Rotational Invariance Techniques Research Articles

Terahertz Bistatic Synthetic Aperture Radar for 1-D Near-Field High-Resolution Imaging

Considering the difficult transceiver-isolation problem of the monostatic synthetic aperture radar (SAR) in the terahertz (THz) band, this paper proposes a compact THz bistatic SAR (BiSAR) geometry. The system allows the separately distributed transmitter and receivers. At the receiving end, there are a direct-wave receiver and an echo receiver, both operating at the heterodyne and in-phase mode. The echo receiver runs along a linear rail to fulfill the scene scanning, while the direct-wave one is fixed as a reference. Furthermore, assuming that the receivers are synchronized, both the problem of synchronization between the separated transmitter and receivers and the problem of timing at the signal acquisition would be solved by utilizing the high coherence between the echo and the direct wave. Based on such a system, the application of THz BiSAR for one-dimensional imaging is taken into consideration. Then, a high-resolution imaging algorithm is proposed benefitting from the total least squares estimating signal parameters via rotational invariance techniques (TLS-ESPRIT) and the spatial smoothing process (SSP). The imaging performance is then demonstrated by both simulations and the experiments in the 0.183 THz.

Tensor-Based Angle Estimation Approach for Strictly Noncircular Sources with Unknown Mutual Coupling in Bistatic MIMO Radar

In the paper, the estimation of joint direction-of-departure (DOD) and direction-of-arrival (DOA) for strictly noncircular targets in multiple-input multiple-output (MIMO) radar with unknown mutual coupling is considered, and a tensor-based angle estimation method is proposed. In the proposed method, making use of the banded symmetric Toeplitz structure of the mutual coupling matrix, the influence of the unknown mutual coupling is removed in the tensor domain. Then, a special enhancement tensor is formulated to capture both the noncircularity and inherent multidimensional structure of strictly noncircular signals. After that, the higher-order singular value decomposition (HOSVD) technology is applied for estimating the tensor-based signal subspace. Finally, the direction-of-departure (DOD) and direction-of-arrival (DOA) estimation is obtained by utilizing the rotational invariance technique. Due to the use of both noncircularity and multidimensional structure of the detected signal, the algorithm in this paper has better angle estimation performance than other subspace-based algorithms. The experiment results verify that the method proposed has better angle estimation performance.

Doppler Frequency Estimation of Point Targets in the Single-Channel SAR Image by Linear Least Squares

This paper presents a method and results for the estimation of residual Doppler frequency, and consequently the range velocity component of point targets in single-channel synthetic aperture radar (SAR) focused single-look complex (SLC) data. It is still a challenging task to precisely retrieve the radial velocity of small and slow-moving objects, which requires an approach providing precise estimates from only a limited number of samples within a few range bins. The proposed method utilizes linear least squares, along with the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, to provide optimum estimates from sets of azimuth subsamples that have different azimuth temporal distances. The ratio of estimated Doppler frequency to root-mean square error (RMSE) is suggested for determining a critical threshold, optimally selecting a number of azimuth subsample sets to be involved in the estimation. The proposed method was applied to TerraSAR-X and KOMPSAT-5 X-band SAR SLC data for on-land and coastal sea estimation, with speed-controlled, truck-mounted corner reflectors and ships, respectively. The results demonstrate its performance of the method, with percent errors of less than 5%, in retrieved range velocity for both on-land and in the sea. It is also robust, even for weak targets with low peak-to-sidelobe ratios (PSLRs) and signal-to-clutter ratios (RCSs). Since the characteristics of targets and clutter on land and in the sea are different, it is recommended that the method is applied separately with different thresholds. The limitations of the approach are also discussed.

A Tensor Approach to Model Order Selection of Multiple Sinusoids

The letter presents a covariance tensor based estimator that can effectively provide the model order for multiple sinusoids in noise. For moderate to high signal-to-noise ratios the estimator works effectively even for short length observations. Unlike the conventional methods that use a covariance matrix, the proposed estimator makes use of a three-way covariance tensor formed from the one-dimensional data. Estimate of the model order has been determined by processing the incremental Frobenius norms of the leading principal subtensors of the core tensor obtained via higher order singular value decomposition. Simulations under additive white Gaussian noise show that the new estimator offers significant improvements over conventional methods such as multiple signal classification (MUSIC), estimation of signal parameters via rotational invariance technique+maximum a posteriori , and entropy-based MUSIC. The improvement is particularly notable at larger orders or when frequency separation is small.

