Rotational Invariance Techniques Research Articles

Geometric Algebra based 2D-DOA Estimation for Non-circular Signals with an Electromagnetic Vector Array

This paper presents two novel methods based on geometric algebra (GA) to estimate two-dimensional (2D) direction-of-arrival (DOA) of non-circular (NC) signals for uniform rectangular array (URA). Traditional methods treat the received NC signals as a long vector which will inevitably lose orthogonality inside each electromagnetic vector sensor (EMVS) and thus miss some information of second-order statistical properties. Furthermore, the computational complexity will also increase. By contrast, the GA-based estimating signal parameter via rotational invariance techniques (ESPRIT) and propagation method (PM) algorithms are proposed to estimation DOA of NC signals. Taking advantage of GA, the relationship among multidimensional signals can be maintained. First, the six components of the EMVS are represented as a multivector in GA space. Then, we construct the GA-based extended covariance matrix to utilize the signal information more completely. The DOA parameters can be estimated through the ESPRIT and PM principle. The proposed GA-based estimation of signal parameter via rotational invariance techniques for NC signals processing (GANC-ESPRIT) can estimate DOA with high estimation accuracy. The proposed GA-based propagation method for NC signals estimation (GANC-PM) uses linear transformation to calculate angle parameters. Our model has much lower memory requirements and less computational burden compared with long vector models. Simulation results demonstrate the robustness and superiority of the proposed GANC-ESPRIT algorithm in terms of angular resolution. Complexity analysis shows that the proposed GANC-PM algorithm performances better with less computations.

Research on Direction Finding Method under Impulsive Noise Based on Nonuniform Linear Array

Direction of arrival (DOA) estimation under impulsive noise has always been an important research area in array signal processing. The traditional methods under impulsive noise mostly rely on prior parameters and have high computational complexity. Based on the filtering theory, we present an effective pretreatment filtering technology to cut out the impulse mixed in the array received data and employ the nonuniform linear array to improve the estimation performance further. First, according to the amplitude characteristics of impulse noise, the pretreatment filtering technology is proposed to cut out the impulse based on the median filter and sliding average filter, which is valid for both strong and weak impulsive noise. Second, the minimum redundant array is adopted to carry out array virtual expansion so that the array aperture can be increased and the estimation performance can be improved. Finally, based on the idea of matrix reconstruction, we propose the improved estimation of signal parameters via rotational invariance techniques algorithm and an improved root multiple signal classification algorithm for DOA estimation. Theoretical analysis and simulation results show that the proposed method has a simple processing process, small calculation load, good array expansion ability, and excellent noise adaptability. Moreover, the proposed methods greatly improve the direction-finding performance under the condition of low signal-to-noise ratio and strong impulsive noise.

A High Degree of Freedom Radiation Near-Field Source Localization Algorithm with Gain–Phase Error

The limitation of the number of estimable sources in the localization of radiation near-field sources with gain–phase error is examined in this paper. When only the reference element has no gain–phase error, a new method based on an accurate model is proposed to enhance the maximum number of estimable sources. Based on the location parameter details of the auxiliary source, the method first derives the gain–phase error estimate matrix. Second, the source steering vector including errors is estimated using the total least square estimating signal parameter via rotational invariance techniques (TLS-ESPRIT), and the time-shifted data matrix is built utilizing the space–time combination idea, thus increasing the degree of freedom of the array. Then, the source steering vector containing the error is modified by the error compensation matrix constructed according to the moment of gain–phase error estimation. Finally, the estimated values of the source position parameters are obtained by using the closed formula of the gain phase of the modified source steering vector and the source position parameters. The experimental results show that the maximum estimable source number of the proposed algorithm is significantly improved compared with the previous results when only the reference array element has no gain–phase error. When the array number is 5 and 9, the maximum estimable source number of the algorithm is 9 and 17, respectively.

