spacing inside each array, highly accurate but ambiguous direction-cosine estimates, coarse direction-of-arrival (DOA) estimates, and polarization parameter estimation can be obtained jointly. The coarse DOA estimates are then employed to disambiguate the phase ambiguities in the fine estimates. Compared with collocated EMVS, the proposed array overcomes the mutual coupling problem. Moreover, the DOA estimation accuracy is promoted due to the sparse array aperture extension. Simulation results demonstrate the effectiveness of the proposed algorithm.

Tensor Approach to DOA Estimation of Coherent Signals with Electromagnetic Vector-Sensor Array.

This paper addresses the direction-of-arrival (DOA) estimation problem using a uniform rectangular array with electromagnetic vector-sensors in correlated/coherent signal environments. The polarization information is separated from the steering matrix to decorrelate the signals. By developing a tensorial structured received measurements of the array, we propose a tensor-based eigenvector DOA estimation method. Then we apply the forward-backward averaging to the tensor since it obeys the centro-Hermitian structure. In addition, a tensor-based polarization parameters estimation method is presented. The proposed algorithms are superior to the state-of-the-art algorithms in terms of estimation accuracy of coherent signals while only demand a modest computation burden comparing with the latter ones. Simulation results are given to demonstrate the effectiveness of the proposed methods under different scenarios.

Vector-Sensor-Based Signal Parameter Estimation by Exploiting CPD of Tensors

An approach for parameter estimation of signals impinging on an array of electromagnetic vector sensors is presented by exploiting canonical polyadic decomposition of tensors. The uniqueness of the approach is that it can distinguish the signals with the same direction of arrival (DOA) and copolarized state: one function that has not been fulfilled by the up-to-date approaches such as the derivative approaches of multiple signal classification and estimation of signal parameters via rotational invariance techniques, which are the traditional tensor-based approaches. Regarding the reason of our superiority in this function, it lies in that the traditional approaches usually require that the matrices involved in the operations are full column rank. However, in this article, the parameters can be estimated by virtue of the factor matrices, as long as the matrices satisfy the requirement that at least one is full column rank. In other words, as long as the signals comply with any one of the spatial, temporal, and polarized diversities, the proposed approach can effectively estimate the parameters of these signals.

Spatially spread dipole/loop quint for vector‐cross‐product‐based direction finding and polarisation estimation

We propose a spatially spread quint (SS-quint) of only dipoles or loops, for direction of arrival (DOA) and polarisation estimation. The proposed SS-quint is spatially centrosymmetric. Based on this centrosymmetry, the authors develop a computationally low-cost DOA and polarisation estimator via vector-cross-product. Compared with the spatially spread electromagnetic vector-sensor, the proposed SS-quint consists of only dipoles or loops, and thus, its components have more consistent responses. Compared with a previously proposed SS-quint configuration, which is required to be strictly uniformly L-shaped, the proposed SS-quint has a more flexible array configuration in the sense that it is not restricted to any particular shape. The Cramer-Rao bounds are derived and simulation results are provided, to demonstrate the performance of the proposed SS-quint array configuration.

Integrated polarisation and diversity smoothing algorithm for DOD and DOA estimation of coherent targets

This study proposes a novel integrated polarisation and diversity smoothing (IPDS) algorithm to solve the direction estimation problem of coherent targets in bistatic multiple-input multiple-output (MIMO) radar with electromagnetic vector sensors (EVSs). The IPDS algorithm partitions the transmit and receive arrays into multiple subarrays based on the sensor elements and the spatial phase shift factors. Then the covariance matrices of the received signals from coherent targets associated with these subarrays are smoothened to restore the rank inadequacy of the reflection coefficient covariance matrix. After applying the IPDS algorithm, the direction of departure (DOD) and the direction of arrival (DOA) are estimated using the estimation of signal parameters via rotational invariance technique and the multiple signal classification methods. The effectiveness of the proposed algorithm in terms of decorrelation factor, estimation accuracy, precision and the spatial spectrum is evaluated through computer simulations. Cramér–Rao lower bound is derived for the bistatic MIMO radar with EVSs to substantiate the proposed algorithm. The simulation results are compared with the diversity smoothing and the polarisation smoothing algorithms available in literature. The results obtained by using the proposed algorithm were found to be impressive.

Successive Method for Angle-Polarization Estimation With Vector-Sensor Array

A successive method for joint angle and polarization estimation of multiple narrowband incoherent sources using linear electromagnetic vector-sensor (EMVS) arrays is proposed in this article. First, the polarization field smoothing root-multiple signal classification (MUSIC) algorithm is presented to estimate the elevation angles. Second, the estimated elevation angles are applied to extract the EMVS manifolds and then to estimate the azimuth angles. Finally, the estimated angles are used to provide the polarization parameter estimates. Compared with most of the previous algorithms, the proposed algorithm first uses the polarization field vector smoothing, which enables the offering of more accurate elevation angle estimates for correlated sources, with no loss of array aperture, and, second, requires no spectral searching and parameter pairing procedures. Simulations results are provided to show the efficacy of the proposed algorithm.

