ESPRIT Algorithm Research Articles

Signal Emitters Localization by Spectral Methods

Methods are considered of generating signals in a radar sensor receiver provided with a colocated antenna system of Multiple Input Multiple Output (MIMO) configuration when synthesizing virtual antenna arrays. Review of the basic spectral methods used in beamforming with digital automobile radars, such as Capon method, MUSIC and ESPRIT was carried out. Spatial spectra obtained by various methods were constructed for a radar signal model, and comparative spectra characteristic by angular resolution is provided. Output heatmaps in the angle-distance coordinate were constructed to represent methods operation according to the real target situation based on data sampling from the front-mounted automobile radar. Advantages of decomposition methods based on MUSIC and ESPRIT algorithms in solving the problem of a signal emitter localization are presented

DOA Estimation for Unfolded Coprime Arrays: Successive-MUSIC Algorithm

In this paper, we investigate the problem of direction of arrival (DOA) estimation of unfolded coprime arrays with successive-MUSIC algorithm which cascades multiple signal classification (MUSIC) algorithm and rotational invariance techniques (ESPRIT).We propose An algorithm with low computational complexity and high estimation accuracy, which first use ESPRIT algorithm for initial estimation, then according to the results of initial estimation narrow the search scope, finally, more accurate estimation results are obtained by MUSIC algorithm. Compared with the traditional MUSIC algorithm, this algorithm only needs to conduct a small range of angle search, which greatly reduces the algorithm complexity. Compared with the traditional ESPRIT algorithm, this algorithm also effectively improves the angle estimation performance of the algorithm. Moreover, comparing with traditional coprime linear arrays, the enhanced degrees of freedom (DOFs) can be achieved due to larger array aperture, Simulations are presented to validate the superiority of the proposed algorithm.

Near-Field Noncircular Sources Localization Based on Fourth-Order Cumulant

This paper presents a cumulant-based algorithm for near-field noncircular sources localization with a symmetric uniform linear array. It first constructs three extended matrices. Then, based on the rotational invariance property in extended cumulant-domain signal subspace, coarse direction-of-arrival (DOA) estimates are obtained. With the course results used as reference, the algorithm is able to disambiguate the cyclic phase ambiguities when the equivalent sub-array spacing exceeds a half wavelength. Thus, higher precision DOA estimates can be obtained. Finally, with the estimated DOAs, only one-dimensional searching is needed to obtain the range estimates via rank-reduction algorithm. The proposed algorithm avoids two-dimensional searching and parameters pairing. In addition, compared with the existing near-field noncircular sources localization algorithm, the significant characteristic of the proposed algorithm is that it exploits cumulant and the noncircularity of signal to achieve extended steering vector. Cumulant is insensitive to Gaussian (white or color) noise. Consequently, the proposed one provides DOA estimates with improved precision especially at low signal-to-noise ratios. Furthermore, it doubles the number of detectable sources. Total least square ESPRIT algorithm is exploited to yield search free estimates of near-field bearing parameters. Computer simulations are carried out to demonstrate the superiority of the proposed algorithm.

High-Resolution DOA Estimation Algorithm for a Single Acoustic Vector Sensor at Low SNR

In order to improve the angular resolution of direction-of-arrival (DOA) estimation based on portable microphone at low signal-noise-ratio (SNR), this paper proposes a new high-resolution DOA estimation algorithm based on single acoustic vector sensor (AVS), namely Virtual-AVS algorithm. The innovative algorithm is mainly composed of two parts: the preprocessing method and the DOA estimation method with ambiguity elimination. The preprocessing method is implemented based on higher-order cumulants with Gaussian noise suppression characteristic. This method not only suppress Gaussian noise to effectively enhance SNR, but also achieve AVS virtual expansion. The computational burden can be significantly reduced by effectively expanding one necessary AVS to perform the ESPRIT algorithm. To extend the application range of the innovative algorithm to support non-point-like geometry AVS, we introduce a new DOA estimation method with ambiguity elimination. This method can eliminate the cyclic ambiguity caused by the channel spacing of the non-point-like geometry AVS exceeding the half-wavelength of the incident source. We prove that the Virtual-AVS algorithm is asymptotically unbiased with large number of snapshots. We also derive the Cram $\mathbf {\acute{e}}$ r-Rao bound. The simulations of closely-spaced sound sources show that the algorithm has better angular resolution than the existing algorithms. The real-world experiments of semi-anechoic chamber also verify the feasibility of the algorithm.

