Rotational Invariance Techniques Research Articles

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

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

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

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

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

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

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

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

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.

RCS Diagnostic Imaging Using Parameter Extraction Technique of State Space Method

AbstractThe signature extraction and processing are the key aspects of enhancing recognition ability for radar target characteristics. In this paper, to reveal the intrinsic property of the target and improve the accuracy of radar cross section (RCS), we proposed RCS diagnostic imaging technique, extracting the parameters of scattering center model by state space method (SSM), to analyze the signature of GTD‐based returns. To demonstrate the effectiveness of SSM, the comparison with estimating signal parameter via rotational invariance techniques method by the analysis of goodness‐of‐fit and root mean square error, reconstructing the RCS profile through original signal model, and employing SSM to extract the signature of specular and creeping wave from the PEC sphere. Furthermore, the RCS diagnostic imaging by SSM extracting position and amplitude is discussed, and range‐isolated pole technique specific to the creeping wave extraction is addressed the advantage of SSM.

Harmonic/inter-harmonics detection using modified exact model order-based ESPRIT

Problems related to harmonics/interharmonics are growing rapidly in power system with the increasing use of power electronic devices. This paper focuses on estimating the harmonics/interharmonics using modified exact model order - estimation of signal parameters via rotational invariance technique (MEMO-ESPRIT). The modified exact model order (EMO) method is used to reduce the computational burden in detecting the harmonics/interharmonics components. Comparison has been made between EMO and MEMO to demonstrate the effectiveness of MEMO based method. Moreover, various parameter values like noise, size of autocorrelation matrix, etc. are varied to see their effects on the computational burden and accuracy of MEMO method. The performance of MEMO-ESPRIT algorithm is analysed with synthetic signals, single-phase PWM inverter and 250 kW grid-connected PV arrays using MATLAB/Simulink. The root-mean-square relative error has been obtained to validate the accuracy of the algorithm.

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.

DOA Estimation Method in Echo-localization Ability for Human-beings

The principle of echo-localization processing of human beings is quite similar with animals like bats and dolphins, which has been widely applied in sonar. Direction of Arrival (DOA) methods plays an important role in estimating the radar, sonar and many other echo-localization communication fields. Typical methods in resolving echo-localization problems including classical (Multiple Signal Classification) MUSIC, (Estimation of Signal Parameter via Rotational Invariance Technique), ESPRIT and compressed sensing. The echo-localization methods and the resolving ambiguity methods via uniform array are systematically introduced in this paper. On this basis, the fast and accurate algorithms for human-being echo-localization in parameter (azimuth angle, elevation angle and range) estimation of signal are further introduced from time domain and frequency domain. The accuracy of the angle and distance estimation of the algorithm calculated by computer simulation experiment is over 99.9% and 97% respectively. The effectiveness of DOA method was verified according to MUSIC algorithm, which provides a rapid and accuracy information in echo-localization ability of human being.

Performance Analysis of 2D-ESPRIT Algorithm for URA in Estimation of 2D-DOA in Massive-MIMO Systems

Purpose: The performance of smart antenna is affected by antenna array configuration and the direction of arrival estimation (DOA) algorithm used .To have a suitable DOA for an uniform rectangular array (URA),The performance of two dimensional estimation of signal parameters via rotational invariance techniques (2D-SPRIT) that are applied for two different planar dispositions of antenna for URA in Massive Multiple Inputs Multiple Output (Massive MIMO) systems when subjected to the same simulation conditions is comparatively analyzed. The performance of the proposed 2D-ESPRIT algorithm with URA in vertical plane (the case of full-dimensional MIMO) has been compared with that of the existing 2D-ESPRIT algorithm that is applied with URA in horizontal plane.&#x0D; Methodology: Implementation and simulation of analyzed 2D-ESPRIT algorithms was done in MATLAB and compared considering computational complexity efficiency, DOA estimation precision, estimation failure and variation of Root mean square Error (RMSE) with Signal to Noise Ratio (SNR) and angular spread. MATLAB simulation results got from similar input parameters in a multipath environment are compared to derive a conclusion.&#x0D; Findings: Simulation results show that the proposed 2D-ESPRIT algorithm applied in vertical plane outperforms the existing 2D-ESPRIT algorithm applied in horizontal plane for all considered performance criteria that include estimation precision, running time and Root mean square error (RMSE).&#x0D; Recommendation: Other researchers interested in working on 2D-ESPRIT algorithms are recommended to improve the work reported in this paper by further reducing computational complexity observed in 2D-ESPRIT algorithm with URA in vertical plane at large antenna array size to reflect the standard of full-dimension MIMO.

Real-time intelligent system for wind turbine monitoring using fuzzy system

In these last ten years, the use of wind energy has become a strategic alternative in several countries; the increase in reliability of these systems has become a crucial issue. This is explained by the economic, human or environmental) losses that could generate even if only for a moment, their malfunctioning or their shutdown. In this context, many research methods have been developed to monitor these machines during their operation time. But the problem with these methods was that they did not take into account the criticality, the type of fault, or the degradation degree of the components to trigger an alert, so that the real-time monitoring and the decisions taken were distorted. In this work, four types of defects encountered in wind turbines are studied. Three models of the fuzzy logic system are compared on the severity of the faults in order to know which one is the most efficient. However, an estimation of the fault parameters by the Fast-Estimation of Signal Parameters via Rotational Invariant Techniques (Fast-ESPRIT) algorithm followed by an identification of each fault type by the Classification Algorithm of Fault Harmonics (CAFH) algorithm are first performed. The obtained results show the possibility of monitoring the severity of faults in electric induction machines using the Tsukamoto model in real time. The simulations are performed by using MATLAB software and the obtained results demonstrate the feasibility of such a system.

