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Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments

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A special issue of Sensors (ISSN 1424-8220). This special issue belongs to the section "Radar Sensors".

Deadline for manuscript submissions: closed (30 July 2024) | Viewed by 18576

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Dr. Jianfeng Li

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College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
Interests: array signal processing; direction-of-arrival estimation; source localization; multi-array system
Special Issues, Collections and Topics in MDPI journals

Dr. Ding Wang

E-Mail Website
Guest Editor

1. College of Information System Engineering, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China
2. National Digital Switching System Engineering and Technology Research Center, Zhengzhou 450002, China
Interests: wireless localization; array signal processing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Sensor arrays have been widely applied in various fields, e.g., wireless communication, radar, sonar, and navigation. The key roles of sensor arrays include providing spatial parameter estimations, for example, for predicting the direction-of-arrival and source position, and for enhancing parameter estimation performances in other domains. However, with the present complex electromagnetic environment, general estimation methods have great performance degradations when encountering complex signal propagation, such as multipath or occlusion situations. Meanwhile, a sensor array system itself also suffers from uncertainties, such as gain-phase errors, position errors, and mutual coupling, which are classical but long-term problems. So, there are urgent requirements for robust estimation methods, including model-driven and data-driven methods, which can obtain high-precision, high-resolution, and large-capacity parameter estimation, regardless of complex influencing factors. This Special Issue invites contributions on the latest developments and advances of robust processing methods, schemes, or architectures on sensor array systems.

Topics to be covered include, but are not limited to, the following:

Direction-of-arrival estimation with unknown array uncertainties;
Direction-of-arrival estimation under multipath propagation;
Distributed array data fusion under complex propagation;
Source localization in complex electromagnetic environments;
Array structure design to suppress the array uncertainties or complex propagation;
Data-driven methods for robust parameter estimation or classification;
Robust detection or estimation methods in array radar system;
Array system calibration methods;
Cooperative estimation methods for distributed multi-array parameters;
Parameter estimation methods of sensor arrays based on artificial intelligence technology.

Dr. Jianfeng Li
Dr. Ding Wang
Guest Editors

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Keywords

sensor array
parameter estimation
robust estimation methods
direction-of-arrival estimation
multi-array system
source localization
digital array radar
array structure design
data-driven methods

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Related Special Issue

Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments: 2nd Edition in Sensors (1 article)

Published Papers (12 papers)

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Research

17 pages, 6007 KiB

Open AccessArticle

An Improved Unfolded Coprime Linear Array Design for DOA Estimation with No Phase Ambiguity

by Pan Gong and Xiaofei Zhang

Sensors 2024, 24(19), 6205; https://doi.org/10.3390/s24196205 - 25 Sep 2024

Viewed by 624

Abstract

In this paper, the direction of arrival (DOA) estimation problem for the unfolded coprime linear array (UCLA) is researched. Existing common stacking subarray-based methods for the coprime array are invalid in the case of its subarrays, which have the same steering vectors of source angles. To solve the phase ambiguity problem, we reconstruct an improved unfolded coprime linear array (IUCLA) by rearranging the reference element of the prototype UCLA. Specifically, we design the multiple coprime inter pairs by introducing the third coprime integer, which can be pairwise with the other two integers. Then, the phase ambiguity problem can be solved via the multiple coprime property. Furthermore, we employ a spectral peak searching method that can exploit the whole aperture and full DOFs of the IUCLA to detect targets and achieve angle estimation. Meanwhile, the proposed method avoids extra processing in eliminating ambiguous angles, and reduces the computational complexity. Finally, the Cramer–Rao bound (CRB) and numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed method. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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14 pages, 515 KiB