Low-Complexity DOA Estimation Based on Constraint Solution Space

The Weighted Subspace Fitting (WSF) algorithm is one of the universal algorithms in Direction-Of-Arrival (DOA) estimation, which is of high accuracy. However, it involves the multi-dimensional nonlinear optimization problem, and the computational complexity is usually high. In this paper, we propose a low-complexity DOA estimation algorithm based on constraint solution space. Firstly, we use ESPRIT algorithm to limit the solution space around the best solution and reduce the computational range. Then, we find the best solution in a smaller solution space constraint by Cramr-Rao Bound (CRB), and seek repeatedly until reaching the global optimal solution of WSF algorithm by using the space of the best solution. By limiting the searching process in smaller solution space, this strategy controls the direction of convergence and reduces computational complexity. The experimental results show that this algorithm needs less iterations when the same DOA accuracy is required, and the computational complexity is apparently reduced.

Closed-Loop Sparse Channel Estimation for Wideband Millimeter-Wave Full-Dimensional MIMO Systems

This paper proposes a closed-loop sparse channel estimation (CE) scheme for wideband millimeter-wave hybrid full-dimensional multiple-input multiple-output and time division duplexing based systems, which exploits the channel sparsity in both angle and delay domains. At the downlink CE stage, random transmit precoding matrix is designed at base station (BS) for channel sounding, and receive combining matrices at user devices (UDs) are designed whereby the hybrid array is visualized as a low-dimensional digital array for facilitating the multi-dimensional unitary ESPRIT (MDU-ESPRIT) algorithm to estimate respective angle-of-arrivals (AoAs). At the uplink CE stage, the estimated downlink AoAs, namely, uplink angle-of-departures (AoDs), are exploited to design multi-beam transmit precoding matrices at UDs to enable BS to estimate the uplink AoAs, i.e., the downlink AoDs, and delays of different UDs, whereby the MDU-ESPRIT algorithm is used based on the designed receive combining matrix at BS. Furthermore, a maximum likelihood approach is proposed to pair the channel parameters acquired at the two stages, and the path gains are then obtained using least squares estimator. According to spectrum estimation theory, our solution can acquire the super-resolution estimations of the AoAs/AoDs and delays of sparse multipath components with low training overhead. Simulation results verify the better CE performance and lower computational complexity of our solution over state-of-the-art approaches.

The Design of Simulator for Inter-Harmonic Detection with ESPRIT

Inter-harmonics which exist in non-integer multiples of main harmonics cause power quality problems. In this study, in order to overcome power quality problems, ESPRIT algorithm which is one of the methods used for inter-harmonic detection which couldn’t be accomplished by conventional spectrum analysis methods such as Fast Fourier Transform was realized in MATLAB environment. Software which was prepared in MATLAB environment has properties which are creating input signals, importing external signals, plotting frequency spectrum which is computed from obtained values with ESPRIT and presenting relative error rate of real signal values and ESPRIT algorithm values.

Generalized Three Dimensional Coprime Array for Two-Dimensional DOA Estimation

In this paper, we extend the coprime planar array to coprime cubic array and propose a three dimensional coprime array (TDCA) for two-dimensional direction of arrival (DOA) estimation, which possesses larger inter-element spacing so that the mutual coupling effects can be effectively relieved. Moreover, due to the larger array aperture, better DOA estimation performance can be achieved. To obtain more degrees of freedom (DOFs), a generalized TDCA (G-TDCA) configuration is proposed, which has a flexible array geometry and can extend the array aperture to obtain performance improvement. The principle for optimal array design of G-TDCA is derived to achieve the maximum DOF. And the Cramer–Rao Bounds which denotes as a theoretical benchmark for the lower bound of unbiased estimate are derived. Then we propose Khatri–Rao estimation signal parameters via rotational invariance techniques (KR-ESPRIT) algorithm and obtain the close-form expression. The algorithm can achieve angles with automatic pairing and doesn’t need spectrum peak searching. In order to decrease the computational complexity, we propose KR-Unitary ESPRIT algorithm, which can achieve approximate DOA estimation performance of the KR-ESPRIT algorithm with the lower computational complexity. Numerical simulation results verify the superiority of G-TDCA with proposed algorithms.