High-resolution bottom detection algorithm for a multibeam echo-sounder system with a U-shaped array

High-resolution approaches such as multiple signal classification and estimation of signal parameters via rotational invariance techniques (ESPRIT) are currently employed widely in multibeam echo-sounder (MBES) systems for sea floor bathymetry, where a uniform line array is also required. However, due to the requirements in terms of the system coverage/resolution and installation space constraints, an MBES system usually employs a receiving array with a special shape, which means that high-resolution algorithms cannot be applied directly. In addition, the short-term stationary echo signals make it difficult to estimate the covariance matrix required by the high-resolution approaches, which further increases the complexity when applying the high-resolution algorithms in the MBES systems. The ESPRIT with multiple-angle subarray beamforming is employed to reduce the requirements in terms of the signal-to-noise ratio, number of snapshots, and computational effort. The simulations show that the new processing method can provide better fine-structure resolution. Then a highresolution bottom detection (HRBD) algorithm is developed by combining the new processing method with virtual array transformation. The application of the HRBD algorithm to a U-shaped array is also discuss. The computer simulations and experimental data processing results verify the effectiveness of the proposed algorithm.

An Approach to Suppress Low Frequency Oscillation in the Traction Network of High-Speed Railway Using Passivity-Based Control

The traction blockade in depots of multiple electric multiple units (EMUs) is generally considered to be caused by the voltage low frequency oscillation (LFO) of the high-speed railway traction network. As a possible solution, a strategy using single-phase EMUs rectifiers with passivity-based control (PBC) is proposed in this paper. First, the mathematical model of the four-quadrant pulse width modulation rectifier is constructed based on the port controlled Hamiltonian with dissipation. Next, with the insertion of damping, the new energy function can be minimized at the equilibrium point of the system, which enables the derivation of the rectifier control law based on the interconnection and damping assignments PBC. Comparison of simulation results with those of the traditional proportional integral (PI) scheme, autodisturbance rejection control and multivariable control verifies that the proposed PBC controller has better dynamic and static performance. Among all strategies considered, the resulting line current has the least total harmonic distortion, and the dc-link voltage of single-phase EMUs rectifier has the least oscillation and the shortest adjustment time, when using the PBC. Meanwhile, the simulations of multi-EMUs accessed a traction network show that the proposed method significantly suppresses the voltage LFO of the traction network. Finally, the LFO signal modal analysis is performed using the fast Fourier transform and the estimating signal parameters via the rotational invariance techniques. It indicates that PBC can suppress the symmetrical frequency components and effectively reduce the third, fifth, and other harmonic components compared with the PI control in EMUs.

Joint DOD and DOA estimation for bistatic multiple‐input multiple‐output radar target discrimination based on improved unitary ESPRIT method

Target position estimation of radar system has attracted much attention. Researchers have proposed a variety of joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation algorithms over the last few decades for this well-known problem. However, traditional estimation algorithms require a pairing process between the DOD and DOA estimation. In this study, the authors propose an improved unitary estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm for joint DOD and DOA estimation without a pairing operation. The waveforms are transmitted by an array with M sensors and received by two detached sub-arrays with and sensors, respectively. Specifically, the proposed algorithm eliminates a pairing process via sharing the eigenvectors of DOD and DOA. Theoretical derivation demonstrates that the proposed algorithm requires less computational complexity than two-dimensional multiple signal classification (MUSIC), reduced-dimension MUSIC, and ESPRIT. Simulation results show that the proposed algorithm can effectively enhance the accuracy of identifying and locating targets for the bistatic multiple-input multiple-output radar system.