Enhanced IpD2FT-Based Synchrophasor Estimation for M Class PMUs Through Adaptive Narrowband Interferers Detection and Compensation

One of the most challenging problems in the design of next-generation Phasor Measurement Units (PMUs) is related to the need to minimize the impact of multiple harmonics and out-of-band interharmonics (OOBI) on the measurement of synchrophasors over short observation intervals. Most of the existing solutions aim at removing such narrowband disturbances before synchrophasor estimation. However, when data records are short, accurate OOBI filtering may be infeasible. The algorithm described in this paper tackles this problem through a prior estimation of the number and the frequency of the significant narrowband interferers emerging from the noise floor. This result is achieved using a non-parametric signal detector based on random matrix theory and hypothesis testing, followed by the application of the estimation of signal parameters via the rotational invariance technique (ESPRIT). Once the number and the frequency of the narrowband components are known, these parameters are used to augment the dimension of the frequency-domain linear system of equations employed by the Interpolated Dynamic Discrete Fourier Transform (IpD2FT) for synchrophasor estimation. The results of multiple simulations confirm not only that the proposed approach for narrowband components detection is robust and more accurate than other model-order estimation algorithms described in the scientific literature, but also that the synchrophasor estimation accuracy over two-cycle observation intervals is generally higher than using other for M Class PMUs algorithms when OOBIs or a mixture of OOBIs and harmonics are considered.

Parallel Complementary Virtual Arrays Algorithm for Direction of Arrival (DOA) Estimation

This Paper discusses the challenges faced by previous method 2D Direction of Arrival (DOA) systems, such as low degrees of freedom, poor resolution, and significant estimation errors in scenarios with small snapshots. In response to these issues, the present method proposes a low-complexity 2D Direction of Arrival (DOA) estimation algorithm based on a parallel complementary virtual array.
 The algorithm utilizes two mutually parallel complementary linear arrays to generate a virtual array, addressing the limitations of traditional parallel arrays. It constructs an extended matrix with enhanced 2D angular degrees of freedom using covariance and cross-covariance matrices. The final step involves obtaining automatic matching 2D angle estimates through Singular Value Decomposition (SVD) and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT).
 In comparison to traditional 2D DOA estimation methods, the proposed algorithm better exploits the information from the array's received data. It can identify more incoming signals, offering high resolution without the need for 2D linear search or angle parameter matching. Importantly, it demonstrates effective estimation even in scenarios with low Signal-to-Noise Ratio (SNR) and small snapshots. Experimental simulation results validate the effectiveness and reliability of the proposed algorithm.

Comparison of modelled pursuits with ESPRIT and the matrix pencil method in the modelling of medical percussion signals

The objective of this paper is to compare Modelled Pursuits (MoP), a recently developed iterative signal decomposition method, with more established matrix based subspace methods used to aid or automate medical percussion diagnoses.Medical percussion is a technique used by clinicians to aid the diagnosis of pulmonary disease. It requires considerable expertise, so it is desirable to automate this process where possible. Previous work has examined the application of modal decomposition techniques, since medical percussion signals (MPS) can be intuitively characterised as combinations of exponentially decaying sinusoidal (EDS) vibrations. Best results have typically been reported with matrix based subspace methods such as Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) and the Matrix Pencil Method (MPM).Since ESPRIT and MPM are computationally expensive, this paper investigates whether an iterative method such as MoP can produce similar results with less computation and/or memory overheads. Using randomly generated synthetic signals designed to replicate typical ‘tympanic’ and ‘resonant’ percussion signals, we compared each method: MoP, ESPRIT, and MPM, for accuracy, speed and memory usage.We find that for low Signal to Noise Ratios (SNRs) MoP gives less accuracy than both ESPRIT and MPM, however for high SNRs (as would be typically encountered in a clinical setting) it is more accurate than MPM but less accurate than ESPRIT. We conclude that in embedded clinical applications where both operations-per-second and memory-usage are a factor, MoP is less computationally intensive than ESPRIT and thus is worth considering for use in those contexts.