Reduced-Dimension DOA and Polarization Parameters Joint Estimation Method for Electromagnetic Vector Sensor Array

MUSIC algorithm is a very typical algorithm in the joint estimation of DOA and polarization parameters. But the two spectral peak searches of two-dimensional parameter space in the algorithm cause a damaging effect on calculation, which limits the application of the algorithm in practice. Therefore, this paper proposes a joint estimation algorithm of dimensionality reduction DOA and polarization parameters based on successive MUSIC in the case of uniform linear array arrangement of the electromagnetic vector sensor. The proposed algorithm improves the classical MUSIC algorithm from two two-dimensional parameter searches to four one-dimensional parameter searches in the joint estimation of DOA and polarization parameters, which greatly reduces the computational complexity of the algorithm and can lead to the automatic matching of DOA and polarization parameters. Simulation results show that the computational complexity of the proposed algorithm is reduced by 104 orders of magnitude compared to the classical MUSIC algorithm. And the performance of the polarization parameter estimation of this algorithm is about 72%∼85% higher than that of the ESPRIT algorithm. Therefore, the algorithm is more applicable.

Coprime L‐shaped array connected by a triangular spatially‐spread electromagnetic‐vector‐sensor for two‐dimensional direction of arrival estimation

The authors propose a hybrid L-shaped array composed of two sparse scalar arrays and a single triangular spatially-spread electromagnetic-vector-sensor (SS-EMVS) for two-dimensional (2D) direction-of-arrival (DOA) estimation. These two sparse but uniform scalar arrays are placed along the x -axis and y -axis, respectively, which constitute two arms of the L-shaped array. These two arms are connected by an SS-EMVS, which consists of a spatially-spread dipole-triad plus a spatially-spread loop-triad. Further, the inter-dipole/loop spacings of SS-EMVS follow a coprime relationship with the inter-sensor spacings of the L-shaped scalar array. In proposed DOA estimation algorithm, they first perform the vector-cross-product algorithm to SS-EMVS to obtain a high-accuracy but ambiguous direction cosine estimation; they then apply the ESPRIT algorithm to the scalar array on each arm to get another high-accuracy but cyclically ambiguous direction cosine estimation; finally, they adopt the Chinese Remainder Theorem to disambiguate the ambiguous estimations. Because the authors’ proposed array has 2D array aperture extension, it can achieve a high angular estimation performance. Moreover, one component of triangular SS-EMVS rather than an SS-EMVS is used as the array unit of two scalar arrays; thus, the whole array cost decreases dramatically. Simulation results validate the array configuration and the developed algorithm.

Fast parameter estimation of distributed sources in shallow water with a new UCA

Due to large number of reflections from surface and bottom in the shallow ocean environment, the radiated noise from the same source can be the distributed source model, instead of the traditional point model. The distributed source will appear two-dimension spatial distribution characteristic in azimuth and elevation. Four important parameters of two-dimensional spatial distribution source are the central angle and extended angle in both dimension, which is very important to identify the type of source. In this paper, a novel UCA array layout is proposed for an two-dimensional incoherent distributed(TDID) source, and a new ESPRIT algorithm for two-dimension distribution source is derived to estimate these parameters analytically with symmetrical structure of UCA. A large mount simulation of underwater environment shows this method can achieve high computational accuracy with low computational burden, and the results also verify the robustness to the different distribution forms and good performance with larger extended angle size.

Numerical simulations of NMR relaxation in chalk using local Robin boundary conditions.

The interpretation of nuclear magnetic resonance (NMR) data is of interest in a number of fields. In Ögren (2014) local boundary conditions for random walk simulations of NMR relaxation in digital domains were presented. Here, we have applied those boundary conditions to large, three-dimensional (3D) porous media samples. We compared the random walk results with known solutions and then applied them to highly structured 3D domains, from images derived using synchrotron radiation CT scanning of North Sea chalk samples. As expected, there were systematic errors caused by digitalization of the pore surfaces so we quantified those errors, and by using linear local boundary conditions, we were able to significantly improve the output. We also present a technique for treating numerical data prior to input into the ESPRIT algorithm for retrieving Laplace components of time series from NMR data (commonly called T-inversion).

