Estimation Of Signal Parameters Via Rotational Invariance Techniques Research Articles

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.

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.

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.

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.

Traveling Wave-Based Fault Localization in FACTS-Compensated Transmission Line via Signal Decomposition Techniques

Modern power systems are structurally complex and are vulnerable to undesirable events like faults. In the event of faults in transmission line, accurate fault location improves restoration process, thereby enhancing the reliability of the overall system. Fault location methods (FLMs) are tools which assist in identifying fault locations quickly. However, the accuracy of these FLMs gets affected in the presence of flexible alternating current transmission system (FACTS) devices. Therefore, in this work, the performance of four different signal decomposition techniques aided traveling wave aided FLMs are qualitatively compared in the context of fault localization in FACTS-compensated systems. FLMs based on intrinsic time decomposition (ITD), empirical mode decomposition (EMD), S-transform (ST), and estimation of signal parameters via rotational invariance technique (ESPRIT) are investigated. The accuracy of FLMs is tested for different cases of series, shunt, and series-shunt FACTS-compensated systems. A 500 kV system employed with 100 MVAr FACTS device is used for simulation. The instant of arrival wave at end of transmission line is from all aforementioned FLMs. The obtained ATWs are used in fault localization. Further, the associated percentage errors are calculated. The results suggest that EMD and ESPRIT-based FLMs are more accurate than others.

Recursive ESPRIT Algorithm for Multi-User OAM Low-Overhead AoA Estimation

Multi-user orbital angular momentum (MU-OAM) wireless backhaul systems require precise alignment of transmitted and received OAM beams in line-of-sight (LoS) scenarios. Therefore, a crucial feature for a macro base station (MBS) is to accurately obtain the angle of arrival (AoA) of OAM beams from the small base stations (SBSs) in the system. Considering the limitations of existing OAM-based AoA estimations, we propose a novel super-resolution AoA estimation method, denoted as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">recursive estimation of signal parameters via rotational invariance techniques (ESPRIT)</i> method. The proposed technique is fundamentally different from traditional ESPRIT algorithm: It is not based on the displacement-invariant array structure, but on the recursive characteristic of Bessel functions in OAM signals. With this method, the inter-mode interference of the LoS MU-OAM system can be significantly suppressed by less training overhead, and the performance is close to that of the ideal system.

Harmonic and Interharmonic Estimation using Poincaré Filtering Assisted ESPRIT Method

Accurate estimation of harmonics/interharmonics components is a crucial task in the electric power system. The parametric methods available for this purpose like Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) give accurate result but suffer from very high computational burden. While on the other hand non-parametric methods like Fast Fourier Transform (FFT) are fast but have low spectral resolution. This paper proposes a Poincare plot-based periodicity filter to detect the presence of interharmonics and then selecting an algorithm based on the requirement of spectral resolution. The proposed Poincare plot-based method has been thoroughly tested for its accuracy by varying different parameters associated with interharmonics components. The method has been tested on synthetic signals as well as experimental validation has also been performed by analyzing the current signal from aeration blower installed at GIFT city, Gujarat.

Toeplitz rectification based DOA estimation under the coexistence of mutual coupling and nonuniform noise

It is studied that both the array mutual coupling (MC) and nonuniform noise could degrade direction-of-arrival (DOA) estimators’ performance substantially, and thus it is of necessity to eliminate them before performing DOA estimation. In this paper, two Toeplitz rectification (TR) based methods for DOA estimation under the coexistence of MC and nonuniform noise are proposed. The first method jointly employs the middle subarray scheme and TR to immunize the effects of MC and nonuniform noise, and further applies the estimation of signal parameters via rotational invariance techniques (ESPRIT) to obtain closed-form DOA estimates. This method can yield a good and low-complexity result. The second method first exploits the least squares (LS) criterion to eliminate the nonuniform noise, and then enhances the major part of sample covariance matrix (SCM) via the TR. With this enhanced SCM and subsequent two-stage spectral searches, an improved DOA estimation is provided. Simulation results validate the effectiveness of the proposed two methods.

