Matrix Pencil Method Research Articles

Super-Resolution Processing for Multiple Aperture Antenna to Suppress Multipath

Angle estimation for low-altitude targets above the sea surface is a challenging problem due to multipath interference from surface reflection signals, and various approaches have been proposed. This paper proposes a matrix pencil method with multiple apertures. The matrix pencil method effectively responds to dynamic scenarios because it performs better when using a single snapshot than other methods. Also, employing multiple apertures is more economical than using one large aperture. Therefore, we propose a computationally efficient approach using this method and structures. The proposed two-stage MP method incrementally improves the resolution in two stages: in stage 1, we extract the denoised signals at each aperture level, and in stage 2, we further improve the resolution with those signals. In comparison with the angular resolution defined by the half-power beamwidth (HPBW) of a uniform linear array (ULA) antenna with an equivalent number of arrays, the proposed method demonstrated a superior resolution of less than 0.087 of the HPBW at a high signal-to-noise ratio (SNR) of 40 dB, and less than 0.31 of it even at a relatively low SNR of 15 dB, based on 90% of the resolving probability. For the multipath problem, the proposed scheme has the advantage of not requiring prior geometric information, and its performance is demonstrated through simulations to be better than the adaptive beamforming method and the composite monopulse method.

Sliding-Window Matrix Pencil Method for Design Optimization with Limit-Cycle Oscillation Constraints

This paper introduces a novel approach to constrain limit-cycle oscillations in design optimization. The approach builds upon a limit-cycle oscillation constraint that bounds the recovery rate to equilibrium, circumventing the need for bifurcation diagrams. Previous work demonstrated the constraint using approximate recovery rates obtained by evaluating the system state velocity for prescribed states. This work proposes a fully nonlinear matrix pencil method that accurately evaluates the recovery rate based on transient simulations. The proposed method captures the amplitude variation in the recovery rate using a short time window that slides along the time history of a quantity of interest. This sliding-window matrix pencil method is first verified for a typical section model. Sensitivity analyses identify guidelines to obtain accurate recovery rates efficiently. The system is then optimized subject to limit-cycle oscillation, flutter, and side constraints, and the results are compared with the ones based on approximate recovery rates. The sliding-window matrix pencil method allows the optimizer to produce a less conservative design while preventing limit-cycle oscillations at desired operating conditions and amplitudes. The approach introduced in this paper can facilitate the inclusion of limit-cycle oscillation considerations in the design phase of a broad class of nonlinear systems.

Synthesis of maximally sparse conformal circular arc array with a required beam pattern by unitary matrix pencil method

This paper extends the unitary matrix pencil (UMP) method to synthesize maximally sparse conformal circular-arc array with a required beam pattern. Due to the nonlinearity between the circular-arc array pattern and its element pattern, Fourier transform preprocessing for the required beam pattern is introduced to achieve a mathematical expression, i.e., sum of a series of undamped complex exponentials, which is related to array element positions and their excitations. Then, the UMP method is used to determine the reduced number of elements and their position distributions. Moreover, the complex excitations of array elements are reconstructed by obtaining the least-square solution of an over-determined equation. A set of examples for synthesizing sparse conformal circular-arc arrays with different desired patterns and E-type patch element including the mutual coupling are conducted. Results show that the proposed UMP method can achieve a considerably lower pattern reconstruction error with a reduced number of elements than results in the literature, which demonstrates its effectiveness and robustness.

Dispersion and Attenuation Estimation of Ultrasonic Guided Waves using Multi-Subarrays Matrix Pencil Method

Abstract Dispersion and attenuation estimation of ultrasonic guided waves is important for waveguide characterization. Matrix pencil (MP) method has been proposed for multimode complex wavenumber estimation, but its performance highly depends on the signal to noise ratio (SNR), which still brings challenges for high attenuation waveguide evaluation. In addition, the model order, i.e., matrix size in MP method, significantly impacts the dispersion curve extraction. In this study, to avoid the model order interference and compensate the SNR sensitivity of the classical MP algorithm, a multi-subarrays MP method is proposed for accurate dispersion and attenuation estimation. Considering with different Hankel matrix sizes, the multi-subarrays MP method estimates the complex wavenumbers from each pair of submatrices to filter uncertain results. A soft threshold strategy is applied to compensate the noise sensitivity of the estimation. Simulated results prove the proposed method can improve the dispersion and attenuation curve estimation.