Coherent DOA Estimation Algorithm with Co-Prime Arrays for Low SNR Signals

The Direction of Arrival (DOA) estimation of coherent signals in co-prime arrays has become a popular research topic. However, traditional spatial smoothing and subspace algorithms fail to perform well under low signal-to-noise ratio (SNR) and small snapshots. To address this issue, we have introduced an Enhanced Spatial Smoothing (ESS) algorithm that utilizes a space-time correlation matrix for de-noising and decoherence. Finally, an Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is used for DOA estimation. In comparison to other decoherence methods, when the SNR is −8 dB and the number of snapshots is 150, the mean square error (MSE) of the proposed algorithm approaches the Cramér–Rao bound (CRB), the probability of resolution (PoR) can reach over 88%, and, when the angular resolution is greater than 4°, the estimation accuracy can reach over 90%.

A novel energy‐efficient routing protocol for industrial WSN using hybrid COOT‐LS algorithm with LSTM‐based DOM prediction

SummaryIndustrial wireless sensor networks (IWSNs) are very important to improve and simplify the way to manage, monitor, and control industrial factories. IWSNs have many benefits, but because of their vulnerability to extremely complex and variable industrial contexts, they also limit some of the potential that is currently available and present difficulties on numerous fronts. The proposed work develops energy‐efficient routing technique to minimize the overall energy consumption. Heterogeneous mobile nodes are randomly deployed in the experimental region; then, region‐based grid formation is done in the proposed method. In each grid, the base node is selected utilizing the parameters like residual energy and distance of mobile nodes. Hybrid COOT‐HOA optimization is used in the proposed method for selecting the optimal base node in each grid. A deep learning‐based machine learning algorithm called long short‐term memory (LSTM) is utilized to predict the future direction of movement (DOM) of each mobile node in the grid. Estimation of signal parameters via rotational invariance technique (ESPRIT) is utilized to find an active zone from the sender node to direction of base node. Then, the sender node transmits the data to its nearest node in the active region. This proposed energy‐efficient routing algorithm is tested with several metrics which attains better performance like 94% packet delivery ratio, 7% packet loss, average residual energy of 9.5 J, and 3.4 Mbps throughput. Thus, the energy‐efficient routing protocol used in the proposed approach transfers the data in an energy‐efficient manner for IWSN.

A Two-Stage Data-Driven Method for Estimating the System Inertia Utilizing Event-Driven PMU Measurements

With the increasing penetration level of renewable energy resources with less system inertia, accurate estimation of the power system inertia has become a critical issue for maintaining the frequency stability of the entire power system. To tackle out this challenging task, a two-stage data-driven method is proposed in this paper for estimating the system inertia from disturbed PMU measurements. First, by integrating its low-order system frequency response model with the first-order turbine model, analytical expressions of the frequency response under the steady-state and these transient oscillatory components are derived. Then, based on this parametric model, a two-stage estimation algorithm will be developed. At the first stage, system parameters of oscillatory components can be extracted from PMU measurements by Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT). By utilizing frequency measurement data from PMUs and those estimated parameters from the ESPRIT algorithm, a weighted nonlinear least square approach is applied at the second stage to estimate physical parameters such as system inertia, damping coefficient, turbine time constant, and regulation coefficient. To validate the effectiveness of the proposed method, simulation studies of IEEE 39- bus system is investigated. Historical PMU measurements from various contingencies of Taiwan Power System will also be explored. All of these results demonstrated that the proposed method provides satisfactory performances with the mean relative error less than 10%. Comparisons with other existing methods are performed to demonstrate the advantage of the proposed method.