Integrated polarisation and diversity smoothing algorithm for DOD and DOA estimation of coherent targets

This study proposes a novel integrated polarisation and diversity smoothing (IPDS) algorithm to solve the direction estimation problem of coherent targets in bistatic multiple-input multiple-output (MIMO) radar with electromagnetic vector sensors (EVSs). The IPDS algorithm partitions the transmit and receive arrays into multiple subarrays based on the sensor elements and the spatial phase shift factors. Then the covariance matrices of the received signals from coherent targets associated with these subarrays are smoothened to restore the rank inadequacy of the reflection coefficient covariance matrix. After applying the IPDS algorithm, the direction of departure (DOD) and the direction of arrival (DOA) are estimated using the estimation of signal parameters via rotational invariance technique and the multiple signal classification methods. The effectiveness of the proposed algorithm in terms of decorrelation factor, estimation accuracy, precision and the spatial spectrum is evaluated through computer simulations. Cramér–Rao lower bound is derived for the bistatic MIMO radar with EVSs to substantiate the proposed algorithm. The simulation results are compared with the diversity smoothing and the polarisation smoothing algorithms available in literature. The results obtained by using the proposed algorithm were found to be impressive.

Performance analysis of propagator‐based ESPRIT for direction of arrival estimation

Compared with the standard estimation of signal parameters via rotational invariance technique (ESPRIT) for direction of arrival estimation, the propagator-based ESPRIT is a more computationally efficient method since it requires no eigenvalue decomposition when calculating the signal subspace. In this study, the propagator-based ESPRIT method is analysed by deriving its theoretical asymptotic error. With first-order perturbation analysis, it is shown that both propagator-based ESPRIT and standard ESPRIT have the same asymptotic error with high signal-to-noise ratio. Simulation results of both the propagator-based ESPRIT and the standard ESPRIT are presented, and they are shown to be consistent with the theoretical derivations.

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.

Two-Dimensional Direction-of-Arrival Fast Estimation of Multiple Signals with Matrix Completion Theory in Coprime Planar Array.

In estimating the two-dimensional (2D) direction-of-arrival (DOA) using a coprime planar array, the main issues are the high complexity of spectral peak search and the limited degree of freedom imposed by the number of sensors. In this paper, we present an algorithm based on the matrix completion theory in coprime planar array that reduces the computational complexity and obtains a high degree of freedom. The algorithm first analyzes the covariance matrix of received signals to estimate the covariance matrix of a virtual uniform rectangular array, which has the same aperture as the coprime planar array. Matrix completion theory is then applied to estimate the missing elements of the virtual array covariance matrix. Finally, a closed-form DOA solution is obtained using the unitary estimation signal parameters via rotational invariance techniques (Unitary-ESPRIT). Simulation results show that the proposed algorithm has a high degree of freedom, enabling the estimation of more signal DOAs than the number of sensors. The proposed algorithm has reduced computational complexity because the spectral peak search is replaced by Unitary-ESPRIT, but attains similarly high levels accuracy to those of the 2D multiple signal classification algorithm.

RAM-based angle estimation with linear spatially separated polarisation sensitive array

ABSTRACTTwo-dimensional direction of arrival (2D-DOA) and polarisation estimation of multiple incident signals for linear spatially separated polarisation sensitive array (SS-PSA) is investigated with reweighted atomic norm minimisation (RAM) algorithm. Single vector sensor in this paper is composed of spatially separated three dipoles and three loops. Firstly, the received data of the proposed array with single snapshot is converted into the new received data with six virtual snapshots. Each virtual snapshot data is the data sensing by dipoles or loops located in the same direction. Secondly, based on each virtual snapshot data, the complex amplitudes and frequencies of the virtual signals are restored using RAM algorithm. Lastly, 2D-DOA and polarisation angles are derived according to the restored complex amplitudes and frequencies. Simulation results demonstrate that the RAM algorithm used in 2D-DOA and polarisation estimation with SS-PSA exhibits superior performance, which is better compared with polarisation multiple signal classification (PMUSIC) algorithm and rotational invariance techniques (ESPRIT) algorithm.

