Estimating Signal Parameters Via Rotational Invariance Techniques Research Articles

Geometric Algebra based 2D-DOA Estimation for Non-circular Signals with an Electromagnetic Vector Array

This paper presents two novel methods based on geometric algebra (GA) to estimate two-dimensional (2D) direction-of-arrival (DOA) of non-circular (NC) signals for uniform rectangular array (URA). Traditional methods treat the received NC signals as a long vector which will inevitably lose orthogonality inside each electromagnetic vector sensor (EMVS) and thus miss some information of second-order statistical properties. Furthermore, the computational complexity will also increase. By contrast, the GA-based estimating signal parameter via rotational invariance techniques (ESPRIT) and propagation method (PM) algorithms are proposed to estimation DOA of NC signals. Taking advantage of GA, the relationship among multidimensional signals can be maintained. First, the six components of the EMVS are represented as a multivector in GA space. Then, we construct the GA-based extended covariance matrix to utilize the signal information more completely. The DOA parameters can be estimated through the ESPRIT and PM principle. The proposed GA-based estimation of signal parameter via rotational invariance techniques for NC signals processing (GANC-ESPRIT) can estimate DOA with high estimation accuracy. The proposed GA-based propagation method for NC signals estimation (GANC-PM) uses linear transformation to calculate angle parameters. Our model has much lower memory requirements and less computational burden compared with long vector models. Simulation results demonstrate the robustness and superiority of the proposed GANC-ESPRIT algorithm in terms of angular resolution. Complexity analysis shows that the proposed GANC-PM algorithm performances better with less computations.

Coherent DOA Estimation Algorithm with Co-Prime Arrays for Low SNR Signals

The Direction of Arrival (DOA) estimation of coherent signals in co-prime arrays has become a popular research topic. However, traditional spatial smoothing and subspace algorithms fail to perform well under low signal-to-noise ratio (SNR) and small snapshots. To address this issue, we have introduced an Enhanced Spatial Smoothing (ESS) algorithm that utilizes a space-time correlation matrix for de-noising and decoherence. Finally, an Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is used for DOA estimation. In comparison to other decoherence methods, when the SNR is −8 dB and the number of snapshots is 150, the mean square error (MSE) of the proposed algorithm approaches the Cramér–Rao bound (CRB), the probability of resolution (PoR) can reach over 88%, and, when the angular resolution is greater than 4°, the estimation accuracy can reach over 90%.

Distributed Super Nested Arrays: Reduce the Mutual Coupling between Array Antennas

In array, mutual coupling between the antennas is inevitable, which has an adverse effect on the estimation of parameters. To reduce the mutual coupling between the antennas of distributed nested arrays, this paper proposes a new array called the distributed super nested arrays, which have the good characteristics of the distributed nested arrays and can reduce the mutual coupling between the antennas. Then, an improved multiscale estimating signal parameter via rotational invariance techniques (ESPRIT) algorithm is presented for the distributed super nested arrays to improve the accuracy of direction-of-arrival (DOA) estimation. Next, we analyze the limitations of the spatial smoothing algorithm used by the distributed super nested arrays when there are multiple-source signals and the influence of the baseline length of distributed super nested arrays on the accuracy of DOA estimation. The simulation results show that the distributed super nested arrays can effectively reduce the mutual coupling between the array antennas, improve the DOA estimation performance, and significantly increase the number of detectable source signals.

Geometric Algebra-Based ESPRIT Algorithm for DOA Estimation

Direction-of-arrival (DOA) estimation plays an important role in array signal processing, and the Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is one of the typical super resolution algorithms for direction finding in an electromagnetic vector-sensor (EMVS) array; however, existing ESPRIT algorithms treat the output of the EMVS array either as a “long vector”, which will inevitably lead to loss of the orthogonality of the signal components, or a quaternion matrix, which may result in some missing information. In this paper, we propose a novel ESPRIT algorithm based on Geometric Algebra (GA-ESPRIT) to estimate 2D-DOA with double parallel uniform linear arrays. The algorithm combines GA with the principle of ESPRIT, which models the multi-dimensional signals in a holistic way, and then the direction angles can be calculated by different GA matrix operations to keep the correlations among multiple components of the EMVS. Experimental results demonstrate that the proposed GA-ESPRIT algorithm is robust to model errors and achieves less time complexity and smaller memory requirements.

