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Facing the challenge of small open labeled data sets in remote sensing change detection, this letter proposes a novel supervised change detection method by taking advantages of capsule network which can reach the same performance as traditional convolutional neural networks (CNNs) but with less training data. To achieve this aim, we propose a pseudo-Siamese capsule network which takes both rotational invariance and spatial hierarchies between features into account for aerial images change detection. First, the features of image pairs are extracted by two identical nonshared weights convolutional capsule networks. Second, the extracted features are directly concatenated and sent to another convolutional capsule layer. The change probability map is obtained by calculating the length of the capsule vectors in the final layer. Additionally, to reduce the influence of imbalance samples when we optimize our network, we design a margin-focal loss function to pay more attention to the misclassified samples. Finally, binary change map can be produced by a simple threshold. Experimental results carried out on the SZTAKI AirChange Benchmark Set show that the proposed method achieves comparable and even better results with existing state-of-the-art methods in terms of F-measure.

This paper proposes a new algorithm, named Householder Dice (HD), for simulating dynamics on dense random matrix ensembles with rotational invariance. Examples include the Gaussian ensemble, the Haar-distributed random orthogonal ensemble, and their complex-valued counterparts. A “direct” approach to the simulation, where one first generates a dense $n \times n$ matrix from the ensemble, requires at least $\mathcal {O}(n^{2})$ resource in space and time. The HD algorithm overcomes this $\mathcal {O}(n^{2})$ bottleneck by using the principle of deferred decisions: rather than fixing the entire random matrix in advance, it lets the randomness unfold with the dynamics. At the heart of this matrix-free algorithm is an adaptive and recursive construction of (random) Householder reflectors. These orthogonal transformations exploit the group symmetry of the matrix ensembles, while simultaneously maintaining the statistical correlations induced by the dynamics. The memory and computation costs of the HD algorithm are $\mathcal {O}(nT)$ and $\mathcal {O}(nT^{2})$ , respectively, with $T$ being the number of iterations. When $T \ll n$ , which is nearly always the case in practice, the new algorithm leads to significant reductions in runtime and memory footprint. Numerical results demonstrate the promise of the HD algorithm as a new computational tool in the study of high-dimensional random systems.

In this paper, a novel direction of arrival (DOA) estimation algorithm using directional antennas in cylindrical conformal arrays (CCAs) is proposed. To eliminate the shadow effect, we divide the CCAs into several subarrays to obtain the complete output vector. Considering the anisotropic radiation pattern of a CCA, which cannot be separated from the manifold matrix, an improved interpolation method is investigated to transform the directional subarray into omnidirectional virtual nested arrays without non-orthogonal perturbation on the noise vector. Then, the cross-correlation matrix (CCM) of the subarrays is used to generate the consecutive co-arrays without redundant elements and eliminate the noise vector. Finally, the full-rank equivalent covariance matrix is constructed using the output of co-arrays, and the unitary estimation of the signal parameters via rotational invariance techniques (ESPRIT) is performed on the equivalent covariance matrix to estimate the DOAs with low computational complexity. Numerical simulations verify the superior performance of the proposed algorithm, especially under a low signal-to-noise ratio (SNR) environment.

Complex fuzzy sets (CFSs) are a new extension of fuzzy sets, whose membership grades are vectors in the unit circle of the complex plane. Complex fuzzy operations are of high importance in both theoretical and applied studies of CFSs. The property of rotational invariance is highly pertinent to complex fuzzy operations. To enhance and extend the applicability of complex fuzzy operations, this article develops new types of rotational invariance for complex fuzzy operations. These rotational invariances are raised by different rotation operations of the arguments of complex fuzzy operations. After that, rotational invariance of several complex fuzzy operations is studied.

