Estimation Of Signal Parameters Via Rotational Invariance Techniques Algorithm Research Articles

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.

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.

Scalable ESPRIT Processor for Direction-of-Arrival Estimation of Frequency Modulated Continuous Wave Radar

The estimation of signal parameters via rotational invariance techniques (ESPRIT) is an algorithm that uses the shift-invariant properties of the array antenna to estimate the direction-of-arrival (DOA) of signals received in the array antenna. Since the ESPRIT algorithm requires high-complexity operations such as covariance matrix and eigenvalue decomposition, a hardware processor must be implemented such that the DOA is estimated in real time. Additionally, the ESPRIT processor should support a scalable number of antenna configuration for DOA estimation in various applications because the performance of ESPRIT depends on the number of antennas. Therefore, we propose an ESPRIT processor that supports two to eight scalable antenna configuration. In addition, since the proposed ESPRIT processor is based on multiple invariances (MI) algorithm, it can achieve a much better performance than the existing ESPRIT processor. The execution time is reduced by simplifying the Jacobi method, which has the most significant computational complexity for calculating eigenvalue decomposition (EVD) in ESPRIT. Moreover, the ESPRIT processor was designed using hardware description language (HDL), and an FPGA-based verification was performed. The proposed ESPRIT processor was implemented with 10,088 slice registers, 18,207 LUTs, and 80 DSPs, and the slice register, LUT, and DSP were reduced by up to 71.45%, 54.5%, and 68.38%, respectively, compared to the existing structure.

A Novel ESPRIT Algorithm for Analysis of Low Frequency Oscillations in Power System

With rapidly increasing load and randomly varying load scenario in a densely connected power system may lead to low-frequency oscillations which can further make a power system unstable. To keep the power system in stable operating limits identifying such dominant low-frequency oscillations is essential. Numerous signal processing techniques are used to detect low-frequency oscillations in a power system. Different techniques have their advantages and disadvantages. Estimation of signal parameters via rotational invariance technique (ESPRIT) is a signal processing technique by which low-frequency oscillations can be identified even under noisy conditions . In this paper, a novel ESPRIT algorithm for identifying low-frequency oscillations is proposed. This methodology is based on the ESPRIT algorithm, whose key concept is that real modes existing in oscillations emerge consistently regardless of the algorithm's order. The performance of this algorithm is verified through a set of synthetic signals generated in MATLAB with different noise levels and varying PMU rates and compared with traditional Prony algorithm. The performance of the proposed algorithm is also verified on real-time test data obtained from the Western Electricity Coordinating Council (WECC). This technique performs fairly well in finding low-frequency oscillation characteristics in the power grid.

DOA Estimation Based on ESPRIT Algorithm Method for Frequency Scanning LWA

In this paper, an improved estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm is proposed. As to the frequency scanning leaky wave antenna (LWA), the direction of arrival (DOA) can be effectively estimated by the algorithm. Compared with ESPRIT algorithm based on array antennas or electronically controlled beam scanning LWA, the ESPRIT algorithm using frequency scanning LWA obviously simplifies the hardware implementation. Furthermore, the wideband DOA can be simultaneously estimated by this proposed algorithm. The simulation results show that the estimated DOA results are in good agreement with the predicted angles, with root mean square error (RMSE) less than 1.6% on 38% relative bandwidth (ultra wide band).

DOA estimation method of electronically controlled beam‐scanning LWA based on ESPRIT algorithm

A novel direction-of-arrival (DOA) estimation method based on electronically controlled beam scanning leaky-wave antenna (LWA) combined with estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm is proposed. In order to implement this method, a virtual partial pattern synthesis method is presented to construct an array manifold of subarrays from LWA for the ESPRIT algorithm. Then, the multi-channel receiver model and signal subspace are established based on the beam scanning property of LWA. As the traditional array antenna is substituted by LWA, the rotation operator of the algorithm has to be changed. From this point, the preprocessing ESPRIT algorithm based on the Hadamard product is proposed to extract the directional matrix of LWA. Numerical simulations are conducted, and the DOA performance is demonstrated through estimation error, response rate, and compared with the Cramer-Rao bound. Simulation results show that the DOA method utilising LWA exhibits satisfactory estimation performance and fast response speed. In addition, the influence of antenna parameters on the estimation accuracy and the method to improve the performance of DOA estimation for LWA are discussed.

A Novel Unitary ESPRIT Algorithm for Monostatic FDA-MIMO Radar.

