Matrix Pencil Method Research Articles

Pole Extraction of Radar Target in Resonant Region Based on Sliding-Window Matrix Pencil Method

In the complex battlefield environment, stealth radar target recognition has been paid increasing attentions. Previous studies have demonstrated that the stealth target can be identified well by pole extraction based on matrix pencil method (MPM). However, MPM suffers from the difficulty in setting model order and the time-domain resonant response aliasing problem. This paper proposes a new sliding-window matrix pencil method (SW-MPM) based on dynamic order setting and sliding window. Dynamic order setting scheme is used to overcome the difficulty of setting the order in matrix pencil method, while sliding window can avoid the aliasing problem of time-domain resonant response to some extent. The time-domain scattering data used in SW-MPM are obtained by inverse Fourier transform of the frequency domain scattering data in the resonance region. Taking typical stealth aircraft identification as example, the simulation results verify that the proposed method may extract more number of poles with better azimuth consistency, which is beneficial to improve the accuracy of pole-based target identification.

Savitzky-Golay Filter integrated matrix pencil method to identify high impedance fault in a renewable penetrated distribution system

Detection and discrimination of a High Impedance Fault (HIF) is difficult from other noteworthy switching events because of the fault path resistance and current signature. The nonlinear current variation poses several protection challenges to existing methods. To mitigate this issue, a Savitzky-Golay Filter (SGF) integrated with a Matrix Pencil Method (MPM) is used to develop a Transient Detection Index (TDI). The SGF-MPM offers advanced filtering to the noisy signal. The extracted SGF is then reconstructed using MPM and an error is estimated which contains only fault generated components. The Teager energy of the error is estimated and compared with an adaptive threshold for secure detection of HIF. The index is verified for several HIFs and non-HIFs using Aalborg test feeder, and modified IEEE 30 bus test systems. The impacts of noise, harmonics, unbalanced loading of lines, voltage sag, system grounding configuration, distribution operating mode, and different switching events on the performance of the proposed method are verified. A comparison with other existing methods is done. From the detailed analysis, it is found that the percentage of accuracy and dependability for the proposed adaptive HIF detection method are obtained as 98.6% and 98.1% respectively.

Direction of arrival estimation in time modulated linear arrays using matrix pencil method with single snapshot and optimized time steps

The direction of arrival estimation by the time modulated linear array with a proposed novel approach has been analyzed and proven. By merging Matrix Pencil method with time modulated linear array, a great advantage has been obtained by the virtue of using a single snapshot. A new formulation is developed by the authors which combines the Time Modulation and Matrix Pencil methods. The time steps were optimized using differential evolution algorithm for the estimation of the angle of incidence. The effects of the noise level, the number of signal sources, the number of antenna elements and different angles of incidence were examined with the simulations and comparisons were presented. Compared to traditional methods, the simulation results show that the proposed novel approach maintains significant advantages from the viewpoint of estimation accuracy, especially for scenarios with single snapshot number and low SNR.

An Effective Method for Fast Evaluation of Lightning-Induced Voltages on the Overhead Transmission Lines Combining Electromagnetic Topology and Matrix Pencil Method

In this article, an effective method combining electromagnetic topology (EMT) and matrix pencil method (MPM) for the fast evaluation of the lightning-induced voltages on the overhead transmission line (TL) is proposed. First, the EMT of the TL network is established based on the structure characteristic of the TL network and the scattering hypermatrix is constructed according the information of the junctions and terminal loads. Then, the piecewise sampling is performed for the spectrum of lightning signal, and the calculation of the lightning electromagnetic fields (LEMFs) of all observation points along the TL at the sampling frequency point is accomplished. Next, the supervector of the excitation source is constructed to realize the generation of the Baum–Liu–Tesche matrix equation, and the results of the lightning-induced voltages of all junctions on the TL network at the sampling frequencies are obtained. Finally, the lightning-induced voltages at all frequencies are obtained by using MPM to fit the sampled results, and the time-domain results can be generated by inverse fast Fourier transform (IFFT). In the proposed method, the LEMFs above the lossy ground are solved by the C–R formula and those below the lossy ground are calculated by the Cooray formula. Moreover, the feasibility of using EMT to analyze the lightning-induced voltages of the junctions on the TL network and adopting MPM to fit the sampled values of the lightning-induced voltages is verified. The correctness and efficiency of the proposed method are validated and proved by several numerical examples.