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.

Coherent Targets Parameter Estimation for EVS-MIMO Radar

As an emerging technique for detection, electromagnetic vector sensor multiple-input multiple-output (EVS-MIMO) radar has attracted extensive interest recently. This paper focuses on the coherent targets issue in EVS-MIMO radar, and a spatial smoothing estimator is developed to estimate the multiple parameters. It first recovers the rank of the array data via forward spatial smoothing. Then, it estimates the elevation angles via the rotational invariance technique. Combined with the vector cross-product method, the azimuth angles are obtained. Thereafter, with the previously achieved direction angles, the polarized parameters are acquired by using the least squares technique. Unlike the existing polarization smoothing techniques, the proposed estimator is able to estimate the two-dimensional direction parameter. Furthermore, it can provide a polarized parameter of the target. In addition, the proposed estimator is computationally efficient, since it offers closed-form and automatically paired solutions to all the parameters. Numerical experiments are carried out to show its superiority and effectiveness.

Search-Free Angle, Range, and Velocity Estimation for Monostatic FDA-MIMO

The monostatic frequency diverse array multiple-input multiple-output (FDA-MIMO) has attracted much attention recently. However, much research is concentrated on the estimation of angle-range parameters based on the FDA-MIMO radar, and the velocity has not been considered. In this study, we propose a search-free method to estimate these parameters. To overcome the problem of the high computational complexity associated with the searching estimation algorithms, the parallel factor (PARAFAC) decomposition is introduced to estimate the space-time steering vector. Next, we can utilize the least square method to solve the angle, range, and velocity of each target. In addition, the Cramér–Rao bounds (CRBs) of angle, range, and velocity are derived. Besides, the other performance analysis consists of the root mean square error, and complexity is derived. We compare the PARAFAC decomposition algorithm with the estimation of signal parameters via the rotational invariance techniques (ESPRIT) algorithm, and our method owns a superior performance. Finally, the proposed method is verified by simulations and has the ability to achieve greater estimation accuracy than existing algorithms.

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.

A Gridless Fourth-Order Cumulant-Based DOA Estimation Method Under Unknown Colored Noise

To reduce the adverse impacts of the unknown colored noise on the performance degradation of the direction-of-arrival (DOA) estimation, we propose a new gridless DOA estimation method based on fourth-order cumulant (FOC) in this letter. We first introduce the non-redundancy single measurement vector (SMV) through FOC, which is capable of suppressing the Gaussian colored noise. Next, we analyze the distribution of the estimation error and design an estimation error tolerance scheme for it. We then combine the atomic norm minimization of the non-redundancy SMV with the above constraint scheme. This combination poses the stability of the sparsest solution. Finally, the DOA estimation is retrieved through rotational invariance techniques. Moreover, this method extends the gridless DOA estimation to the sparse linear array. Numerical simulations validate the effectiveness of the proposed method.

Joint range and velocity estimation for orthogonal frequency division multiplexing‐based high‐speed integrated radar and communications system

The integrated radar and communications (IRC) waveform can simultaneously estimate the range and velocity of other targets while communicating with other facilities. In high-speed scenarios, the IRC echo signal based on orthogonal frequency division multiplexing (OFDM) needs to consider the intra-symbol and inter-subcarrier Doppler effects. This paper first builds a receiving model of the integrated echo signal by including the intra-symbol and inter-subcarrier Doppler effects. On this basis, we propose a two-step joint range and velocity estimation method, where rough estimation is performed by an improved estimating the signal parameters via the rotational invariance technique (ESPRIT), and a least-square weighted (LSW) method is applied for fine estimation. The Cramer-Rao lower bound (CRLB) of the receiving model is also provided, and the computational complexity of the proposed method is analyzed. Simulation results demonstrate the superiority of the proposed method.

A Hybrid Technique for Analysis of Low-Frequency Oscillation in Power System

Estimating the low-frequency oscillation in an interconnected power system is the most important requirement to keep the power system in a stable operating condition. This research work deals with a hybrid robust and accurate approach using a combination of Estimation of signal parameters via rotational invariant techniques (ESPRIT) and Prony algorithm to extract the low-frequency oscillatory modes present in the power system. The observation inspires the hybrid method that the true modes of the signal are present in any signal processing technique (for example, Prony algorithm) along with other fictitious modes regardless of the order of the power system. Moreover, this research obtained true modes by calculating Euclidean distance and applying the threshold value concept. The proposed technique is tested with different noise conditions and varying sampling rates of Phasor Measurement Unit (PMU) to check the proposed hybrid technique’s robustness compared to Prony and the multiple ESPRIT method. Finally, the proposed method is applied to the real signal obtained from the Western Electricity Coordinating Council (WECC) network, and it estimates accurate and precise parameters compared to other methods. The accuracy for estimation of frequency and attenuation factor is calculated for the three-mode synthetic signal at a noise level of 10dB by the hybrid algorithm, multiple ESPRIT, and Prony algorithm, which shows that hybrid algorithm has minimum percentage error. Thus, the proposed hybrid algorithm accurately estimates the parameters of low-frequency oscillation as compared to other existing methods without involving any fictitious modes.