Polarization Direction of Arrival Estimation Using Dual Algorithms Based on Time-Frequency Cross Terms

In radar array signal processing, weak nonstationary polarization signal direction of arrival (DOA) estimation is a challenging and significant issue when both strong and weak nonstationary signals coexist. Time-frequency (T-F) analysis is an effective method to deal with nonstationary signals. In the last decade, spatial time-frequency distributions (STFDs) have been proposed for multiple dual-polarization antenna arrays and efficaciously used for nonstationary signal DOA estimation. In this article, we introduced a novelty means for estimating weak nonstationary polarization signal DOA by utilizing spatial polarimetric time-frequency distributions (SPTFDs) of cross terms when there are strong nonstationary polarization interference signals and additive Gaussian white noise. The cross terms’ SPTFDs are considered via a replaceability matrix for data covariance in multiple signal classification (MUSIC) and the estimation of signal parameters using the rotational invariance technique (ESPRIT). Combining the STFDs of cross terms with polarization information about weak nonstationary signals improves signal DOA estimation accuracy. The combined MUSIC and ESPRIT are used in the algorithm to further ensure the success probability and accuracy of DOA estimation. Through simulation analyses, the proposed algorithm is more suitable for the required application scenarios than other algorithms and is superior to other algorithms.

An Improved Two-Stage Spherical Harmonic ESPRIT-Type Algorithm

Sensor arrays are gradually becoming a current research hotspot due to their flexible beam control, high signal gain, robustness against extreme interference, and high spatial resolution. Among them, spherical microphone arrays with complex rotational symmetry can capture more sound field information than planar arrays and can convert the collected multiple speech signals into the spherical harmonic domain for processing through spherical modal decomposition. The subspace class direction of arrival (DOA) estimation algorithm is sensitive to noise and reverberation, and its performance can be improved by introducing relative sound pressure and frequency-smoothing techniques. The introduction of the relative sound pressure can increase the difference between the eigenvalues corresponding to the signal subspace and the noise subspace, which is helpful to estimate the number of active sound sources. The eigenbeam estimation of signal parameters via the rotational invariance technique (EB-ESPRIT) is a well-known subspace-based algorithm for a spherical microphone array. The EB-ESPRIT cannot estimate the DOA when the elevation angle approaches 90°. Huang et al. proposed a two-step ESPRIT (TS-ESPRIT) algorithm to solve this problem. The TS-ESPRIT algorithm estimates the elevation and azimuth angles of the signal independently, so there is a problem with DOA parameter pairing. In this paper, the DOA parameter pairing problem of the TS-ESPRIT algorithm is solved by introducing generalized eigenvalue decomposition without increasing the computation of the algorithm. At the same time, the estimation of the elevation angle is given by the arctan function, which increases the estimation accuracy of the elevation angle of the algorithm. The robustness of the algorithm in a noisy environment is also enhanced by introducing the relative sound pressure into the algorithm. Finally, the simulation and field-testing results show that the proposed method not only solves the problem of DOA parameter pairing, but also outperforms the traditional methods in DOA estimation accuracy.

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

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.

Quasi-Synchronous Random Access for Massive MIMO-Based LEO Satellite Constellations

Low earth orbit (LEO) satellite constellation-enabled communication networks are expected to be an important part of many Internet of Things (IoT) deployments due to their unique advantage of providing seamless global coverage. In this paper, we investigate the random access problem in massive multiple-input multiple-output-based LEO satellite systems, where the multi-satellite cooperative processing mechanism is considered. Specifically, at edge satellite nodes, we conceive a training sequence padded multi-carrier system to overcome the issue of imperfect synchronization, where the training sequence is utilized to detect the devices’ activity and estimate their channels. Considering the inherent sparsity of terrestrial-satellite links and the sporadic traffic feature of IoT terminals, we utilize the orthogonal approximate message passing-multiple measurement vector algorithm to estimate the delay coefficients and user terminal activity. To further utilize the structure of the receive array, a two-dimensional estimation of signal parameters via rotational invariance technique is performed for enhancing channel estimation. Finally, at the central server node, we propose a majority voting scheme to enhance activity detection by aggregating backhaul information from multiple satellites. Moreover, multi-satellite cooperative linear data detection and multi-satellite cooperative Bayesian dequantization data detection are proposed to cope with perfect and quantized backhaul, respectively. Simulation results verify the effectiveness of our proposed schemes in terms of channel estimation, activity detection, and data detection for quasi-synchronous random access in satellite systems.