Wave forecast and its application to the optimal control of offshore floating wind turbine for load mitigation

Abstract Control algorithms play an important role in energy capture and load mitigation for offshore floating wind turbines (OFWTs). One of the advanced and effective control techniques is the feedforward or model predictive control approach, which requires the forecast of incoming environment conditions. For OFWTs, wave loading is one of the dominant sources to excite structural responses. This study is thus motivated to develop forecasting algorithms for wave elevations and wave excitation forces with the purpose of applying feedforward controllers on OFWTs. Two forecasting algorithms, the approximate Prony Method based on ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) and SVM (Support Vector Machine) regression, are developed and validated using wave records from tank tests. Utilizing the forecasted wave elevations and wave excitation forces, a feedforward LQR controller is designed to mitigate structural loads of an OFWT system.

Wireless channel parameter estimation algorithms: Recent advances and future challenges

Temporal and three-dimensional (3D) spatial information is important for the characterization of wireless channels. In this paper, the commonly used array signal processing (ASP) methods to estimate channel parameters are summarized. Firstly, algorithms that can be used to estimate azimuth angle of arrival (AAoA) and elevation AoA (EAoA) are introduced. They include multiple signal classification (MUSIC), estimation of signal parameter via rotational invariance techniques (ESPRIT), and Unitary ESPRIT algorithms. Secondly, algorithms that can be used to jointly estimate delay, AAoA, and EAoA are given. They include joint angle and delay estimation (JADE) MUSIC, JADE ESPRIT, shift-invariance (SI) JADE, and space-alternating generalized expectation-maximization (SAGE) algorithms. We also propose an improved SI-JADE algorithm to further reduce computation complexity by incorporating with the Unitary ESPRIT algorithm. Performance of the above algorithms to extract only spatial information and to jointly extract temporal and spatial information is compared in both synthetic and 60 GHz real channel environments. Simulation results show that with the inclusion of delay estimation, the joint temporal and spatial estimation algorithms can provide better resolution than algorithms estimating only angles. Measurement data processing results show that MUSIC algorithm can provide comparable results with SAGE algorithm in estimating AAoA and EAoA. SI-JADE and the improved SI-JADE algorithms are also applicable to process 60 GHz channel measurement data. However, MUSIC, SI-JADE, and the improved SI-JADE algorithms can greatly reduce computational burden compared with SAGE algorithm. At last, some future directions are pointed out.

Mxpfit: A library for finding optimal multi-exponential approximations

mxpfit is a library implemented in C++ to find optimal approximations of functions by multi-exponential sums with complex-valued parameters. The library provides an interface for evaluating exponents and coefficients from sampling data on a uniform grid using the fast Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm originally proposed by Potts and Tasche (2015). The parameters can be estimated efficiently from a sampling data even including noise. A modified balanced truncation algorithm to find the multi-exponential sum with a smaller order is also provided. These features are useful for finding optimal exponential sum approximations of analytic functions or large-scale numerically sampled data set. Program summaryProgram Title: mxpfitProgram Files doi:http://dx.doi.org/10.17632/vjygkwpss4.1Licensing provisions: MITProgramming language: C++Nature of problem: Nonlinear curve fitting by multi-exponential function, frequency estimation of signals, and reduction of multi-exponential sumSolution method: The modified fast Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm originally proposed in [1] is utilized for the parameter estimation of multi-exponential sums from sampled data on a uniform grid. In this method, partial Lanczos bidiagonalization is used to find a low-rank approximation of a Hankel matrix constructed from sampled data. An overdetermined Vandermonde system is solved by the conjugate gradient least square (CGLS) method with preconditioner to obtain the coefficients of the multi-exponential sum. The truncation of the multi-exponential sum is performed by a modified balanced truncation method in [2]. The projection matrix to obtain the truncated system is determined by computing con-eigenvalues of a Gramian matrix, which can be computed efficiently with highly relative accuracy using the algorithm in [3].Additional comments: A C++ compiler supporting the C++11 standard is required to compile programs using the mxpfit library. mxpfit depends on the Eigen (http://eigen.tuxfamily.org/) and FFTW3 (http://www.fftw.org/) libraries. CMake (https://cmake.org/) is used for building example programs.