Computationally Efficient Unitary ESPRIT Algorithm in Bistatic MIMO Radar

A low complexity unitary estimating signal parameter via rotational invariance techniques (ESPRIT) algorithm is presented for angle estimation in bistatic multiple-input-multiple-output (MIMO) radar. The devised algorithm only requires calculating two submatrices covariance matrix, which reduces the computation cost in comparison with subspace methods. Moreover, the signal subspace can be efficiently acquired by exploiting the NystrÖm method, which only needs O M N K 2 flops. Thus, the presented algorithm has an essentially diminished computational effort, especially useful when K ≪ M N , while it can achieve efficient angle estimation accuracy as well as the existing algorithms. Several theoretical analysis and simulation results are provided to demonstrate the usefulness of the proposed scheme.

AoA Estimation for OAM Communication Systems With Mode-Frequency Multi-Time ESPRIT Method

Radio orbital angular momentum (OAM) communications require accurate alignment between the transmit and receive beam directions. Accordingly, a key feature of OAM receivers is the ability to reliably estimate the angle of arrival (AoA) of multi-mode OAM beams. Considering the limitations of existing AoA estimation techniques, in this paper, we propose an easier-to-implement AoA estimation method based on applying multiple times the estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm to the received training signals in OAM mode and frequency domains, which is denoted as the mode-frequency (M-F) multi-time (MT)-ESPRIT algorithm. With this method, the misalignment error of real OAM channels can be greatly reduced and the performance approaches that of ideally aligned OAM channels.

A new model for DOA estimation and its solution by multi-target intermittent particle swarm optimization

Currently, the widely used methods for direction of arrival (DOA) estimation were constructed based on the subspace, such as Multiple Signal Classification (MUSIC) and Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT), which required that the number of sources is known beforehand. In this paper, a new method based on the Vector Error Model (VEM) for estimating the DOAs was proposed, which do not need the sources number in advance. The comparison of the performance between the VEM and the MUSIC model for DOA problem was given to demonstrate the effectiveness of our method. The algorithm of multi-target intermittent particle swarm optimization (MIPSO) was adopted to solve the VEM, and the performance of the VEM-MIPSO method was analysed through simulations for a uniform linear array and an L-shaped array respectively. The results showed that: (1) the VEM was an effective model to solve the DOA estimation without prior knowledge of the sources number; (2) the MIPSO was an efficient algorithm to solve the DOA estimation with high precision.

A Low-Complexity 2D-DOA Estimation Algorithm with Massive URA

Conventional Direction of Arrival (DOA) estimation algorithms, such as Multiple Signal Classification (MUSIC), Root-MUSIC, and Estimating Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithms, are difficult to apply to large-scale antenna arrays. Because these algorithms not only require a lot of snapshots of the received data, but also the hardware equipment cannot meet the algorithm complexity requirements. This paper presents a low-complexity DOA estimation algorithm for large-scale Uniform Rectangle Array (URA). We first obtain coarse initial DOA estimates via the two-dimensional fast Fourier transform and then search for the accurate estimates within a very small region. The proposed algorithm only needs one snapshot of the received data to obtain the estimation accuracy of the traditional algorithm. The algorithm also has good robustness, and it can estimate DOA accurately even under extremely low signal-to-noise ratio and many sources. Theoretical results and numerical simulations are provided to assess the superiority of the proposed algorithm.

2D-DOD and 2D-DOA Estimation for a Mixture of Circular and Strictly Noncircular Sources Based on L-Shaped MIMO Radar.

