Rotational Invariance Techniques Research Articles

A Robust ALOHA and Sequential clustering-based mode estimator for low frequency oscillations in power system using synchrophasors

Accurate estimation of low frequency modes in power system are very much important for improving small signal stability. The parametric model parameters estimator known as Total least square estimation of signal parameters via rotational invariance techniques (TLS-ESPRIT) works effectively even in noisy conditions. However, this model parameter estimator requires prior information about numbers of modes of the signal. There are different Model order (MO) estimation techniques discussed in the recent past, which consider the significant eigenvalues of auto-correlation matrix (ACM) for its estimation. As the eigenvalues of ACM highly affected by bad measurements and Outliers, making these techniques inefficient and harder to automate in real time. So, to overcome aforementioned limitations, this paper proposes a robust mode estimation technique that can precisely detect the signal low frequency modes even in the presence of high variance noise and outliers. So, in this proposed work, an annihilating filter-based low-rank Hankel matrix (ALOHA) technique is implemented to obtain the rank deficient Hankel matrix to nullify the existence of noise and outliers in Phasor measurement unit (PMU) signal, thereafter approximated low rank Hankel matrix is considered for estimation of signals dominant modes. Wherein a sequential clustering technique (Sequential K-Mean++) is implemented for detection of numbers of prominent low frequency modes by segregating eigenvalues of ACM into two opponents i.e the signal and noise subspace. Thereafter the estimated MO is considered for estimation of modes through TLS-ESPRIT. The robustness of the proposed technique is validated by scheduling comparative study with recently developed techniques for synthetic signal, two area data, real PMU data of Western Electricity Coordinating Council (WECC) and oscillatory power data obtained from Western System Coordinating Council (WSCC) 9 bus system and IEEE68 bus system simulated through Real Time Digital Simulator (RTDS).

Broadband VHF lightning radiation sources localization by ESPRIT algorithm

Fast and fine radiation source localization algorithm is of vital importance to lightning warning and protection. Current high-accuracy localization techniques, such as the time reversal technique (TR) and the multiple signal classification (MUSIC), are based on traversal search mechanism, which takes a long time. In this paper, the estimation of signal parameters via rotational invariance technique (ESPRIT) is applied to lightning radiation source localization, and the direction of arrival (DOA) can be directly solved through the covariance matrix, so it is very efficient. For the broadband VHF signal, the incoherent signal method (ISM) is combined with ESPRIT. Two classical structures of uniform L-shaped array and uniform circular array are studied and applied to ESPRIT algorithm. As for the uniform circular array, the fourth order cumulant matrix is constructed to find the translation invariant subarrays. To unwrap the phase ambiguity caused by the calculated phase angle of ESPRIT algorithm, the total least difference of slope (TLDS) principle is proposed. The proposed ESPRIT algorithm is more than 1400 times faster than MUSIC while its localization accuracy is still pretty high, which is able to detect the radiation source under -8 dB signal to noise ratio (SNR) according to the result of numerical simulations, and can map continuous and fine lightning development channel in the experiments on the measured lightning data.

Joint range and velocity super-resolution estimation with Doppler effects for innovative OFDM-based RFA RadCom system

Conventional radar and communication signals face challenges when integrating for accurate sensing in dense electromagnetic environments, especially in scenarios involving high-velocity targets estimation. To address this issue, we propose the random frequency agile-orthogonal frequency division multiplexing-based radar and communication (RFA-OFDM-based RadCom) signal, a novel framework that combines RFA hopping radar signal and OFDM signal. This framework effectively handles high-velocity Doppler scenarios, enhancing electronic countermeasure capabilities. In high-velocity scenarios, achieving accurate range and velocity estimation is crucial. We introduce a comprehensive received signal model that considers intrapulse and intersubcarrier Doppler effects, often overlooked in traditional high-velocity contexts. The proposed two-phase hierarchical perceptual methodology enables joint super-resolution estimation using the shared signal. We transform the shared signal echo model into a uniform linear array-like model and employ the matrix decomposition algorithm based on bidirectional weighted frequency smoothing (BWFS-MD) for decoherence processing. Subsequently, the estimation of signal parameters via rotational invariance techniques (ESPRIT)-complementary integrated subspace fitting (E-CISF) algorithm accurately estimates joint range and velocity. Meanwhile, the contrastive analysis of the mutual impacts between radar and communication functions is conducted. Theoretical analysis and simulation results robustly validate the superior performance of the proposed BWFS-MD algorithm. Furthermore, considering the precision of joint range-velocity estimation, real-time constraints, and super-resolution capability (which is emphasized), the E-CSIF algorithm demonstrates the best overall performance from a comprehensive perspective.

A High-Precision, Ultra-Short Baseline Positioning Method for Full Sea Depth

To fulfill the demand for high-precision underwater acoustic positioning at full sea depth, an ultra-short baseline (USBL) positioning method with the square array based on the least squares estimating signal parameters via rotational invariance techniques (LS-ESPRIT) algorithm is presented in this paper. A combination of beam tracking and beamforming is employed to improve the accuracy of direction-of-arrival (DOA) estimation and, consequently, enhance overall positioning accuracy. In order to mitigate the issue of position jumping resulting from phase ambiguity in traditional four-element cross arrays, we have improved the stability of the positioning algorithm by utilizing a multi-element square array and employing the LS-ESPRIT algorithm for DOA estimation. Furthermore, the signal detection method integrating the correlation coefficient and ascending/descending chirp signals is employed to enhance the reliability of the location algorithm. Simulation analysis and experimental results demonstrate that the proposed algorithm effectively enhances positioning accuracy and improves the problem of jumping in positioning results.

On the Identification of Solid-Like Clusters in a Crystallizing Yukawa System

The crystallization of systems with soft interaction potentials is analyzed for a Yukawa system as an example. The crystallization pathway in the plane of rotational invariants q4 and q6 is studied in detail. The recently proposed invariants bcc1 and bcc2, calculated using 12 nearest neighbors, are applied for the first time to study the crystallization. It is shown that the combination of the rotational invariant technique and the method of Voronoi polyhedra allows us to identify quite simply all types of solid-like clusters formed during the solidification of the system, including bcc-like clusters, which are hardly identified by conventional methods.

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.

A Study on Restoration Plan after Blackout of a System with 100% Inverter Based Resources Considering Bus Inertia

This paper introduces a sequential black-start system restoration procedure in a system with 100% inverter based resources considering system inertia. First, the capability of virtual inertia supported by controlled grid-forming inverters at various locations in a 100% inverter based resources system is calculated through estimation of signal parameters via rotational invariance and nonlinear least square technique; second, a set of radiality constraints is designed for network topology to track inertia value at each bus to find the best restoration paths. Case studies on the modified 39 bus New England system demonstrate that the proposed approach outperforms the existing state-of-the-art approaches in tracking speed and accuracy.

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.

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.

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.