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.

Extended-Aperture Unitary Root MUSIC-Based DOA Estimation for Coprime Array

Direction of arrival (DOA) estimation using coprime array is studied, and an extended-aperture unitary root multiple signal classification (MUSIC)-based method is proposed. The geometry of prototype coprime array is modified through some translations, which enable one subarray of the coprime array to achieve aperture extension after unitary transformation. Then, the aperture of the other subarray can also be extended based on the rotational invariance of the extended subarray, and 2-D parameter estimations from the two extended subarrays can be achieved in succession via 1-D root MUSIC-based technique. Finally, unique DOA is determined from the intersection of the two automatically paired and coprime estimations. In contrast to the partial search MUSIC method, the estimation of signal parameters via rotational invariance technique based method, the root MUSIC-based method, and the real-valued cross covariance matrix based method, the proposed method gives better DOA estimation results and manages more sources. Furthermore, it has low complexity for the real-valued decomposition. Simulation results verify the improvement of the proposed approach.

Robust Angle Estimation for MIMO Radar with the Coexistence of Mutual Coupling and Colored Noise.

This paper deals with joint estimation of direction-of-departure (DOD) and direction-of- arrival (DOA) in bistatic multiple-input multiple-output (MIMO) radar with the coexistence of unknown mutual coupling and spatial colored noise by developing a novel robust covariance tensor-based angle estimation method. In the proposed method, a third-order tensor is firstly formulated for capturing the multidimensional nature of the received data. Then taking advantage of the temporal uncorrelated characteristic of colored noise and the banded complex symmetric Toeplitz structure of the mutual coupling matrices, a novel fourth-order covariance tensor is constructed for eliminating the influence of both spatial colored noise and mutual coupling. After a robust signal subspace estimation is obtained by using the higher-order singular value decomposition (HOSVD) technique, the rotational invariance technique is applied to achieve the DODs and DOAs. Compared with the existing HOSVD-based subspace methods, the proposed method can provide superior angle estimation performance and automatically jointly perform the DODs and DOAs. Results from numerical experiments are presented to verify the effectiveness of the proposed method.

The Critical Patients Localization Algorithm Using Sparse Representation for Mixed Signals in Emergency Healthcare System

In this paper, a new architecture for the emergency healthcare system based on mobile cloud computation (MCC) and fifth-generation (5G) wireless link is proposed. Based on the processing speed of MCC and the communication rate of 5G scheme, this system can monitor and locate patients in real time. Multiple base stations of the massive multiple input multiple output cooperate with each other to locate the patients using cross-location method. Then, a new direction-of-arrival (DOA) estimation algorithm is proposed in the presence of unknown mutual coupling. The uncorrelated signals are first estimated using the estimation of signal parameters via rotational invariance technique algorithm. Then, these estimators construct the manifold matrix of uncorrelated signals to estimate the mutual coupling coefficients. The information about uncorrelated signals and mutual coupling is eliminated based on oblique projection technique in order to estimate the DOAs of coherent signals using the original array. Finally, the DOAs of coherent signals are achieved based on sparse representation theory. Simulation results demonstrate the effectiveness and performance of the proposed algorithm.

Wide area damping of electromechanical low frequency oscillations using phasor measurement data

A wide area controller using modern multi-band power system stabilizer (PSS) is proposed to damp low frequency oscillations (LFOs) in the presence of wind power penetration. The proposed scheme is perfected in two stages. In the first stage, as the online stage, the generation re-dispatch is utilized to improve the damping of LFOs. In the second stage, as the real-time stage, the modern multiband PSSs are tuned in a wide area basis using ambient synchro-phasor measurements. A hybrid subspace identification approach based on estimation of signal parameters via rotational invariance technique (ESPRIT) and robust project approximation subspace tracking (PAST) technique is developed for online estimation of electromechanical modal properties using ambient phasor measurement data. The estimated modal information is then utilized for optimal wide area tuning of multi-band PSSs. Performance of the proposed scheme is then compared with local and global conventional PSSs. The proposed wide area damping controller is simulated over the IEEE-39 Bus test systems.