A Convolutional Neural Network for Parameter Estimation of the Bi-GTD Model

In this paper, a novel parameter estimation method based on a convolutional neural network (CNN) is proposed to extract geometrical features of radar objects. The CNN’s design is inspired by the inversion process of a physically relevant model, called the geometrical theory of diffraction (GTD) model, whose bistatic form can be used to describe the bistatic scattering response from the target in the netted radar system. This model-inspired inversion method can automatically compensate for phase errors between multiple signal channels and obtain better parameter estimation performance than traditional methods, such as the orthogonal matching pursuit (OMP), the estimation of signal parameters via rotational invariance techniques (ESPRIT) and the multiple signal classification (MUSIC). The experimental results not only verify the validity of the proposed intelligent inversion method but also demonstrate the interpretability and generalization ability of the CNN, whose architecture is designed based on mathematical derivation.

Deep Learning-Based Multipath DoAs Estimation Method for mmWave Massive MIMO Systems in Low SNR

To realize the direction-of-arrivals (DoAs) estimation without the prior information about the multipath number, a novel method using the deep learning is introduced for the millimeter (mmWave) massive multiple-input and multiple-output (MIMO) systems. In particular, the DoAs estimation is decomposed into three sub-problems, which are solved by the corresponding convolutional neural network (CNN), respectively. The estimation of multipath number is achieved by a multi-label classification model using the proposed CNN-I. Then, the proposed CNN-II is introduced for the DoA estimation of the line-of-sight (LOS) path. Based on the predicted multipath number obtained by the CNN-I, a regression model using the proposed CNN-III is applied for the DoAs estimation of non-line-of-sight (NLOS) paths. The proposed DoAs estimation method is implemented by learning the non-linear relationship between the sample covariance matrix of the received signal and the angles, thus reconstructing the mapping model. A series of results validate the superiority of the proposed DoAs estimation method in low signal-to-noise-ratio (SNR) regimes. The CNN-I is capable of achieving the good multipath number estimation performance across a range of SNRs. The classification model based on the proposed CNN-II and the regression model using the proposed CNN-III achieve the lower DoAs estimation root mean square error (RMSE) compared with some deep learning-based methods, estimation of signal parameters via rotational invariance techniques (ESPRIT) and Root-MUltiple SIgnal Classification (Root-MUSIC) methods. Remarkably, the proposed method using the CNN-II exhibits the good robustness in the DoA estimation of the LOS path. Furthermore, the low DoAs estimation RMSE is also achieved in the uniform planar array.

A Novel Subspace Decomposition with Rotational Invariance Technique to Estimate Low-Frequency Oscillatory Modes of the Power Grid

This paper proposes modified Karhunen–Loeve transform with total least square estimation of signal parameters using rotational in-variance technique (MKLT-TLS-ESPRIT) to approximate the low-frequency oscillatory modes. MKLT decreases the impact of highly correlated additive colored Gaussian noise (ACGN) from the signal by differentiating the correlation matrix w.r.t from the final time instance. A quantitative study of the suggested method with other estimation methods is used to evaluate the effectiveness of the proposed method. Monte Carlo simulations with 50,000 runs are conducted to test the robustness of the estimation scheme for MKLT-TLS-ESPRIT. The evaluation of the efficiency of the proposed method in real-time perspective, the two-area system, and New England sixty-eight bus test system has been considered. The analysis shows that the suggested methodology correctly measures the interarea modes and lowers their mean and standard deviation to a minimum value.