A novel unitary estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, for the joint direction of arrival (DOA) and range estimation in a monostatic multiple-input multiple-output (MIMO) radar with a frequency diverse array (FDA), is proposed. Firstly, by utilizing the property of Centro-Hermitian of the received data, the extended real-valued data is constructed to improve estimation accuracy and reduce computational complexity via unitary transformation. Then, to avoid the coupling between the angle and range in the transmitting array steering vector, the DOA is estimated by using the rotation invariance of the receiving subarrays. Thereafter, an automatic pairing method is applied to estimate the range of the target. Since phase ambiguity is caused by the phase periodicity of the transmitting array steering vector, a removal method of phase ambiguity is proposed. Finally, the expression of Cramér–Rao Bound (CRB) is derived and the computational complexity of the proposed algorithm is compared with the ESPRIT algorithm. The effectiveness of the proposed algorithm is verified by simulation results.

PMU-Assisted Zone-3 Protection Scheme for PV Integrated Power Systems Immune to Interharmonics

In this article, the impact of interharmonics generated in photovoltaic (PV) integrated systems on phasor measurement unit (PMU)-assisted zone-3 protection scheme (Z3PS) is investigated. Generally, PMUs integrated with conventional discrete Fourier transform (DFT) algorithm are employed to compute time-synchronized voltage and current phasors. However, the presence of interharmonics in PV integrated systems may force to cease the proper performance of Z3PS since DFT algorithm integrated with PMUs fails to identify and eliminate closely spaced interharmonics resulting in incorrect computation of phasors. This phenomena further leads to improper estimation of apparent impedances by relays. To overcome this issue, a phasor signal processing model (PSPM) is proposed where a preprocessing filtering step involving signal processing by an estimation of signal parameters via rotational invariance techniques (ESPRIT) or matrix pencil (MP) algorithm is added before PMUs. Proposed PSPM helps in eliminating noise and closely spaced interharmonics present in the signals and consequently, enhances the performance of PMU-assisted Z3PS. Integration of PV to IEEE 39-bus system is done in PSCAD/EMTDC software whereas ESPRIT and MP algorithms are implemented in MATLAB. Comparative analysis with exiting methods are carried out for systems operating under different conditions to examine the performance of the proposed Z3PS.

Research on ESPRIT estimation algorithm for the central frequency of gain spectrum in Brillouin optical time-domain reflectrometry

In fiber-optic Brillouin optical time-domain reflectometer (BOTDR) system, the estimation of the center frequency of Brillouin scattering spectrum in fiber is the key and the most time-consuming part of the measurement, which makes BOTDR system difficult to achieve fast response. In this paper, estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm is proposed to estimate the center frequency of Brillouin scattering spectrum in BOTDR system. Due to fairly low requirement on data length, ESPRIT algorithm can obtain good frequency estimation over short data length, and makes it possible to increase measurement speed at high spatial resolution and measurement performance.

Angle Estimation in Monostatic MIMO Radar with Low-Complexity Beamspace Unitary ESPRIT

A low-complexity angle estimation method for multiple-input multiple-output (MIMO) radar using beamspace unitary estimation of signal parameters via rotational invariance techniques (ESPRIT) is presented. Reduced-dimensional transformation is firstly utilized as a pre-processing to obtain the reduced-dimensional data matrix, and then a conjugate centrosymmetric discrete Fourier transform (DFT) matrix is employed to map the received data into lower-dimensional beamspace and transforms the complex covariance matrix into a realvalued one. At last, the rotational invariance structure of the real-valued signal subspace is constructed in the beamspace to obtain the estimation of direction of arrival (DOA). Compared with the other ESPRIT algorithms, the proposed method can achieve improved estimation performance with a significantly reduced computational complexity. Simulation results are presented to demonstrate the effectiveness of the proposed method.

Successive ESPRIT Algorithm for Joint DOA-Range-Polarization Estimation With Polarization Sensitive FDA-MIMO Radar

Polarization sensitive frequency and frequency diversity array (FDA)-MIMO (PSFDA-MIMO) hybrid radar is an emerging technology. The existing algorithms for parameter estimation with PSFDA-MIMO radar need multiple-dimensional searches, whose computational complexity is high. To reduce the computational complexity, in this paper, a search-free algorithm is proposed to estimate 4-D parameters with PSFDA-MIMO radar. First, direction of arrival (DOA) is estimated with the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm using the rotational invariance of the receiving array. Second, based on the estimated DOA parameter, range estimation is obtained with the ESPRIT algorithm using the rotational invariance of the transmitting array. Finally, polarization parameters are estimated with the ESPRIT algorithm using the rotational invariance of the polarization domain. Thus, the proposed algorithm is termed the successive ESPRIT algorithm. Simulation results demonstrate the effectiveness of the proposed algorithm.