Guided elastic wave propagation in elastic metamaterial plate with periodic array of interfacial crack-like voids

Abstract A special kind of elastic metamaterials with periodic unit-cells composed of two layers with internal crack-like voids situated at the interfaces between two neighboring sub-layers is studied. To investigate experimentally guided waves propagation in EMMs with arrays of voids, several specimens with periodic arrays of crack-like voids have been manufactured using additive manufacturing techniques. The elastic waves have been excited by a rectangular piezoelectric transducer bonded at the surface of the specimen, while the wave-fields on the surface of the EMM specimen are measured by a laser Doppler vibrometer. The dispersion characteristics are investigated using the matrix pencil method and band-gaps are observed experimentally.

Multi-method piecewise low-frequency identification

Inter-area frequency modes of electromechanical oscillations are decisive factors that influence the performance of electrical power systems. However, the accurate estimation of these frequencies remains a challenge due to the non-linear behavior of the response system following a disturbance and the strong coupling among the frequencies. This work describes a curve fitting and electromechanical frequency estimation algorithm, called Multi-method Piecewise Identification (MPI), based on a combination of the Matrix Pencil Method (MPM), the Prony method, and Subspace Identification (SSI), choosing the best approximation of an interval basis according to the model accuracy index (MAI) and the mean square error (MSE). The advantages and limitations of MPI were analyzed by computational analyses that were carried out with Python-based code that estimates the low frequencies for several ringdown signals, including oscillating signals from Australian and Brazilian systems that arise after large disturbances. To ensure robustness to random and noisy conditions, the method was tested with a synthetic signal with Gaussian white noise and time-variant frequencies, and compared to the methods mentioned above, the Hilbert–Huang Transform (HHT), and Eigensystem Realization Algorithm (ERA). The MPI has shown robust results and is capable of obtaining a better fitting for the signal than the other methods.

Prediction of amplitude of fault generated travelling wave in medium-voltage grids for fault type classification

This paper proposes a new solution for the classification of short-circuits in medium-voltage distribution grids. The solution requires the measurements of the phase voltages at the time of the short-circuit and the voltage amplitudes of the short-circuit wave resulting from the fault. The values of the voltage before the short-circuit are used to calculate the expected values of the short-circuit wave amplitudes for the different types of short circuits. These calculations are based on an analysis of the charge flow between the capacitances of the power line due to the disturbance. The short-time matrix pencil method was used to detect the incoming short-circuit waves. Tests of the algorithm were carried out on the IEEE 34-bus Feeder model, taking into account the influence of voltage sensors on the measured signal values. The classification algorithm uses only non-zero components due to their relatively low attenuation. Despite that, it achieves high performance in the classification of single- and two-phase short-circuits.

Dual grid energy management strategy for electric vehicles in hybrid microgrid utilizing matrix pencil method

Abstract This study introduces a cutting-edge Matrix Pencil-based Dual Grid Energy Management System (MP-DEMS) aimed at seamlessly integrating electric vehicles (EVs) into power grids while enhancing power quality (PQ) and reliability (PR). Operating within an AC-DC hybrid microgrid (HMG) framework, the MP-DEMS reduces the necessity for additional conversion devices, simplifying the integration of EVs and batteries. The core of the proposed DEMS comprises three key modules: the Wind Energy Management Module (WEMS), Smart Storage and EV Power Coordination (SS-EVPC), and Coordinated Power Conversion Control (CPCC). These modules work together to optimize energy usage, leverage renewable sources effectively, and manage EV charging/discharging schedules to minimize grid impact. An innovative aspect of the MP-DEMS is its use of Matrix Pencil-based techniques, offering several advantages over traditional Discrete Fourier Transform (DFT) methods. These advantages include swift dynamic response, resilience to voltage variations, and precise voltage phase estimation. Software simulations and Hardware-in-the-Loop (HIL-402) testing validate the efficacy of the MP-DEMS approach, showcasing enhanced power transfer capabilities, improved harmonic performance, and superior voltage/frequency regulation within EV-HMS applications. Overall, the MP-DEMS presents a promising solution for advancing the integration of EVs into microgrid systems, contributing to a more sustainable and reliable energy future.