Mixed Near-Field and Far-Field Sources Localization via Oblique Projection

This paper presents a novel mixed source localization algorithm based on high-order cumulant (HOC) and oblique projection techniques. To address the issue of lower accuracy in near-field source (NFS) localization compared to the far-field source (FFS) localization, the presented algorithm further enhances the accuracy of NFS localization. First, the FFS’s direction-of-arrival (DOA) estimate is acquired utilizing a multiple signal classification (MUSIC) spectral peak search. To classify mixed sources more effectively, we utilize the oblique projection technique, which can successfully prevent FFS information from influencing the estimation of NFS parameters. A HOC matrix with solely NFS DOA information is built by choosing array elements in a specific sequence. The estimation of the NFS DOA is then derived using the estimation of signal parameters via a rotational invariance technique (ESPRIT)-like algorithm. Finally, the NFS range is acquired by a MUSIC search. The performance of the presented algorithm is discussed in several aspects. Compared to existing matrix difference methods, the presented algorithm, which adopts the oblique projection method, achieves superior results in the separation of mixed sources. Without excessively increasing the computational complexity, it not only ensures the performance of localization parameter estimation for FFS but also estimates the NFS with higher precision. The numerical simulations attest to the superior performance of the presented algorithm.

An auxiliary source-based near field source localization method with sensor position error

In order to avoid the influence of errors brought by simplified model and sensor position error on near-field source location, a non-uniform linear array source location algorithm using precise model and based on auxiliary source (AS) is proposed under the condition of sensor position error. The array model used in this algorithm has position errors except for reference sensor. AS method is used to accurately estimate the position of the special sensor. Then, the generalized eigenvalue including the estimated position of the special sensor is obtained by using the fourth-order cumulant and the idea of Least Squares-Estimating Signal Parameter via Rotational Invariance Techniques (LS-ESPRIT). Finally, the estimation results of the source location can be obtained by using the correlation formula. In addition, the Cramér Rao Lower Bound (CRLB) is proposed for the parameter estimation problem, which determines a lower bound for the variance of any unbiased estimator. Two cases of near - field source and mixed source are simulated respectively. The results show that the proposed algorithm is applicable to both cases and has very accurate source location estimation results.

Acoustic-Based Rolling Bearing Fault Diagnosis Using a Co-Prime Circular Microphone Array.

This study proposes a high-efficiency method using a co-prime circular microphone array (CPCMA) for the bearing fault diagnosis, and discusses the acoustic characteristics of three fault-type signals at different rotation speeds. Due to the close positions of various bearing components, radiation sounds are seriously mixed, and it is challenging to separate the fault features. Direction-of-arrival (DOA) estimation can be used to suppress noise and directionally enhance sound sources of interest; however, classical array configurations usually require a large number of microphones to achieve high accuracy. To address this, a CPCMA is introduced to raise the array's degrees of freedom in order to reduce the dependence on the microphone numbers and computation complexity. The estimation of signal parameters via rotational invariance techniques (ESPRIT) applied to a CPCMA can quickly figure out the DOA estimation without any prior knowledge. By using the techniques above, a sound source motion-tracking diagnosis method is proposed according to the movement characteristics of impact sound sources for each fault type. Additionally, more precise frequency spectra are obtained, which are used in combination to determine the fault types and locations.

Artificial Neural Network and ESPRIT-TLS Combination-Based Approach for Fault Bearing Recognition in Induction Machines

Several studies have been conducted in recent decades on the detection of bearing faults to develop methods for real-time monitoring. Faults are found in almost all electromechanical systems and the major cause of damage to machinery, resulting in serious accidents to humans and material environments. While methods such as MCSA (Motor Current Signature Analysis) and PCA (Principal Component Analysis) have been widely used for obtaining and analyzing the machine's stator current and reducing its dimensions and noise, they do not allow for easier detection and parameter estimation when a defect appears, and sometimes help from an expert is needed to explain the signals. In this paper, the use of ANN-GA (Artificial Neural Networks-Genetic Algorithm) is investigated in combination with the best variant of the ESPRIT (Estimation of Signal Parameters via Rotational Invariant Techniques) method applied on stator current signals for efficient real-time bearing fault detection, to avoid any help being required from experts. MATLAB simulations of these variants revealed that the TLS variant highly discriminates the fault. By using this variant to prepare the data in the search of the best ANN model, in combination with genetic algorithms (used for optimizing the search of ANN parameters), two architectures capable of discriminating this bearing fault in real time in time and frequency domain were obtained.