DOD and DOA estimation using the spatial smoothing in MIMO radar with the EmV sensors

This paper deals with the directions of departure (DOD) and directions of arrival (DOA) estimation of coherent and noncoherent targets in bistatic MIMO radar with the electromagnetic vector (EmV) sensors. The high-resolution eigenspace-based methods such as, estimation of signal parameters via rotational invariance technique (ESPRIT), multiple signal classification, etc., fails to estimate DOD and DOA of fully or partially correlated targets. In order to employ these methods, a new pre-processing method is developed based on the spatial smoothing in MIMO radar with the EmV sensors. Then, the directions are estimated using the ESPRIT algorithm. Monte-Carlo simulations are performed to investigate the estimation-accuracy and resolution-capability of the proposed approach, and to compare with no pre-processing and the existing method. The simulation result shows that, the proposed methodology improves the performance significantly.

ESPRIT and Unitary ESPRIT Algorithms for Coexistence of Circular and Noncircular Signals in Bistatic MIMO Radar

In bistatic multiple input multiple output (MIMO) radar, more number of detectable incident signals and a higher angle estimation performance can be obtained by using conjugate estimation of signal parameters via rotational invariance techniques (ESPRITs) with the characteristic of noncircularity. The result is achieved under the assumption that all the received signals are noncircular. When the incident signals are the coexistence of noncircular and circular signals, the conjugate ESPRIT will not valuable. Therefore, this paper proposes a method of the joint of direction of departure (DOD) and direction of arrival (DOA) estimation, which is appropriate for the coexistence of noncircular and circular signals in bistatic MIMO radar. First, the received data model of the bistatic MIMO radar is given. Second, we modify the received signal model by the use of noncircularity characteristic. Third, we derive out the equation of spatially rotational invariant containing the DOD and DOA information. Last, we solve the equation to obtain the DOD and DOA by means of total least squares technology. The proposed algorithm has the three advantages. One is that it has better angle estimation accuracy than that of method which does not use the noncircularity characteristic. Another one is that it has more number of detectable incident signals. The last one is that the more number of noncircular signals, the higher angle estimation accuracy will be. Results from numerical experiments are used to show the effectiveness of our proposed algorithm.

English

Source Direction of arrival (DOA) estimation plays an important role in array signal processing, and has a wide range of application. Array signal processing is an important branch in the field of signal processing. In recent years, it has developed dramatically. It can be applied in fields such as radar, communication, sonar, earthquake, exploration, astronomy and biomedicine. Over the past few years, all kinds of algorithms which can be used in DOA estimation have made great achievements, the most classic algorithms among which are Multiple Signal Classification (MUSIC) and Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT).In this paper, we will give an overview on performance of the DOA estimation based on MUSIC as well as ESPRIT (both TLS and Pro ESPRIT) algorithm on uniform linear array (ULA) and in the presence of white noise. We will describe what DOA estimation is, and give a mathematical model of DOA estimation for subspace based DOA methods such as MUSIC, TLS ESPRIT and Pro ESPRIT. Then estimate DOA based on the MUSIC, TLS ESPRIT as well as Pro ESPRIT algorithm, with simulations with MATLAB to simulate factors that affect accuracy and resolution of DOA estimation. The performance of these DOA algorithms for a set of input parameters such as number of snapshots, number of array elements, signal-to-noise ratio, angular separation, element spacing are investigated.

Fast ESPRIT algorithms based on partial singular value decompositions

Let h(x) be a nonincreasing exponential sum of order M. For N given noisy sampled values hn=h(n)+en(n=0,…,N−1) with error terms en, all parameters of h(x) can be estimated by the known ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) method. The ESPRIT method is based on singular value decomposition (SVD) of the L-trajectory matrix (hℓ+m)ℓ,m=0L−1,N−L, where the window length L fulfills M≤L≤N−M+1. The computational cost of the ESPRIT algorithm is dominated by the cost of SVD. In the case L≈N2, the ESPRIT algorithm based on complete SVD costs about 218N3+M2(21N+913M) operations. Here we show that the ESPRIT algorithm based on partial SVD and fast Hankel matrix–vector multiplications has much lower cost. Especially for L≈N2, the ESPRIT algorithm based on partial Lanczos bidiagonalization with S steps requires only about 18SNlog2⁡N+S2(20N+30S)+M2(N+13M) operations, where M≤S≤N−L+1. Numerical experiments demonstrate the high performance of these fast ESPRIT algorithms for noisy sampled data with relatively large error terms.