An Innovative Method Based on Wavelet Analysis for Chipless RFID Tag Detection

Chipless RFID tags have attractive low-cost advantages. However, traditional RFID anti-collision algorithms cannot be applied due to a lack of computing and processing capabilities. Problems with multitag detection must be solved to commercialize chipless RFID tags. In this paper, an innovative method for frequency-domain chipless RFID tag detection is proposed. The tags’ scattered signals are processed via wavelet analysis, and a time–frequency plot that can read the code is obtained. When the distance between tags is too close to distinguish in the time–frequency plot, independent component analysis is used to separate individual scattered signals from mixed echo signals; then, the code is read by means of wavelet analysis. To validate the proposed method, C-shaped frequency-domain chipless RFID tag models and a multitag detection simulation scenario were constructed in selected software. The short-time matrix pencil method (STMPM), short-time Fourier transform (STFT), and the proposed method were compared. When the tag spacing is 0.05 m, the code can be read successfully. Compared with the STMPM, the proposed method greatly reduces the computational quantity and shortens the reading time. Furthermore, adjustment of the window width and search step parameters is avoided.

Poles and residues of lossy and dispersive electromagnetic metamaterials

This paper proposes a system-based pole-residue approach to describe loss and dispersion in double-positive (DPS), epsilon-negative (ENG), and epsilon-near-zero (ENZ) isotropic metamaterials. The matrix pencil (MP) method extracts the poles and residues from the damped sinusoids of the singular expansion (SEM) of the impulse responses of the transmitted and reflected waves. The complex values of poles and residues serve as a basis for a computational tool to discriminate between lossless, lossy, and dispersive materials. The extracted poles and residues can also be used to classify the material under test as a DPS, an ENG, or an ENZ metamaterial. The proposed method delivers reliable results even with noisy transmission and reflection data.

High-speed impulsive stimulated Brillouin microscopy

Brillouin microscopy, which maps the elastic modulus from the frequency shift of scattered light, has evolved to a faster speed for the investigation of rapid biomechanical changes. Impulsive stimulated Brillouin scattering (ISBS) spectroscopy has the potential to speed up measurement through the resonant amplification interaction from pulsed excitation and time-domain continuous detection. However, significant progress has not been achieved due to the limitation in signal-to-noise ratio (SNR) and the corresponding need for excessive averaging to maintain high spectral precision. Moreover, the limited spatial resolution also hinders its application in mechanical imaging. Here, by scrutinizing the SNR model, we design a high-speed ISBS microscope through multi-parameter optimization including phase, reference power, and acquisition time. Leveraging this, with the further assistance of the Matrix Pencil method for data processing, three-dimensional mechanical images are mapped under multiple contrast mechanisms for a millimeter-scale polydimethylsiloxane pattern immersed in methanol, enabling the identification of these two transparent materials without any contact or labeling. Our experimental results demonstrate the capability to maintain high spectral precision and resolution at a sub-millisecond integration time for one pixel. With a two-order improvement in the speed and a tenfold improvement in the spatial resolution over the state-of-the-art systems, this method makes it possible for ISBS microscopes to sensitively investigate rapid mechanical changes in time and space.