In this paper, a joint diagonalization based two dimensional (2D) direction of departure (DOD) and 2D direction of arrival (DOA) estimation method for a mixture of circular and strictly noncircular (NC) sources is proposed based on an L-shaped bistatic multiple input multiple output (MIMO) radar. By making full use of the L-shaped MIMO array structure to obtain an extended virtual array at the receive array, we first combine the received data vector and its conjugated counterpart to construct a new data vector, and then an estimating signal parameter via rotational invariance techniques (ESPRIT)-like method is adopted to estimate the DODs and DOAs by joint diagonalization of the NC-based direction matrices, which can automatically pair the four dimensional (4D) angle parameters and solve the angle ambiguity problem with common one-dimensional (1D) DODs and DOAs. In addition, the asymptotic performance of the proposed algorithm is analyzed and the closed-form stochastic Cramer–Rao bound (CRB) expression is derived. As demonstrated by simulation results, the proposed algorithm has outperformed the existing one, with a result close to the theoretical benchmark.

A Robust Direction of Arrival Estimation Method for Uniform Circular Array.

Estimating the Direction of Arrival (DOA) is a basic and crucial problem in array signal processing. The existing DOA methods fail to obtain reliable and accurate results when noise and reverberation occur in real applications. In this paper, an accurate and robust estimation method for estimating the DOA of sources signal is proposed. Incorporating the Estimating Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm with the RANdom SAmple Consensus (RANSAC) algorithm gives rise to the RAN-ESPRIT method, which removes outliers automatically in noise-corrupted environments. In this work, a uniform circular array (UCA) is converted into a virtual uniform linear array (ULA) to begin with. Then, the covariance matrix of the received signals of the virtual linear array is reconstructed, and the ESPRIT algorithm is deployed to estimate initial DOA of the source signal. Finally, the modified RANSAC method with automatically selected thresholds is used to fit the source signal to obtain accurate DOA. The proposed method can remove the unreliable DOA feature data and leads to more accuracy of DOA estimation of source signals in reverberation environments. Experimental results demonstrate that the proposed method is more robust and efficient compared to the traditional methods (i.e., ESPRIT, TLS-ESPRIT).

MIMO Radar Accurate 3-D Imaging and Motion Parameter Estimation for Target with Complex Motions

In this paper, three-dimensional (3-D) multiple-input multiple-output (MIMO) radar accurate localization and imaging method with motion parameter estimation is proposed for targets with complex motions. To characterize the target accurately, a multi-dimensional signal model is established including the parameters on target 3-D position, translation velocity, and rotating angular velocity. For simplicity, the signal model is transformed into three-joint two-dimensional (2-D) parametric models by analyzing the motion characteristics. Then a gridless method based on atomic norm optimization is proposed to improve precision and simultaneously avoid basis mismatch in traditional compressive sensing (CS) techniques. Once the covariance matrix is obtained by solving the corresponding semi-definite program (SDP), estimating signal parameters via rotational invariance techniques (ESPRIT) can be used to estimate the positions, then motion parameters can be obtained by Least Square (LS) method, accordingly. Afterwards, pairing correction is carried out to remove registration errors by setting judgment conditions according to resolution performance analysis, to improve the accuracy. In this way, high-precision imaging can be realized without a spectral search process, and any slight changes of target posture can be detected accurately. Simulation results show that proposed method can realize accurate localization and imaging with motion parameter estimated efficiently.

Efficient 2-D DOA and frequency estimation for L-shaped array via RD-PM

ABSTRACTThis paper addresses the issue of joint two-dimensional direction of arrival (2-D DOA) and frequency estimation via reduced-dimensional propagator method (RD-PM) with L-shaped array. The proposed algorithm has no need for eigenvalue decomposition of the sample covariance matrix and simplifies three-dimensional global spectral search within the three-dimensional propagator method (3-D PM) to one-dimensional local search, which greatly reduces computational complexity. Furthermore, the proposed algorithm can work under both uniform and non-uniform L-shaped array and can achieve paired 2-D DOA and frequency estimates automatically. In addition, the 2-D DOA and frequency estimation performance for the proposed method is approximate 3-D PM algorithm and parallel factor (PARAFAC) method but exceeds the estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm and improved PM algorithm. The detailed derivation of Cram´er-Rao bound (CRB) is provided and the simulation results demonstrate the effectiveness and superiority of the proposed approach.