Approximating generalized laplace transforms

An extension of the Laplace transform (LT) obtained by using Bell polynomials and Laguerre-type exponentials was recently introduced. Computational techniques for evaluating the transformed functions numerically are developed. To this end, Tricomi’s method is applied in combination with the matrix pencil method for approximating the kernel of generalized Laplace transforms

Decimeter Level Indoor Localization Using WiFi Channel State Information

Indoor localization using WiFi signal parameters is challenging, with encouraging decimeter localization results available with enough line-of-sight coverage and hardware infrastructure. This paper proposes a new 2-dimensional multiple packets based matrix pencil (2D M-MP) method to estimate the Angle of Arrival (AoA) and Time of Flight (ToF) based on WiFi channel state information (CSI). Compared with the conventional parameter estimation algorithms, this method has two advantages. First, 2D M-MP method uses the discrete Fourier transform (DFT) to convert the complex computation into real computation to reduce the computational complexity significantly without losing accuracy. Second, it accumulates multiple CSI packets to improve the parameter estimation accuracy effectively, especially at low values of signal-to-noise-ratio (SNR) environment. To verify the practicability of our proposed 2D M-MP method, we set up a localization system in an actual scenario using commodity WiFi cards which demonstrates that the performance of 2D M-MP method is better than conventional parameter estimation algorithms and can achieve a localization accuracy of 42 cm in indoor hall deployment.

From ESPRIT to ESPIRA: estimation of signal parameters by iterative rational approximation

AbstractWe introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm for rational approximation of the discrete Fourier transform of the given equidistant signal values. We show that ESPIRA can be interpreted as a matrix pencil method (MPM) applied to Loewner matrices. These Loewner matrices are closely connected with the Hankel matrices that are usually employed for signal recovery. Due to the construction of the Loewner matrices via an adaptive selection of index sets, the MPM is stabilized. ESPIRA achieves similar recovery results for exact data as ESPRIT and the MPM, but with less computational effort. Moreover, ESPIRA strongly outperforms ESPRIT and the MPM for noisy data and for signal approximation by short exponential sums.

Efficient Beampattern Synthesis for Sparse Frequency Diverse Array via Matrix Pencil Method.

Due to the introduction of frequency offsets, the pattern synthesis problem of sparse Frequency diverse array (FDA) becomes more complicated than that of the phased array. A typical way to solve this problem is to use a global optimization algorithm, but this is usually time-consuming. In this paper, we propose an efficient non-iterative beampattern synthesis approach for sparse FDA. For a given reference pattern, which can be generated by other synthesis methods, we first sample it uniformly and construct the Hankel matrix with the sampled data. By low-rank processing, a low-rank approximation version of the Hankel matrix can then be obtained. Finally, the matrix enhancement and matrix pencil (MEMP) and matrix pencil (MP) methods are applied to estimate the antenna positions, frequency offsets, and excitations of the obtained array from the approximated matrix. Besides this, two typical FDA frameworks including multi-carrier FDA (MCFDA) and standard FDA (SFDA) are considered. Numerical simulation results prove that the proposed method outperforms the existing methods in terms of synthesis error, average runtime, and percentage of saving elements.

Development of an allocation method to synthesis of unequally spaced arrays with minimum number of elements and mutual coupling considerations

A method is proposed to synthesize unequally spaced arrays so that it has minimum number of elements. Also, it is shown that the proposed method can reduce the total number of elements of equally spaced arrays. The advantage of the proposed method is that it is very fast and straightforward. In this method, the locations of array elements are calculated by considering the mutual coupling between two adjacent array elements, first. After determining the elements locations, two scenarios may be existed. In the first scenario, conventional least square method is proposed. In the second scenario and to increase the accuracy of the final design, recursive least square estimation algorithm is suggested. Mean square error between the desired and synthesized pattern is considered to measure the performance of the method. Several arrays are examined to check the performance of the proposed method. Since, the matrix pencil method (MPM) method has been widely used in the design of nonuniformly spaced arrays, in all examples, the results of MPM technique are considered in comparison process. The obtained results show that the proposed method has a good performance both in reducing the number of array elements and in the accuracy of the synthesized pattern, especially for arrays with beam-shaped pattern such as flat-top and cosecant radiation patterns.

Desempeño del método de Prony y del método del método del haz de matrices en la determinación de las frecuencias complejas naturales de resonancia de un sistema lineal

Characterization of a physical system is an important issue to approach some applied physics and engineering problems. The complex natural resonance frequencies of the system which are included in its impulsive response are characteristic of such system and are part of its description. Few works written in English language show a comparison among discrete methods that extract natural complex frequencies from a system impulsive response. Much less common is to find works written in Spanish language about this important research topic. Given this situation, important discrete numeric methods to estimate the complex natural resonance frequencies of a system through its impulsive response are described, tested and compared in different simulation scenarios in this document. According to the obtained results, the matrix pencil method with a SVD filter is the less sensitive method to the noise, while the Prony method and its different versions are the fastest ones. Scenarios that could be more suitable for each method are discussed.