Compensating voltage waveform distortions using a practical topology of series active power filters

Addressing harmonics, voltage sags, voltage swells, and asymmetrical variations is essential to seamlessly integrate renewable energy sources, electric vehicle charging stations, and power electronics devices into electric power grids. These issues can significantly impact the sinusoidal symmetry of voltage waveforms. Series Active Power Filters (APFs) present a promising solution that can dramatically improve power quality (PQ) by effectively addressing voltage distortions. This paper first identifies several topology-related impracticalities in the existing literature on series APFs, such as using nonlinear loads or linear loads with a current source. Secondly, to understand the motivations behind these impracticalities, commonly used reference extraction methods, namely, Instantaneous Reactive Power Theory (IRPT) and Synchronous Reference Frame (SRF), are tested on a practical topology consisting of a distorted voltage source and a linear RL load. Results conducted in the MATLAB/Simulink environment show that IRPT fails to extract the reference signal under the practical topology, and SRF leads to unacceptable THDs surpassing the 5% threshold mandated by relevant standards set forth for such applications. Thirdly, the matrix pencil method (MPM), a model-based parameter estimation technique that exploits a voltage waveform's underlying exponential signal model to extract the series APF's reference voltage, is proposed. Extensive simulations showcase the superior performance of the MPM-based series APF. It successfully reduces voltage total harmonic distortion (THD) to below 1.13% across various scenarios, including situations involving harmonic-polluted voltage sources, incorporating nonlinear loads, sag and swell phenomenon, and capacitor utilization in DC link implementation.

Moving harmonic source depth estimation by MDFMD-v in a weakly range-depend waveguide

To estimate the depth of a non-cooperative moving sound source in a range-depend waveguide, a passive depth estimation method combining depth-polarity search for a harmonic moving source is proposed in this paper. Firstly, the method obtains each mode parameters at the source and horizontal linear array (HLA) locations by utilizing the modal depth function constrained modal Doppler velocity estimation (MDFMD-v) and matrix pencil (MP) methods, respectively. Subsequently, mode amplitudes are calculated by compressive sensing. To determine the polarity of each mode amplitude, a depth-polarity search method is given in this paper. Finally, a depth ambiguity function with mode amplitude polarity is used to obtain the depth estimation results. Simulation results verify the effectiveness of the method.

ЗАДАЧА ЭКСПОНЕНЦИАЛЬНОГО АНАЛИЗА – ПРИМЕНЕНИЯ, МЕТОДЫ, ПРОБЛЕМЫ

This review article presents the problem of exponential analysis, its applications, limitations and problems that are relevant despite its more than two hundred years of history. During this time, many methods for solving the problem have been developed, but the greatest popularity and efficiency are demonstrated by Prony-like methods: the Padé–Laplace method, Prony method and the matrix pencil method, which are the subject of research in this work. The purpose of the study: to present the current state of the problem of exponential analysis, its main problems and methods for solving them. The main problems of these methods are: the issue of determining the number of exponents, choosing the optimal signal sampling frequency and reducing computational costs. The article presents solutions to these problems. Materials and methods. To solve problems, an analysis of scientific literature was carried out and linear algebra methods were used. Results. Modifications of the methods to solve their problems are described. The algorithm for calculating the Padé approximation with a minimum degree denominator solves the problem of Froissart doublets in the Padé–Laplace method. To increase the accuracy of calculations of Taylor coef-ficients, splines are used in the same method. To select the optimal signal sampling frequency, use the estimation of the matrix condition number in the Prony method. For the matrix pencil method, the problem of computational costs is solved due to its recurrent and multichannel versions. Conclusion. Various formulations of this problem are presented, which find their numerous applications. The limitations, problems of the exponential analysis problem, and their solutions are described. Three parametric methods are considered: Prony, Padé–Laplace and the matrix pencil method.