High-frequency distributed super nested arrays based on Hermitian Toeplitz matrix reconstruction

In array processing, mutual coupling between antenna elements is inevitable, which has an adverse effect on the estimation of parameters. Meanwhile, the expensive computational requirements are also not conducive to the real-time processing. In this paper, a new Hermitian Toeplitz matrix reconstruction algorithm suitable for distributed sparse arrays with contiguous difference co-array is proposed. The computational complexity of the new algorithm is quantitatively analyzed, which is much lower than that of the spatial smoothing algorithm. Then, a new array called distributed super nested arrays (DSNA) is proposed to reduce the mutual coupling between antenna elements. In contrast to super nested arrays (SNA) and nested arrays (NA), the proposed array can further improve the accuracy of direction-of-arrival (DOA) estimation by using the multiscale estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. In high-frequency surface wave radar (HFSWR), the proposed array and algorithm can effectively reduce the mutual coupling in a wide frequency range, improve DOA estimation performance, significantly increase the number of detectable source signals, and reduce computational complexity. Numerical simulations demonstrate the superiority of DSNA using the proposed Hermitian Toeplitz matrix reconstruction algorithm.

High-Resolution Direction of Arrival Estimation of Underwater Multitargets Using Swarming Intelligence of Flower Pollination Heuristics

Developing the parameter estimation, particularly direction of arrival (DOA), utilizing the swarming intelligence-based flower pollination algorithm (FPA) is considered an optimistic solution. Therefore, in this paper, the features of FPA are applied for viable DOA in the case of several robust underwater scenarios. Moreover, acoustic waves impinging from the far-field multitarget are evaluated using the different number of hydrophones of uniform linear array (ULA). The measuring parameters like robustness against noise and element quantity, estimation accuracy, computation complexity, various numbers of hydrophones, variability analysis, frequency distribution and cumulative distribution function of root mean square error (RMSE), and resolution ability are applied for analyzing the performance of the proposed model with additive white Gaussian noise (AWGN). For this purpose, particle swarm optimization (PSO), minimum variance distortion-less response (MVDR), multiple signal classification (MUSIC), and estimation of signal parameter via rotational invariance technique (ESPRIT) standard counterparts are employed along with Crammer–Rao bound (CRB) to improve the worth of the proposed setup further. The proposed scheme for estimating the DOA generates efficient outcomes compared to the state-of-the-art algorithms over the Monte Carlo simulations.

Fast BSC-based algorithm for near-field signal localization via uniform circular array

In this paper, we propose a beam space coversion (BSC)-based approach to achieve a single near-field signal localization under uniform circular array (UCA). By employing the centro-symmetric geometry of UCA, we apply BSC to extract the two-dimensional (2-D) angles of near-field signal in the Vandermonde form, which allows for azimuth and elevation angle estimation by utilizing the improved estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. By substituting the calculated 2-D angles into the direction vector of near-field signal, the range parameter can be conse-quently obtained by the 1-D multiple signal classification (MUSIC) method. Simulations demonstrate that the proposed algorithm can achieve a single near-field signal localization, which can provide satisfactory performance and reduce computational complexity.

Semi-Passive Elements Assisted Channel Estimation for Intelligent Reflecting Surface-Aided Communications

In this paper, we propose a novel semi-passive elements-aided channel estimation framework for intelligent reflecting surface (IRS), where a small portion of IRS reflecting elements are able to process the received signal for facilitating the channel estimation. Specifically, the BS-IRS channel is estimated by applying the estimation of signal parameters via rotational invariance technique (ESPRIT), while the user-IRS channels are estimated by combining the use of total least square (TLS) ESPRIT and multiple signal classification (MUSIC) methods. The required training time of the proposed channel estimation scheme is irrelevant to the number of IRS reflecting elements, thus substantially reducing the training overhead. Simulation results show the great advantages of our proposed scheme over both the conventional compressed sensing (CS)-based channel estimation and cascaded channel estimation schemes.

DOA Estimation of Linear Dipole Array With Known Mutual Coupling Based on ESPRIT and MUSIC

AbstractIn this paper, multiple signal classification and estimation of signal parameters via rotational invariance technique (ESPRIT) algorithms are proposed to estimate the direction of arrival (DOA) of multiple incident signals under known mutual coupling among elements of the antenna array. These algorithms use the same subspace based techniques to achieve the separation of the eigenvectors into two subspaces: the signal space and the noise space. However, ESPRIT only uses the signal space. The performance of subspace based DOA estimation algorithm is evaluated using uniform linear arrays of dipole elements. The simulation results show the exact number of samples and elements, signal‐to‐noise ratio and spacing between the antennas elements used are the most important parameters in the algorithms, to sustain the accuracy of the DOA of the incident signals. The problem of calculating mutual coupling coefficient of the array elements is formed into a matrix has been considered. It is shown from the simulation results that the performance of the DOA estimation techniques considering the mutual coupling effect can be improved by the proposed compensation method. The different results obtained are in good agreement with those of the literature.