2D-DOD and 2D-DOA estimation using the electromagnetic vector sensors

A new method is proposed for estimating the two-dimensional (2D) direction-of-departure (DOD) and 2D direction-of-arrival (DOA) in the bistatic MIMO radar using the electromagnetic vector sensors (EVSs). The proposed method constructs two data-subsets with respect to both transmitter and receiver. These subsets are then subjected to the ESPRIT-based method for estimating the EVS components followed by the 2D-DOD and 2D-DOA. This methodology yields closed-form automatically paired azimuth and elevation angles without any additional processing. Further, it resolves the targets with identical DOD/DOA and does not require a priori knowledge of the sensor spacing. In addition, an optimization based formulation is derived for pair matching between the 2D-DOD and 2D-DOA. Simulation results are compared with the Crame´r–Rao bound to signify the effectiveness of the proposed method.

“Blind” calibration of vector sensors whose dipole/loop triads deviate from their nominal gains/phases/orientations/locations

AbstractAn electromagnetic vector sensor consists of a triad of electric dipoles in orthogonal orientation, plus another triad of similarly arranged magnetic loops, all in spatial collocation. This electromagnetic vector sensor has been used in a series of algorithms to estimate the incident sources' directions‐of‐arrival and polarizations. However, these algorithms have presumed the dipole triads and the loop triads of perfect ideality in their gain/phase responses, their orientations, and locations. Such idealization is rarely (if ever) attained in actual field deployment. Instead, the nonidealities need to be calibrated, often blindly with no training signal impinging from any prior known direction‐of‐arrival at any prior known polarization. For such a scenario, this work proposes a new algorithm for direction finding, for polarization estimation, and for “blind” calibration (a.k.a. “self‐calibration,” “autocalibration,” or “unaided calibration”) of all above nonidealities. This new algorithm is orders‐of‐magnitude computationally simpler than maximum likelihood estimation. This reduction in complexity is achieved here by exploiting the electromagnetic vector sensor's quintessential array manifold and by a judicious breakdown of the originally high‐dimensional problem (of estimating the directions‐of‐arrival, polarizations, and the antenna nonidealities) into suitably chosen/sequenced low‐dimensional subproblems. This proposed algorithm is first in the open literature to exploit the electromagnetic vector‐sensor's quintessential array manifold for “blind” calibration of all above mentioned nonidealities simultaneously. Monte Carlo simulations verify this proposed algorithm's effectiveness in “blind” calibration and this algorithm's orders‐of‐magnitude computational efficiency over the maximum likelihood approach.

DOD and DOA estimation using the spatial smoothing in MIMO radar with the EmV sensors

This paper deals with the directions of departure (DOD) and directions of arrival (DOA) estimation of coherent and noncoherent targets in bistatic MIMO radar with the electromagnetic vector (EmV) sensors. The high-resolution eigenspace-based methods such as, estimation of signal parameters via rotational invariance technique (ESPRIT), multiple signal classification, etc., fails to estimate DOD and DOA of fully or partially correlated targets. In order to employ these methods, a new pre-processing method is developed based on the spatial smoothing in MIMO radar with the EmV sensors. Then, the directions are estimated using the ESPRIT algorithm. Monte-Carlo simulations are performed to investigate the estimation-accuracy and resolution-capability of the proposed approach, and to compare with no pre-processing and the existing method. The simulation result shows that, the proposed methodology improves the performance significantly.

A Type-2 Block-Component-Decomposition Based 2D AOA Estimation Algorithm for an Electromagnetic Vector Sensor Array.

This paper investigates a two-dimensional angle of arrival (2D AOA) estimation algorithm for the electromagnetic vector sensor (EMVS) array based on Type-2 block component decomposition (BCD) tensor modeling. Such a tensor decomposition method can take full advantage of the multidimensional structural information of electromagnetic signals to accomplish blind estimation for array parameters with higher resolution. However, existing tensor decomposition methods encounter many restrictions in applications of the EMVS array, such as the strict requirement for uniqueness conditions of decomposition, the inability to handle partially-polarized signals, etc. To solve these problems, this paper investigates tensor modeling for partially-polarized signals of an L-shaped EMVS array. The 2D AOA estimation algorithm based on rank- BCD is developed, and the uniqueness condition of decomposition is analyzed. By means of the estimated steering matrix, the proposed algorithm can automatically achieve angle pair-matching. Numerical experiments demonstrate that the present algorithm has the advantages of both accuracy and robustness of parameter estimation. Even under the conditions of lower SNR, small angular separation and limited snapshots, the proposed algorithm still possesses better performance than subspace methods and the canonical polyadic decomposition (CPD) method.