Open AccessArticle

Direct Position Determination of Non-Gaussian Sources for Multiple Nested Arrays: Discrete Fourier Transform and Taylor Compensation Algorithm

by Hao Hu, Meng Yang, Qi Yuan, Mingyi You, Xinlei Shi and Yuxin Sun

Sensors 2024, 24(12), 3801; https://doi.org/10.3390/s24123801 - 12 Jun 2024

Viewed by 606

Abstract

This paper delves into the problem of direct position determination (DPD) for non-Gaussian sources. Existing DPD algorithms are hindered by their high computational complexity from exhaustive grid searches and a disregard for the received signal characteristics by multiple nested arrays (MNAs). To address these issues, the paper proposes a novel DPD algorithm for non-Gaussian sources with MNAs: the Discrete Fourier Transform (DFT) and Taylor compensation algorithm. Initially, the fourth-order cumulant matrix of the received signal is computed, and the vectorizing method is applied. Subsequently, a computationally efficient DPD cost function is proposed by leveraging a normalized DFT matrix to reduce complexity. Finally, first-order Taylor compensation is utilized to enhance the accuracy of the localization results. The superiority of the proposed algorithm is demonstrated through numerical simulation results. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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18 pages, 2539 KiB

Open AccessArticle

A Circularly Polarized Non-Resonant Slotted Waveguide Antenna Array for Wide-Angle Scanning

by Guodong Han and Weihang Liu

Sensors 2024, 24(10), 3056; https://doi.org/10.3390/s24103056 - 11 May 2024

Viewed by 1233

Abstract

A compact circularly polarized non-resonant slotted waveguide antenna array is proposed with the aim of achieving wide-angle scanning, circular polarization, and low side-lobe levels. The designed antenna demonstrates a scanning range of +11° to +13° in the frequency domain and a beam scanning range of −45° to +45° in the phase domain. This design exhibits significant advantages for low-cost two-dimensional electronic scanning circularly polarized arrays. It employs a compact element that reduces the aperture area by 50% compared to traditional circular polarization cavities. Additionally, the staggered array method is employed to achieve an element spacing of 0.57

λ

within the azimuth plane. Isolation gaps were introduced into the array to enhance the circular polarization performance of non-resonant arrays. The Taylor synthesis method was employed to reduce the side-lobe levels. A prototype was designed, fabricated, and measured. The results indicate superior radiation efficiency, favorable VSWR levels, and an axis ratio maintenance below 3 dB across the scanning range. The proposed antenna and methodology effectively broaden the beam scanning angle of circularly polarized slotted waveguide array antennas. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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11 pages, 2995 KiB

Open AccessCommunication

Efficient Multi-Sound Source Localization Algorithm for Transformer Faults Based on Polyphase Filters

by Hualiang Zhou, Zhantao Su, Yuxuan Huang, Lu Lu and Mingwei Shen

Sensors 2024, 24(2), 604; https://doi.org/10.3390/s24020604 - 17 Jan 2024

Cited by 1 | Viewed by 1133

Abstract

Power transformers play a critical role in power systems, and the early detection of their faults and defects, accounting for over 30%, can be achieved through abnormal sound analysis. Sound source localization based on microphone arrays has proven effective in focusing on the troubleshooting scope, preventing potential severe hazards caused by delays in fault removal, and significantly reducing operational and maintenance difficulties and costs. However, existing microphone array-based sound source localization algorithms face challenges in maintaining both accuracy and simplicity and especially suffer from a sharp decrease in performance when dealing with multiple sound sources. This paper presents a multi-sound source localization algorithm for transformer faults based on polyphase filters, integrating the sum-difference monopulse angle measurement technique into the microphone array. Firstly, the signals received from the transformers are divided into multiple subbands using polyphase filters, allowing for multi-source separation and reducing the sampling rate of each subband. Next, the time-domain signals in subbands subject to noise suppression are processed into sum and difference beams. The resulting beam outputs are transformed into frequency-domain signals using the Fast Fourier Transform (FFT), effectively enhancing the signal-to-noise ratio (SNR) for separate sound sources. Finally, each subband undergoes sum-difference monopulse angle measurement in the frequency domain to achieve the high-precision localization of specific faults. The proposed algorithm has been demonstrated to be effective in achieving higher localization accuracy and reducing computational complexity in the presence of actual amplitude-phase errors in microphone arrays. These advantages can facilitate its practical applications. By enabling early targeting of fault sources when abnormalities occur, this algorithm provides valuable assistance to operation and maintenance personnel, thereby enhancing the maintenance efficiency of transformers. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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12 pages, 2662 KiB