Measurement-Based Black-Box Harmonic Stability Assessment of Single-Phase Power Electronic Devices Based on Air Coils

The increasing share of power electronic (PE) devices in public electricity networks has increased the chance of harmonic instabilities, which are caused by the interaction of the device control with the network impedance. Usually, the detailed internal design of PE devices is not available and only measurement-based black-box approaches are feasible for the analysis of harmonic instabilities. A major drawback of such black-box approaches is the need for expensive programmable grid simulators. To overcome that issue, this article proposes a new approach to identify the sensitivity of a PE device for harmonic instabilities, which solely requires two air coils and which can simply be connected to any available power supply including the low voltage (LV) network. By systematically increasing the resulting inductance of air coils, the proposed method is able to identify the frequency regions that are critical with regard to the harmonic stability of the PE device. Critical frequency regions are determined by analyzing the measurement results in time-frequency domain using the estimation of signal parameters via rotational invariance techniques (ESPRITs). The proposed method is applied to a commercially available single-phase photovoltaic (PV) inverter. The critical frequency region has been determined at around 500 Hz, which is confirmed by formal stability analysis.

Toward Ant-Sized Moving Object Localization Using Deep Learning in FMCW Radar: A Pilot Study

We propose a deep learning-based approach to localizing a small moving object with a single millimeter-wave frequency-modulated continuous-wave (FMCW) radar. The main challenge that foils conventional localization techniques, such as 3-D fast Fourier transform (3-D-FFT), Pisarenko method, multiple signal classification (MUSIC), estimation of signal parameters via rotational invariance technique (ESPRIT), Capon’s method, and Burg’s method, is the low signal-to-noise ratio of the reflected signal from millimeter-sized objects. Our key idea is to combine useful but noisy features from classical transforms [e.g., fast Fourier transform (FFT)] with neural networks that can refine and interpret those features into range and angle estimates by training on a large dataset of examples. Importantly, our networks were designed to be translation-equivariant, which enables accurate predictions of unseen object locations and improves the range and azimuth root mean square error (RMSE) scores by 34%–46% and 41%–60%, respectively, over state-of-the-art approaches. This pilot study establishes a new baseline for small-object tracking using FMCW and can enable tracking of small animals, such as ants inside the colony for behavior studies. Our first FMCW-small-object dataset and the source code are publicly available on <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/shikuzen/RA-CNN</uri> .

Fast Computation of Green Function for Layered Seismic Field via Discrete Complex Image Method and Double Exponential Rules

A novel computational method to evaluate the Sommerfeld integral (SI) efficiently and accurately is presented. The method rewrites the SI into two parts, applying discrete complex image method (DCIM) to evaluate the infinite integral while using double exponential quadrature rules (DE rules) for the computation of the finite part. Estimation of signal parameters via rotational invariance techniques (ESPRIT) is used to improve the accuracy and efficiency of extracting DCIM compared to the generalized pencil of function (GPOF). Due to the symmetry of the horizontal layered media, the Green function, representing the seismic fields due to a point source, can be written in the form of Sommerfeld integral in cylindrical coordinate system and be calculated by the proposed method. The performance of the method is then compared to the DE rules with weighted average partition extrapolation (WA), which shows a good agreement, with computational time reduced by about 40%.

Harmonic/interharmonic estimation using standard deviation assisted ESPRIT method

PurposeThis paper aims to accurately estimate harmonics/interharmonics in modern power system. There are several high spectral resolution techniques that have been in use for several years like Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), Prony methods, etc. but these techniques require prior knowledge of number of modes present in the signal. Model Order (MO) estimation techniques have to make a trade-off between accuracy and their speed i.e., computational burden. Therefore, there is always a requirement of a technique that is fast as well as accurate.Design/methodology/approachThe proposed standard deviation (SD) method eliminates the requirement of energy validation test and analyses the distribution pattern, i.e. standard deviation of eigenvalues to identify the number of modes present in the signal. Signal is reconstructed using estimated modes and reconstruction error is obtained to show accuracy of the proposed estimation.FindingsSix test synthetic signals as well as one practical signal have been taken for validating the proposed method. The paper shows that proposed methodology has a better accuracy compared to modified exact model order (MEMO) method in high noise environment and takes very less computation time compared to the exact model order (EMO) method.Practical implicationsThe proposed method has been practically implemented for harmonic/interharmonic analysis at a sewage treatment plant at GIFT City, Gujarat, India. Apart from this the proposed method is modeled in python-based tool and is run into low-cost Raspberry Pi like hardware to create an onsite as well as remote monitoring device.Originality/valueSD-based approach for model order estimation is novel to this area. Further, the proposed method is compared with EMO and MEMO under varying noise conditions to check for accuracy and estimation time.