This work provides an efficient sampling method for the covariance matrix adaptation evolution strategy (CMA-ES) in large-scale settings. In contract to the Gaussian sampling in CMA-ES, the proposed method generates mutation vectors from a mixture model, which facilitates exploiting the rich variable correlations of the problem landscape within a limited time budget. We analyze the probability distribution of this mixture model and show that it approximates the Gaussian distribution of CMA-ES with a controllable accuracy. We use this sampling method, coupled with a novel method for mutation strength adaptation, to formulate the mixture model based evolution strategy (MMES) -- a CMA-ES variant for large-scale optimization. The numerical simulations show that, while significantly reducing the time complexity of CMA-ES, MMES preserves the rotational invariance, is scalable to high dimensional problems, and is competitive against the state-of-the-arts in performing global optimization.

In the present paper, the first three modal frequencies obtained through recorded vibration signal of a steel truss bridge is investigated at three different vehicular speeds. The denoising and extraction of modal frequencies from vibration response signals of steel truss bridge is performed using Hilbert transform (HT) in combination with high-frequency resolution enhancing techniques. The modal frequency extracting techniques applied includes Fast Fourier transform (FFT), multiple signal classification (MUSIC), and estimation of signal parameters by rotational invariance technique (ESPRIT). The comparisons of the outcomes of HT-FFT, HT-root-MUSIC, and HT- ESPRIT are computed. It is observed that HT-FFT computed results with the low resolution which hindered in obtaining distinct modal frequencies while HT-MUSIC and HT-ESPRIT achieved the most denoised, robust and reliable outcomes. The HT-ESPRIT outperforms HT-MUSIC in the elimination of unwanted noise. Further, the application of the sliding window HT-ESPRIT method clearly shows the variation of modal frequencies with the change in vehicular speeds. The first three analytical modal frequencies of 4.56 Hz, 10.44 Hz and 16.66 Hz frequencies are compared with the experimental frequencies obtained through vibrations at 10 km/h, 20 km/h and 30 km/h vehicular speeds, respectively. The joints (also denoted as nodes) 6, 7, and 8 exhibited irregular behaviour with no or minimum frequency peaks due to increased flexibility of member at these locations.

The Zernike and pseudo-Zernike moments (ZMs/PZMs) have been found useful for a variety of applications requiring feature extraction due to their favorable properties, such as low information redundancy, rotational invariance, higher noise resilience and extendibility to the color space. In this paper, we propose an approach for color face recognition based on Zernike/pseudo-Zernike quaternion moment vector (QMV) features and a novel normalized-discriminant hybrid color space. The proposed XnSBr color space is composed by taking Xn from the normalized-XYZ, S from HSV and Br from the discriminant RGB-r color spaces to capture the features efficiently. In addition, we propose the use of quaternion vector distance (QVD) similarity measure for the QMV features in order to enhance the recognition accuracy. The exhaustive comparative performance analyses with the state-of-the-art approaches in the different color spaces demonstrate the superiority of the proposed approach in terms of accuracy and speed.

The noise robustness and parameter estimation performance of the classical three-dimensional estimating signal parameter via rotational invariance techniques (3D-ESPRIT) algorithm are poor when the parameters of the geometric theory of the diffraction (GTD) model are estimated at low signal-to-noise ratio (SNR). To solve this problem, a modified 3D-ESPRIT algorithm is proposed. The modified algorithm improves the parameter estimation accuracy by proposing a novel spatial smoothing technique. Firstly, we make cross-correlation of the auto-correlation matrices; then by averaging the cross-correlation matrices of the forward and backward spatial smoothing, we can obtain a novel equivalent spatial smoothing matrix. The formula of the modified algorithm is derived and the performance of this improved method is also analyzed. Then we compare root-mean-square-errors (RMSEs) of different parameters and the locating accuracy obtained by different algorithms. Furthermore, radar cross section (RCS) of radar targets is extrapolated. Simulation results verify the effectiveness and superiority of the modified 3D-ESPRIT algorithm.