Open AccessCommunication

Direction of Arrival Estimation of Coherent Wideband Sources Using Nested Array

by Yawei Tang, Weiming Deng, Jianfeng Li and Xiaofei Zhang

Sensors 2023, 23(15), 6984; https://doi.org/10.3390/s23156984 - 6 Aug 2023

Viewed by 1542

Abstract

Due to their ability to achieve higher DOA estimation accuracy and larger degrees of freedom (DOF) using a fixed number of antennas, sparse arrays, etc., nested and coprime arrays have attracted a lot of attention in relation to research into direction of arrival (DOA) estimation. However, the usage of the sparse array is based on the assumption that the signals are independent of each other, which is hard to guarantee in practice due to the complex propagation environment. To address the challenge of sparse arrays struggling to handle coherent wideband signals, we propose the following method. Firstly, we exploit the coherent signal subspace method (CSSM) to focus the wideband signals on the reference frequency and assist in the decorrelation process, which can be implemented without any pre-estimations. Then, we virtualize the covariance matrix of sparse array due to the decorrelation operation. Next, an enhanced spatial smoothing algorithm is applied to make full use of the information available in the data covariance matrix, as well as to improve the decorrelation effect, after which stage the multiple signal classification (MUSIC) algorithm is used to obtain DOA estimations. In the simulation, with reference to the root mean square error (RMSE) that varies in tandem with the signal-to-noise ratio (SNR), the algorithm achieves satisfactory results compared to other state-of-the-art algorithms, including sparse arrays using the traditional incoherent signal subspace method (ISSM), the coherent signal subspace method (CSSM), spatial smoothing algorithms, etc. Furthermore, the proposed method is also validated via real data tests, and the error value is only 0.2 degrees in real data tests, which is lower than those of the other methods in real data tests. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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15 pages, 400 KiB

Open AccessArticle

Low-Complexity Joint Angle of Arrival and Time of Arrival Estimation of Multipath Signal in UWB System

by Weiming Deng, Jianfeng Li, Yawei Tang and Xiaofei Zhang

Sensors 2023, 23(14), 6363; https://doi.org/10.3390/s23146363 - 13 Jul 2023

Cited by 4 | Viewed by 1699

Abstract

In an ultra-wideband (UWB) system, the two-dimensional (2D) multiple signal classification (MUSIC) algorithms based on high-precision 2D spectral peak search can jointly estimate the time of arrival (TOA) and angle of arrival (AOA). However, the computational complexity of 2D-MUSIC is very high, and the corresponding data model is only based on the dual antennas. To solve these problems, a low-complexity algorithm for joint AOA and TOA estimation of the multipath ultra-wideband signal is proposed. Firstly, the dual antenna sensing data model is extended to the antenna array case. Then, based on the array-sensing data model, the proposed algorithm transforms the 2D spectral peak search of 2D-MUSIC into a secondary optimization problem to extract the estimation of AOA via only 1D search. Finally, the acquired AOA estimations are brought back, and the TOA estimations are also obtained through a 1D search. Moreover, in the case of an unknown transmitted signal waveform, the proposed method can still distinguish the main path signal based on the time difference of arrival of different paths, which shows wider applications. The simulation results show that the proposed algorithm outperforms the Root-MUSIC algorithm and the estimation of signal parameters using the rotational invariance techniques (ESPRIT) algorithm, and keeps the same estimation accuracy but with greatly reduced computational complexity compared to the 2D-MUSIC algorithm. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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20 pages, 444 KiB