A Tensor-Based Subspace Approach for Bistatic MIMO Radar in Spatial Colored Noise

In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD) and the direction of arrival (DOA) for bistatic multiple-input multiple-output (MIMO) radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD) of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen's method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method.

Direction Finding and Positioning Algorithm with COLD-ULA Based on Quaternion Theory

Electromagnetic vector sensor arrays have been widely applied in the communication, radio, navigation, and so on. The application of electromagnetic vector sensor antenna array will greatly improve the overall performance of the communication system. In this paper, a novel quaternion- ESPRIT (estimation of signal parameters via rotational invariance techniques) algorithm for direction finding and positioning based on COLD (cocentered orthogonal loop and dipole) uniform linear array (COLD-ULA) is proposed. First, quaternion data model of COLD-ULA is deduced and constructed. Second, the array steering vector and the angle of arrival (DOA) are estimated using a quaternion eigenvalue decomposition of the data covariance matrix. Finally, the estimation of polarization parameters are required using the relationships between the dipoles and the loops. The proposed technique not only decouples the DOA estimation information from the polarization estimation information, but also improves the ability of signal detection. Moreover, the proposed technique has the advantage of small amount of calculation and parameter automatic matching. Simulation results show that the performance of quaternion method is obviously better than that of the long-vector method.

A RD-ESPRIT algorithm for coherent DOA estimation in monostatic MIMO radar using a single pulse

This paper discusses the problem of coherent direction of arrival (DOA) estimation in a monostatic multi-input multi-output (MIMO) radar using a single pulse, and proposes a reduced dimension (RD)-estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. We reconstruct the received data and then utilise it to construct a set of Toeplitz matrices. After that, we use RD-ESPRIT to obtain the DOAs of the sources. The proposed algorithm is effective for coherent angle estimation based on a single pulse, and it has much better angle estimation performance than the forward backward spatial smoothing (FBSS)-ESPRIT algorithm and the ESPRIT-like of Li, as well as very close angle estimation performance to the ESPRIT-like of Han. For complexity comparison, our algorithm has very close complexity to the FBSS-ESPRIT algorithm, and lower complexity than the ESPRIT-like of Han and the ESPRIT-like of Li. Simulation results present the effectiveness and improvement of our approach.

Concentric circular-shaped electronically steerable parasitic array radiator antennas for full-azimuth directions of arrival estimation with reduced computational load

This study proposes a new uniform concentric circular (UCCA) shape of electronically steerable parasitic array radiator (ESPAR) antennas for directions of arrival (DoAs) estimation problem. The well-known estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm is adapted to this special shape of UCCA and the authors demonstrate that the resulting algorithm yields better DoAs estimation accuracy and solves the failure of estimation problem when the signals&apos; DoAs are in some particular sectors: notably for [0°–30°] and [160°–180°]. This approach has shown interesting performances since it can ensure good DoAs estimation over the entire azimuth plane with a low extra computational overhead. The constraints are the same imposed to the ESPRIT algorithm allowing about 66% reduction on the required computational efforts. The Cramer Rao bound on the variance of DoAs estimated by the proposed array geometry is analysed. Through simulation results, the authors demonstrate that applying ESPRIT in conjunction with the proposed antennas shape not only provides superior high-resolution localisation capabilities but also it drastically reduces computations compared with previous works.

Closed-Form Blind 2D-DOD and 2D-DOA Estimation for MIMO Radar with Arbitrary Arrays

In this paper, we study the problem of four-dimensional angle estimation for bistatic multiple-input multiple-output (MIMO) radar with arbitrary arrays, and propose a close-form joint two-dimensional direction of departure and two-dimensional direction of arrival estimation algorithm. Our work is to extend the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm to angle estimation in MIMO-radar with arbitrary arrays. The algorithm can achieve automatically paired four-dimensional angles, requires no peak searching, has low complexity, and does not need to compensate for the phase. Furthermore, the proposed algorithm has much better angle estimation performance than the interpolated ESPRIT algorithm and propagator method. We also analyze and derive the complexity of the algorithm and the Cramer---Rao bound. The simulation results verify the effectiveness of the algorithm.