Matrix Pencil Method and Singular Value Decomposition Application for DOA Estimation Using Linear Antenna Array with Multiple Signal Sources

The practice of estimating the direction of the signal emitted from signal sources using linear antenna arrays is used effectively in both military and civilian radar systems. While the number of signal sources was single in the first studies, the systems that estimated the direction angle of the source have now gained the ability to estimate the direction angle of the signals emitted from more than one signal source at the same time with high accuracy, thanks to the deepening researches. In this study, it is aimed to estimate the angle of incidence of noisy signals emitted from multiple signal sources with the least error by using the Matrix Pencil Method and linear antenna array, which is one of the signal subspaceanalysis methods. In addition, the signals are separated from the noise factor by using the Singular Value Decomposition method. Simulations have been carried out in many different scenarios, and it has been shown that the combination of Matrix Pencil Method and Singular Value Decomposition methods can be used for highly accurate results in estimating the direction of multiple signals coming into the antenna array.

Traveling wave arrival time detection for two-terminal non-contact measurement based on short time matrix pencil scheme

This paper presents an accurate/efficient scheme to distinguish the first and successive time of arrival signals from the fault points of the transmission lines based on non-contact measurement of traveling wave dataset and short time matrix pencil method. In multiple reflection and refraction of traveling waves at characteristic impedance, the first and successive waves overlap at the local and remote terminals, introducing some difficulties in detecting the reflected wave accurately. In such a situation, the detection of the first reflected wave from the second successive wave becomes a challenge, which leads to difficulties in the detection process. Therefore, with the use of a non-contact measurement signal of the overhead transmission line, and with the short-time matrix pencil method of the non-contact dataset, the waves corresponding to the first and successive time reflected signals are distinguished. The simulation results are discussed, and the validity measurement results from the traveling wave generator have been evaluated and analyzed effectively. This indicates that the proposed scheme is robust and accurate for the time of arrival detection for fault location in overhead transmission lines using a non-contact traveling wave dataset with a short time matrix pencil scheme.

Fast Evaluation of Lightning-Induced Voltages on the Transmission Lines Above a Lossy Ground

To achieve the fast evaluation of the lightning-induced voltages on the transmission lines (TLs) above a lossy ground, the matrix pencil method (MPM) is adopted in this article to perform the fast calculation of the lightning electromagnetic field (LEMF). The feasibility of using MPM to accelerate the calculation of the LEMF is discussed and verified. For the observation point above a lossy ground, the Cooray–Rubinstein formula is selected to complete the calculation of the lightning horizontal electric field. For the observation point below a lossy ground, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cooray</i> method is adopted. Then, on the premise of considering the influence of ground impedance and admittance, the iterative expressions of the voltages and currents on the overhead TLs are derived. Moreover, for the TLs with periodic grounding properties, the iterative expression of the voltage at the node is analyzed according to Kirchhoff's law. Finally, the correctness and efficiency of the proposed method are verified by several numerical examples.

Estimate the spectrum of affine dynamical systems from partial observations of a single trajectory data

In this paper, we study the nonlinear inverse problem of estimating the spectrum of a system matrix, that drives a finite-dimensional affine dynamical system, from partial observations of a single trajectory data. In the noiseless case, we prove an annihilating polynomial of the system matrix, whose roots are a subset of the spectrum, can be uniquely determined from data. We then study which eigenvalues of the system matrix can be recovered and derive various sufficient and necessary conditions to characterize the relationship between the recoverability of each eigenvalue and the observation locations. We propose various reconstruction algorithms with theoretical guarantees, generalizing the classical Prony method, ESPRIT, and matrix pencil method. We test the algorithms over a variety of examples with applications to graph signal processing, disease modeling and a real-human motion dataset. The numerical results validate our theoretical results and demonstrate the effectiveness of the proposed algorithms.

Quadratic spacing of the effective gradient area for spatially encoded diffusion NMR

Diffusion NMR experiments rely on the measurement of signal attenuation as a function of the area of diffusion-encoding pulsed magnetic-field gradients. In conventional experiments, arbitrary series of gradient values can be used, and different gradient spacing strategies have different advantages. Ultrafast diffusion NMR relies on the spatial parallelisation of effective gradient area values to collect full 2D diffusion data sets in a single scan. Until recently, only linear spacing was available. We have shown that quadratic spacing can be achieved using a tailored frequency swept pulse. Here we describe the design of the pulse and validate it with numerical spin simulations, that make it possible to check the effect of the quadratic spacing pulse at different stages of the pulse sequence. We also show that quadratic spacing makes it possible to use a recently reported analysis method for diffusion NMR, the Matrix Pencil Method. We describe the results obtained with the MPM and those obtained with the direct exponential curve resolution algorithm (DECRA), which also requires quadratic gradient spacing. Overall, these developments open new opportunities for applications of spatially encoded diffusion experiments, such as ultrafast DOSY NMR and ultrafast Laplace NMR.