Open AccessArticle

Reweighted Off-Grid Sparse Spectrum Fitting for DOA Estimation in Sensor Array with Unknown Mutual Coupling

by Liangliang Li, Xianpeng Wang, Xiang Lan, Gang Xu and Liangtian Wan

Sensors 2023, 23(13), 6196; https://doi.org/10.3390/s23136196 - 6 Jul 2023

Viewed by 1189

Abstract

In the environment of unknown mutual coupling, many works on direction-of-arrival (DOA) estimation with sensor array are prone to performance degradation or even failure. Moreover, there are few literatures on off-grid direction finding using regularized sparse recovery technology. Therefore, the scenario of off-grid DOA estimation in sensor array with unknown mutual coupling is investigated, and then a reweighted off-grid Sparse Spectrum Fitting (Re-OGSpSF) approach is developed in this article. Inspired by the selection matrix, an undisturbed array output is formed to remove the unknown mutual coupling effect. Subsequently, a refined off-grid SpSF (OGSpSF) recovery model is structured by integrating the off-grid error term obtained from the first-order Taylor approximation of the higher-order term into the underlying on-grid sparse representation model. After that, a novel Re-OGSpSF framework is formulated to recover the sparse vectors, where a weighted matrix is developed by the MUSIC-like spectrum function to enhance the solution’s sparsity. Ultimately, off-grid DOA estimation can be realized with the help of the recovered sparse vectors. Thanks to the off-grid representation and reweighted strategy, the proposed method can effectively and efficiently achieve high-precision continuous DOA estimation, making it favorable for real-time direction finding. The simulation results validate the superiority of the proposed method. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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14 pages, 4571 KiB

Open AccessArticle

Nonlinear Frequency Offset Beam Design for FDA-MIMO Radar

by Yanjie Xu, Chunyang Wang, Guimei Zheng and Ming Tan

Sensors 2023, 23(3), 1476; https://doi.org/10.3390/s23031476 - 28 Jan 2023

Cited by 2 | Viewed by 1626

Abstract

The beam pattern of frequency diversity array (FDA) radar has a range–angle two-dimensional degree of freedom, which makes it possible to distinguish different targets from the same angle and brings a new approach to anti-jamming of radars. However, the beam pattern of conventional linearly frequency-biased FDA radar is range–angle-coupled and time-varying. The method of adding nonlinear frequency bias among the array elements of the FDA array has been shown to eliminate this coupling property while still allowing for better beam performance of the emitted beam. In this paper, we obtain a decoupled and time-invariant beam direction map using the FDA-multi-input–multi-output (FDA-MIMO) radar scheme and then obtain a sharp pencil-shaped main sphere beam pattern with range–angle dependence using a linear frequency offset scheme weighted by a Chebyshev window. Finally, the anti-interference performance of the proposed method is verified in an anti-interference experiment. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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18 pages, 756 KiB

Open AccessArticle

Multi-Target Parameter Estimation of the FMCW-MIMO Radar Based on the Pseudo-Noise Resampling Method

by Yao Jiang, Xiang Lan, Jinmei Shi, Zhiguang Han and Xianpeng Wang

Sensors 2022, 22(24), 9706; https://doi.org/10.3390/s22249706 - 11 Dec 2022

Cited by 5 | Viewed by 1936

Abstract

Subspace methods are widely used in FMCW-MIMO radars for target parameter estimations. However, the performances of the existing algorithms degrade rapidly in non-ideal situations. For example, a small number of snapshots may result in the distortion of the covariance matrix estimation and a low signal-to-noise ratio (SNR) can lead to subspace leakage problems, which affects the parameter estimation accuracy. In this paper, a joint DOA–range estimation algorithm is proposed to solve the above issues. Firstly, the improved unitary root-MUSIC algorithm is applied to reduce the influence of non-ideal terms in building the covariance matrix. Subsequently, the least squares method is employed to process the data and obtain paired range estimation. However, in a small number of snapshots and low SNR scenarios, even if the impact of non-ideal terms is reduced, there will still be cases where the estimators sometimes deviate from the true target. The estimators that deviate greatly from targets are regarded as outliers. Therefore, threshold detection is applied to determine whether outliers exist. After that, a pseudo-noise resampling (PR) technology is proposed to form a new data observation matrix, which further alleviates the error of the estimators. The proposed method overcomes performance degradation in a small number of snapshots or low SNRs simultaneously. Theoretical analyses and simulation results demonstrate the effectiveness and superiority. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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11 pages, 6161 KiB