Research on Forest Height Inversion Algorithm of Three-Stage Full-Polarization SAR Data Based on Improved Coherence Coefficient

Polarimetric SAR interference technology (PolInSAR) has a wide range of applications in the extraction of forest height. At present, some commonly used tree height inversion algorithms, such as ESPRIT algorithm and DEM difference method, seriously underestimate the forest tree height. In this paper, in the process of traditional three-stage algorithm, the extraction of the coherence coefficient is improved, and the improved coherence coefficient is more accurate, thus greatly improving the accuracy of three-stage algorithm tree height inversion results. By highly inverting the 25 m data generated by the PolSARPro simulation software, it is found that the height before the improvement of the coherence coefficient is 18.2 m, and the improved height is 23.7 m.

A Combined ESPRIT-MUSIC Method for FDA-MIMO Radar with Extended Range Ambiguity Using Staggered Frequency Increment

For the problem of joint angle and range estimation with frequency diverse array (FDA), MIMO radar, staggered frequency increment is proposed to expand the range ambiguity and the joint algorithm of ESPRIT and MUSIC is proposed to reduce the computational complexity. The uniformly weighted beampattern of FDA is a SINC-like function. Therefore, the grating lobe of range estimation exists. In this paper, staggered frequency increment is proposed to increase the distance of adjacent grating lobes. The proposed joint estimation algorithm firstly estimates the angle by using ESPRIT algorithm. Then we get the range estimation by MUSIC one-dimensional range search using the above estimated angle. In simulation results section, it is indicated in simulation results that the proposed method improves the range grating lobe and reduces the complexity.

DOA estimation of multipath signals in the presence of gain‐phase errors using an auxiliary source

In this paper, we address the problem of direction‐of‐arrival (DOA) estimation of multipath signals in the presence of gain‐phase uncertainties using an auxiliary source (AS) with uniform rectangular array. Based on the assumption that the waveform of the AS is a known prior, and the signal of the AS impinges on the array without multipath propagation, a two‐step algorithm is proposed to estimate the DOAs along with the fading coefficients and gain‐phase errors. First, a coarse estimation is obtained by extending the traditional spatial smoothing‐based ESPRIT algorithm. Second, in order to overcome the performance deterioration due to a reduction of the effective array aperture, an alternate iterative algorithm is proposed. Meanwhile, the relevant stochastic Cramér‐Rao bound (CRB) is also derived. Simulation results show that the proposed method is capable of approaching the stochastic CRB when the signal–noise ratio (SNR) of the AS is large enough and is greater than the SNR of the unknown source. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

2-D DOA Estimation for Incoherently Distributed Sources Considering Mixed Circular and Noncircular Signals in Massive MIMO System

In practical environment, the received signals cannot be regarded as point sources due to the existence of signal scattering phenomena. Incoherently distributed source model is suitable for this realistic scenarios. The incoherently distributed DOA estimators based on noncircular property can provide a better performance. However, these estimators are not fit for the mixed circular and noncircular signals. In this paper, a conjugate generalized shift invariance algorithm is proposed for incoherently distributed sources comprising of circular and noncircular signals. The general array manifold (GAM) model of incoherently distributed source is established by one-order Taylor series approximation. To utilize the noncircular property, each incoherently distributed circular source is separated as two strictly incoherently distributed noncircular sources. A generalized shift invariance property is derived by dividing the whole uniform rectangular array (URA) into four overlapping subarrays. Then, a modified conjugate generalized least square (CGLS) ESPRIT algorithm is proposed to obtain the central DOAs, which can improve the estimation accuracy without any spectrum searching. In addition, a pair matching method and an angular spreads estimation algorithm are also designed based on the GAM model for this mixed sources scenario. Furthermore, the Cramer-Rao bound (CRB) of proposed algorithm is given and analyzed under the mixed incoherently distributed sources scenario. Numerical results illustrate the validity of the proposed algorithm in this realistic scenario.