Improved Subsynchronous Oscillation Parameter Identification with Synchrophasor Based on Matrix Pencil Method in Power Systems

Improved Subsynchronous Oscillation Parameter Identification with Synchrophasor Based on Matrix Pencil Method in Power Systems

A New Topography Profile Estimation Approach for Spaceborne SAR based on Generalized Pencil-Of-Function (GPOF)

A New Topography Profile Estimation Approach for Spaceborne SAR based on Generalized Pencil-Of-Function (GPOF)

Delayed matrix pencil method for local shear wave viscoelastographic estimation

Shear wave (SW) elastography is an ultrasound imaging modality that provides quantitative viscoelastic measurements of tissue. The phase difference method allows for local estimation of viscoelasticity by computing the dispersion curve using phases from two laterally-spaced pixels. However, this method is sensitive to measurement noise in the estimated SW particle velocities. Hence, we propose the delayed matrix pencil method to investigate this problem, and validated its feasibility both in-silico and in-vitro. The performance was compared with the original phase difference method and other two alternative techniques based on lowpass filtering and discrete wavelet transform denoising. The estimated viscoelastic values are summarized in box plots and followed by statistical analysis. Results from both studies show the proposed method to be more robust to noise with the smallest interquartile range in both elasticity and viscosity.

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.

Improving the Resolution of MPM Recovered Relaxometry Parameters with Proper Time Domain Sampling

The matrix pencil method (MPM) is a powerful tool for processing transient nuclear magnetic resonance (NMR) relaxation signals with promising applications to increasingly complex problems. In the absence of signal noise, the eigenvalues recovered from an MPM treatment of transient relaxometry data reduce to relaxation coefficients that can be used to calculate relaxation time constants for known sampling time ∆t. The MPM eigenvalue and relaxation coefficient equality as well as the resolution of similar eigenvalues and thus relaxation coefficients degrade in the presence of signal noise. The relaxation coefficient ∆t dependence suggests one way to improve MPM resolution by choosing ∆t values such that the differences between all the relaxation coefficient values are maximized. This work develops mathematical machinery to estimate the best ∆t value for sampling damped, transient relaxation signals such that MPM data analysis recovers a maximum number of time constants and amplitudes given inherent signal noise. Analytical and numerical reduced dimension MPM is explained and used to compare computer-generated data with and without added noise as well as treat real measured signals. Finally, the understanding gleaned from this effort is used to predict the best data sampling time to use for non-discrete, distributions of relaxation variables.

Super-resolution of positive near-colliding point sources

Abstract In this paper, we analyze the capacity of super-resolution (SR) of one-dimensional positive sources. In particular, we consider a similar setting as in Batenkov et al. (2020, Inf. Inference, 10, 515–572) and restrict the results to the specific case of super-resolving positive sources. To be more specific, we consider resolving $d$ positive point sources with $p \leqslant d$ nodes closely spaced and forming a cluster, while the rest of the nodes are well separated. Our results show that when the noise level $\epsilon \lesssim \mathrm{SRF}^{-2 p+1}$, where $\mathrm{SRF}=(\varOmega \varDelta )^{-1}$ with $\varOmega $ being the cutoff frequency and $\varDelta $ the minimal separation between the nodes, the minimax error rate for reconstructing the cluster nodes is of order $\frac{1}{\varOmega } \mathrm{SRF}^{2 p-2} \epsilon $, while for recovering the corresponding amplitudes $\{a_j \}$, the rate is of order $\mathrm{SRF}^{2 p-1} \epsilon $. For the non-cluster nodes, the corresponding minimax rates for the recovery of nodes and amplitudes are of order $\frac{\epsilon }{\varOmega }$ and $\epsilon $, respectively. Compared with results for complex sources in Batenkov et al. (2020, Inf. Inference, 10, 515–572), our findings reveal that the positivity of point sources actually does not mitigate the ill-posedness of the SR problem. Although surprising, this fact does not contradict positivity’s significant role in the convex algorithms. In fact, our findings are consistent with existing convex algorithms’ stability results for resolving separation-free positive sources, validating their superior SR capabilities. Moreover, our numerical experiments demonstrate that the Matrix Pencil method perfectly meets the minimax rates for resolving positive sources.