Open AccessCommunication

Leveraging Deep Learning for Practical DoA Estimation: Experiments with Real Data Collected via USRP

by Hyeonjin Chung, Hyunwoo Park and Sunwoo Kim

Sensors 2022, 22(19), 7578; https://doi.org/10.3390/s22197578 - 6 Oct 2022

Viewed by 2456

Abstract

This paper presents an experimental validation of deep learning-based direction-of-arrival (DoA) estimation by using realistic data collected via universal software radio peripheral (USRP). Deep neural network (DNN) and convolutional neural network (CNN) structures are designed to estimate the DoA. Two types of data are used for training networks. One is the data synthesized by the signal model, and the other is the data collected by USRP. Here, the signal model considers both mutual coupling and multipath signals. Experimental results show that the estimation performance is most accurate when training DNN and CNN with the collected data. Furthermore, the estimation tends to be poor in the indoor environment, which suffers from the strong non-line-of-sight (NLoS) signals. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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18 pages, 8648 KiB

Open AccessArticle

Coordinated Positioning Method for Shortwave Anti-Multipath Based on Bayesian Estimation

by Tao Tang, Linqiang Jiang, Paihang Zhao and Na-e Zheng

Sensors 2022, 22(19), 7379; https://doi.org/10.3390/s22197379 - 28 Sep 2022

Cited by 2 | Viewed by 1507

Abstract

Coordinated positioning based on direction of arrival (DOA)–time difference of arrival (TDOA) is a research area of great interest in beyond-visual-range target positioning with shortwave. The DOA estimation accuracy greatly affects the accuracy of coordinated positioning. With existing positioning methods, the elevation angle’s estimation accuracy in multipath propagation decreases sharply. Accordingly, the positioning accuracy also decreases. In this paper, the elevation angle is modeled as a random variable, with its probability distribution reflecting the characteristics of multipath propagation. A new coordinated positioning method based on DOA–TDOA and Bayesian estimation with shortwave anti-multipath is proposed. First, a convolutional neural network is used to learn the three-dimensional spatial spectrogram to make an intelligent decision on the number of single and multiple paths, and to obtain a probability distribution of the elevation angle under multiple paths. Second, the elevation angle’s estimated value is modified using the elevation angle’s probability distribution. The modified elevation angle’s estimated value is substituted into a DOA pseudo-linear observation equation, and the target position’s estimated value is obtained using the matrix QR decomposition iteration algorithm. Finally, a TDOA pseudo-linear observation equation is established using the target estimate obtained in the DOA stage, and the coordinated positioning result is obtained using the matrix QR decomposition iteration algorithm again. Simulation results demonstrated that the proposed method had a stronger anti-multipath capability than traditional methods, and it improved the coordinated positioning accuracy of the DOA and TDOA. Measured data were used to validate the proposed method. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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17 pages, 840 KiB

Open AccessArticle

A New Conformal Map for Polynomial Chaos Applied to Direction-of-Arrival Estimation via UCA Root-MUSIC

by Seppe Van Brandt, Jo Verhaevert, Tanja Van Hecke and Hendrik Rogier

Sensors 2022, 22(14), 5229; https://doi.org/10.3390/s22145229 - 13 Jul 2022

Cited by 1 | Viewed by 1741

Abstract

The effects of random array deformations on Direction-of-Arrival (DOA) estimation with root-Multiple Signal Classification for uniform circular arrays (UCA root-MUSIC) are characterized by a conformally mapped generalized Polynomial Chaos (gPC) algorithm. The studied random deformations of the array are elliptical and are described by different Beta distributions. To successfully capture the erratic deviations in DOA estimates that occur at larger deformations, specifically at the edges of the distributions, a novel conformal map is introduced, based on the hyperbolic tangent function. The application of this new map is compared to regular gPC and Monte Carlo sampling as a reference. A significant increase in convergence rate is observed. The numerical experiments show that the UCA root-MUSIC algorithm is robust to the considered array deformations, since the resulting errors on the DOA estimates are limited to only 2 to 3 degrees in most cases. Full article

(This article belongs to the Special Issue Robust Parameter Estimation with Sensor Arrays in Complex Electromagnetic Environments)

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