Generative model: Impulse response generated from turbulence response in flutter signal

Impulse response facilitates ideal modal parameter estimation in flutter tests. However, impulse excitation is costly, difficult, and risky to execute in flutter engineering tests, so it is difficult to obtain an effective impulse response for modal parameter estimation. Limitations inherent to the physical testing conditions make atmospheric turbulence a common excitation in flutter testing signal processing. Modal analysis of the structural response excited by turbulence from the flutter testing signal is crucial. Existing methods for analyzing structural responses excited by atmospheric turbulence have certain shortcomings. This paper proposes a novel impulse response generative model corresponding turbulence response based on a deep neural network. Frequency and damping ratio calculations become a modal parameter estimation problem for natural excitation relevant to the turbulence response. The turbulence response can be used to calculate the corresponding impulse response through the generative model. The modal parameters of the generated impulse response are estimated by the generative model via Matrix Pencil (MP) method. The results can then be compared with the true model parameters from simulation data. The generative model is shown to accurately generate an impulse response as evidenced by comparison against physical testing data. The impulse response can indeed be generated by the turbulence response based on the generative model. The estimated model parameters of the Stochastic Subspace Identification (SSI) are compared with the generative model via MP in terms of accuracy and computation time, which indicate better on-line monitoring/warning flutter flight test effects. Flutter boundary predictions based on physical testing further validate the engineering applicability of the proposed method.

Direct discrete complex image method for sound field evaluation above a non-locally reacting layer.

Thin layers of porous media are widely adopted in sound absorption and noise control applications due to their compact arrangement. Particularly, porous media with low flow resistivity exhibit complex, non-local reaction behavior. Therefore, sound field prediction above these media is computationally challenging. This is due to singularities and branch points in the expression for the reflection coefficient. This paper introduces a framework based on the direct discrete complex image method to analyze the sound field above a rigid-backed, non-locally reacting porous sample. In contrast to traditional complex image applications, the proposed framework avoids the extraction of the quasi-static term and the poles from the reflection coefficient. Instead, the reflection coefficient-including its singularities-is directly approximated in terms of a series of complex exponentials, whose coefficients are determined with the matrix pencil method. This study analyzes the sound field above two test samples made of melamine and rockwool. The sound field computation is efficient and accurate in the near- and in the far-field. Moreover, predicted specific impedances agree well with experimental in situ impedance measurements. The proposed framework serves for more applications including object detection in multilayered porous grounds or sound propagation prediction in layered atmosphere.

Matrix-Pencil Approach-Based Interference Mitigation for FMCW Radar Systems

A novel matrix pencil-based interference mitigation approach for FMCW radars is proposed in this paper. The interference-contaminated segment of the beat signal is firstly cut out and then the signal samples in the cut-out region are reconstructed by modeling the beat signal as a sum of complex exponentials and using the matrix pencil method to estimate their parameters. The efficiency of the proposed approach for the interference with different parameters (i.e. interference duration, signal-to-noise ratio (SNR), and different target scenarios) is investigated by means of numerical simulations. The proposed interference mitigation approach is intensively verified on experimental data. Comparisons of the proposed approach with the zeroing and other beat-frequency interpolation techniques are presented. The results indicate the broad applicability and superiority of the proposed approach, especially in low SNR and long interference duration situations.

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%.

Visco-elastic material characterization by means of full field Lamb waves

In structural design and structural health monitoring (SHM), the identification of the visco-elastic stiffness tensor of composite materials is considered fundamental, however, the reconstruction of the stiffness coefficients is not straightforward due to the inherent presence of anisotropy and heterogeneity. In the current study, an inverse procedure is proposed based on full field wave dispersion curves to characterize the (18) visco-elastic stiffness parameters of an orthotropic composite plate. The procedure is illustrated by means of finite element method simulations conducted with broadband signals. First, the FEM simulation data, consisting of the in-plane and out-of-plane velocities on the 2D top surface of a composite plate, were converted into the frequency-complex wavenumber domain, including information on elasticity and viscosity, by using the matrix pencil method. The converted data set was then considered as input to a surrogate optimization inversion algorithm, using the semi analytical finite element method (SAFE) as the forward model owing to its accuracy, efficiency and robustness. The full tensorial visco-elastic stiffness parameters were calculated and updated by minimizing the error between the simulated and the calculated complex wavenumbers. The final reconstructed stiffness properties in case of an aluminum plate and of a unidirectional composite laminate show good agreement with the exact input stiffness values, with average errors below 5% for all 18 visco-elastic stiffness parameters.