Joint 2-D DOA and Doppler Estimation for L-Shaped Array via Dual PARAFAC With Triple Matching Implementation

A dual parallel factor (PARAFAC)-based approach to jointly estimating the two-dimensional direction of arrival (2-D DOA) and Doppler is proposed in this paper, where an L-shaped array consisting of acoustic vector-sensor is used. First, we apply the PARAFAC decomposition to the data model formed by concatenating the outputs of multi-level delays of the observations, and we get the parameter matrix H, which accomplish the 2-D DOA estimation and pairing automatically, then the dual PARAFAC decomposition is applied to the achieved composite steering matrix from the first PARAFAC decomposition, and thus, the same permutation matrices link the estimates of steering matrices and delay matrices from X-subarray and Y-subarray, respectively. Following this, the Doppler and 2-D DOA matching information are obtained via triple matching implementation, e.g. 2-D DOA and frequency matching. Finally, Doppler is estimated by delay matrices. The proposed algorithm is computationally effective for both uniform and non-uniform L-shaped array as SNR exceeds 15dB, and its performance outperforms the joint angle and Doppler shift ESPRIT (JAD-ESPRIT) algorithm and the joint angle and Doppler shift PM (JAD-PM) algorithm. The simulation results justified the effectiveness of the proposed algorithm.

Three-dimensional target localization method based on the tensor subspace FDS-MIMO radar with a co-prime frequency offset

Target localization utilizing frequency diversity array (FDA) is one of the most popular research directions in the study of radars. Considering the problems of range ambiguity and localization accuracy, this paper investigates the issue of three-dimensional (3D) target localization based on the proposed frequency diverse-subaperturing multiple-input multiple-output (FDS-MIMO) radar. First, a fifth-order tensor signal model is established by exploiting the inherent multidimensional structure of the matched filter output. To alleviate the difficulty of range ambiguity, the idea of employing co-prime frequency offsets along the two directions in the planer array is provided. This strategy can resolve the contradiction between the range resolution and maximum unambiguous range in beam domain. The tensor-based complex- and real-valued rotational invariance technique (tensor- and unitary tensor-ESPRIT) algorithms are developed based on frequency offset structure. Given that the inherent multidimensional structure is utilized, the proposed methods can resolve range ambiguity with improved localization performance as compared with the existing ESPRIT algorithm and frequency offset manner. Theoretical analysis and numerical results demonstrate the effectiveness of the proposed approaches.

An Angle Estimation Method for Monostatic MIMO Radar Based on RCC-FLOM Algorithm

The performance of the angle estimation algorithm based on the two-order or higher order cumulants in the impact noise background will decline sharply. Therefore, it is necessary to study the new algorithm to estimate target angle in the impact noise background. In order to solve the angle estimation problem of coherent sources in the impulse noise background, a conjugate rotation invariant subspace algorithm based on reduced order fractional lower order covariance matrix is proposed. Use the reduced dimension lower order fraction covariance matrix to reduce the impulse noise influence. And according to the conjugate rotation invariant subspace, the coherent source is decohered. The Monte-Carlo experiments show that the proposed algorithm has the advantages of high estimation probability and low root mean square error in the case of low signal-to-noise ratio, compared with the existing FLOM-MUSIC algorithm and FLOM-Unitary ESPRIT algorithm.

Vector Cross Product-Based 2D-DOA and Polarization Estimation With “Long” Electric-Dipole Quint

Dipole antenna elements whose physical length L is greater than or equal to one-tenth of the wavelength λ are generally denoted as long dipoles. Such radiators are more useful in practical polarization sensitive arrays (PSAs) for electromagnetic sensing applications because their radiation efficiency is greater than that of short dipole radiators for which L <; λ /10. Thus, research focused on estimating the parameters of unknown electromagnetic sources using long dipoles has attracted considerable attention from numerous researchers in recent years. However, the development of PSAs and algorithms for this purpose remains in its infancy. In this paper, we propose a PSA composed of five spatially non-collocated long dipoles in a centrosymmetric configuration and apply an algorithm based on the vector cross product for estimating the 2-D direction of arrival (2D-DOA) and polarization parameters of unknown electromagnetic sources. First, the time-domain rotational invariance of the received data facilitates the use of the ESPRIT algorithm for estimating the steering vector. Second, the relationships between the entries of the steering vector are employed to obtain highly accurate, albeit cyclically ambiguous estimates of the directional cosines of the x- and y-axes. Then, the coarse 2D-DOA parameter estimation is conducted using the vector cross product algorithm. Finally, the course 2D-DOA parameter estimations are employed as a reference to obtain a set of highly accurate and unambiguous directional cosine estimates from the previously determined set of cyclically ambiguous estimates. The effectiveness of the proposed algorithm is verified by the simulation results.