Quaternion based joint DOA and polarization parameters estimation with stretched three-component electromagnetic vector sensor array

The three-component electromagnetic vector sensor (EMVS) consisting of co-centered orthogonally oriented x-dipole, z-dipole and z-loop is considered. In order to make full use of the spatial aperture of each component, the original uniform linear three-component EMVS array (ULTEA) is stretched into one half-wavelength spaced uniform linear loop subarray (ULLSA) along the z axis, and one sparse uniform linear co-centered orthogonally oriented dual-dipole (CODD) subarray (SULCSA) along the x axis. Then, a generalized rotation invariance based quaternion multiple signal classification (GRIQ-MUSIC) algorithm is presented for direction of arrival (DOA) and polarization parameters estimation. According to the proposed algorithm, the elevation angles are firstly estimated based on the half-wavelength spaced ULLSA. Then the polarization phase differences and azimuth angles are obtained based on the coupling relationship between the angle domain and polarization domain, but the azimuth angles are in coarse-resolution since the array aperture is not utilized. Next, the SULCSA is used to re-estimate the azimuth angles in fine resolution, and the ambiguity problem can be resolved by the least square method. Finally, based on the estimated elevation angles, azimuth angles and polarization phase differences, the corresponding auxiliary polarization angles can be estimated by N times one-dimensional parameter search, where N is the sources number, and the parameters high dimensional parameters search problemare matched automatically. Based on the GRIQ-MUSIC algorithm, the high dimensional parameters search problem of the conventional Q-MUSIC algorithm is simplified to a one-dimensional parameter search problem, thus the proposed algorithm not only reduces the computation complexity considerably, but also avoids the performance degradation caused by the failure in parameters pairing. The simulation examples demonstrate the effectiveness and feasibility of the proposed algorithm.

Target detection using weather radars and electromagnetic vector sensors

We propose a method to detect a target in a bistatic passive polarimetric radar network, with weather surveillance radar as our illuminator of opportunity (IO). We build our signal model using electromagnetic vector sensors (EMVS) as the receiver, which captures the reflections from a point-like target present in the scene of interest, surrounded with strong clutter. We develop a generalized likelihood ratio test (GLRT) detector that is robust to inhomogeneous clutter. We also develop a maximum likelihood (ML) solution to extract the signal subspace from the received data contaminated by the clutter interference. We provide the exact distribution of the test statistic for the asymptotic case and evaluate its performance loss by considering a reduced set of data. The proposed GLRT method is a constant false alarm rate (CFAR) detector, which makes it robust against the inhomogeneous clutter. With the help of numerical results, we demonstrate the robustness and the limitations of our proposed method.

DOA and Polarization Estimation Using an Electromagnetic Vector Sensor Uniform Circular Array Based on the ESPRIT Algorithm.

In array signal processing systems, the direction of arrival (DOA) and polarization of signals based on uniform linear or rectangular sensor arrays are generally obtained by rotational invariance techniques (ESPRIT). However, since the ESPRIT algorithm relies on the rotational invariant structure of the received data, it cannot be applied to electromagnetic vector sensor arrays (EVSAs) featuring uniform circular patterns. To overcome this limitation, a fourth-order cumulant-based ESPRIT algorithm is proposed in this paper, for joint estimation of DOA and polarization based on a uniform circular EVSA. The proposed algorithm utilizes the fourth-order cumulant to obtain a virtual extended array of a uniform circular EVSA, from which the pairs of rotation invariant sub-arrays are obtained. The ESPRIT algorithm and parameter pair matching are then utilized to estimate the DOA and polarization of the incident signals. The closed-form parameter estimation algorithm can effectively reduce the computational complexity of the joint estimation, which has been demonstrated by numerical simulations.

Stokes parameters and DOAs estimation of partially polarized sources using a EM vector sensor

In this paper, the problem of polarization and direction-of-arrival (DOA) estimation using an electromagnetic (EM) vector sensor is addressed based on the augmented second-order statistics of quaternions. The augmented quaternion model of an EM vector sensor is introduced by employing the augmented second-order statistics of quaternions, which include the information in both the standard covariance and the pseudo-covariance. The fact is revealed that the Stokes parameters of an EM wave can be extracted from an augmented covariance matrix. An augmented quaternion-based approach is proposed for the Stokes parameters and DOA estimation of polarized EM waves. The proposed approach uses only information in three imaginary parts of both the standard covariance and the pseudo-covariance matrix. In theory, it is guaranteed to remove the effect of the additive noise which is uncorrelated between measurement channels. The proposed approach is applicable to both completely polarized and partially polarized EM waves. Simulations are used to verify the performance of the proposed approach.

Polarisation smoothing for coherent source direction finding with multiple‐input and multiple‐output electromagnetic vector sensor array

This study proposes a new polarisation smoothing algorithm with multiple-input and multiple-output (MIMO) electromagnetic vector sensor array to address the problem of coherent source angle estimation in MIMO radar. This algorithm can be summarised as follows: (i) matched filtering for echoes is performed to get virtual MIMO array; (ii) the virtual array is divided into six spatially identical subarrays according to polarisation information offered by electromagnetic vector sensor; and (iii) the six subarrays covariance matrices are processed with weighted smoothing to obtain polarisation smoothing covariance matrix, which can restore the rank loss of the covariance matrix of coherent sources. When compared with spatial smoothing, the proposed algorithm is suitable for spatially arbitrary array configuration, without the price of reducing effective array aperture. Simulation results show that the proposed algorithm substantially outperforms the spatial smoothing algorithm.