Fast Estimation Method of Space-Time Two-Dimensional Positioning Parameters Based on Hadamard Product

The estimation speed of positioning parameters determines the effectiveness of the positioning system. The time of arrival (TOA) and direction of arrival (DOA) parameters can be estimated by the space-time two-dimensional multiple signal classification (2D-MUSIC) algorithm for array antenna. However, this algorithm needs much time to complete the two-dimensional pseudo spectral peak search, which makes it difficult to apply in practice. Aiming at solving this problem, a fast estimation method of space-time two-dimensional positioning parameters based on Hadamard product is proposed in orthogonal frequency division multiplexing (OFDM) system, and the Cramer-Rao bound (CRB) is also presented. Firstly, according to the channel frequency domain response vector of each array, the channel frequency domain estimation vector is constructed using the Hadamard product form containing location information. Then, the autocorrelation matrix of the channel response vector for the extended array element in frequency domain and the noise subspace are calculated successively. Finally, by combining the closed-form solution and parameter pairing, the fast joint estimation for time delay and arrival direction is accomplished. The theoretical analysis and simulation results show that the proposed algorithm can significantly reduce the computational complexity and guarantee that the estimation accuracy is not only better than estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm and 2D matrix pencil (MP) algorithm but also close to 2D-MUSIC algorithm. Moreover, the proposed algorithm also has certain adaptability to multipath environment and effectively improves the ability of fast acquisition of location parameters.

Stability Research of High-Speed Railway EMUs and Traction Network Cascade System Considering Impedance Matching

Due to the low-frequency oscillation (LFO) between traction network and electric multiple units (EMUs) of high-speed railway, many traction blockades occur in different EMU depots. Aiming at this problem, the mathematical model and small-signal analysis model of EMUs-traction network cascade system (ETNCS) are built in this paper. The system stability mainly affected by the electrical coupling between source and load module is analyzed and discussed in detail. Considering the autotransformer leakage reactance, traction network impedance, and distributed capacitance, the output source module resistance of ETNCS is calculated based on the generalized symmetrical component method. Using the generalized Nyquist criterion and Bode diagram, the ETNCS's stability is analyzed and the quantitative indicators of system impedance matching are given. Then, the simulation model of full ETNCS is built in this paper, which can reproduce the LFO phenomenon. In addition, the theoretical analysis results and the feasibility of inhibition for LFO are verified based on MATLAB/simulink simulation. Finally, the LFO signal modal analysis is implemented by using Prony and estimating signal parameters via rotational invariance techniques (ESPRIT) methods. The conclusions show that the proposed stability and modal analysis methods could be used not only to analyze the LFO more clearly, but also to provide the technical reference for the stable operation of EMUs.

A New Algorithm for Sparse Aperture Interpolation

A new algorithm for filling sparse aperture synthetic aperture radar (SAR)/inverse SAR (ISAR) data, which applies for widely gapped apertures, is proposed in this letter. An Estimating Signal Parameter via Rotational Invariance Techniques(ESPRIT)-based parametric approach is first used to estimate the power distribution with the sparse data. With the estimated power spectrum as prior information, by minimizing a weighted norm as a constraint, the full aperture data can be estimated. Although the algorithm is proposed for the sparse aperture interpolation in SAR/ISAR, it can be applied to other gapped data spectral estimation problems as well. Both numerical and experimental examples are provided to demonstrate the performance of the proposed algorithm.

Application of frequency estimation algorithm based on a single vector sensor in underwater acoustic communication

A method of high resolution frequency estimation based on a single vector sensor using ESPRIT (Estimating Signal Parameters via Rotational Invariance Techniques) algorithm is proposed and applied to the underwater acoustic (UWA) communication system of frequency modulation. Higher resolution frequency estimation can be obtained by this algorithm using fewer snapshots comparing with the sound intensity frequency estimation. Results of simulation and lake experiment show that the proposed algorithm can improve the communication data rate and reduce the bandwidth of the system. Because higher signal-to-noise ratio (SNR) is demanded, this algorithm can be used in high speed short range UWA communication at present.