Due to their good rotational invariance and stability, image continuous orthogonal moments are intensively applied in rotationally invariant recognition and image processing. However, most moments produce numerical instability, which impacts the image reconstruction and recognition performance. In this paper, a new set of invariant continuous orthogonal moments, polar harmonic Fourier moments (PHFMs), free of numerical instability is designed. The radial basis functions (RBFs) of the PHFMs are much simpler than those of the Chebyshev-Fourier moments (CHFMs), orthogonal Fourier-Mellin moments (OFMMs), Zernike moments (ZMs), and pseudo-Zernike moments (PZMs). For the same degree, the RBFs of the PHFMs have more zeros and are more evenly distributed than those of the ZMs and PZMs. Therefore, PHFMs do not suffer from information suppression problem; hence, the image description ability of the PHFMs is superior to that of the ZMs and PZMs. Moreover, the RBFs of the PHFMs are always less than or equal to 1.0 near the unit disk center, whereas those of the OFMMs, PZMs, CHFMs, and radial harmonic Fourier moments (RHFMs) are infinite (implying numerical instability). This indicates that PHFMs can outperform these moments in image reconstruction tasks. We theoretically and experimentally demonstrate that PHFMs outperform the above moments in reconstructing images and recognizing rotationally invariant objects considering noise and various attacks. This paper also details the significance of the PHFM phase in image reconstruction, angle estimation using PHFMs, and the accurate moment selection of the PHFMs.

Locality preserving projections (LPP) method is a classical manifold learning method for dimensionality reduction. However, LPP is sensitive to outliers since squared L2-norm may exaggerate the distance of outliers. Besides, the normalisation constraint of LPP may impair its robustness during embedding. Motivated by this observation, the authors propose a novel robust LPP using angle-based adaptive weight (RLPP-AAW) method. RLPP-AAW not only considers the distance metric of training samples, but also take the reconstruction error into account, so as to reduce the influence of outliers and noise in the embedding process. In the RLPP-AAW, based on the angle between distance metric and reconstruction error, a novel way is used to combine them in the objective function. Besides, RLPP-AAW employs the L21-norm criterion, which retains rotational invariance and is more robust than squared L2-norm. An iterative algorithm is presented to solve the objective function of RLPP-AAW. Experimental results on the benchmark databases illustrate the effectiveness of the proposed algorithm.

In this research paper, we have devised single-snapshot direction-of-arrival (DOA) algorithms for a uniform circular array (UCA) to resolve multiple targets. Estimation of signal parameters via rotational invariance technique (ESPRIT) and the modified multiple signal classification (MUSIC) algorithms are employed for high-resolution estimation of DOAs. Experimental results are shown to validate the efficacy of the proposed methods. Computer simulations prove that the proposed UCA-ESPRIT and the UCA-modified MUSIC algorithms using single snapshot provide the accurate estimation of DOAs but with the reduced computational complexity. The CPU time obtained using an intel i5 processor shows a significant reduction in computation time as compared to the classical methods. Hence the proposed DOA methods using single snapshot for UCA are suitable in wireless location systems when only a few snapshots or, in the worst case, a single snapshot of the antenna array is on hand for the signal estimation.

This paper presents a clustering technique to rank the dominant modes of low frequency oscillations in power systems under model order uncertainty of the signal. The rotational invariance property of the signal subspace is utilized to obtain the modes of oscillations. Rotational invariance of the signal under multiple shifts is considered to obtain the preliminary estimates of the modes. Subsequently, the modes are clustered to obtain the dominant modes that belong to the signal subspace. A signal subspace participation index (SSPI) is used to rank the modes according to their dominance in signal subspace. Thereafter, the convex combination of the preliminary modes, estimated from the multiple shifts of the signal subspace, is used to obtain the final mode estimates. The simulation results are presented for signal generated using the modes obtained from a two-area system. Additionally, the methodology is also tested on field data obtained from the PMU installed at a generating station in India.

A complex-valued Hopfield neural network (CHNN) is a multistate Hopfield model and has been applied to the storage of image data. It has the weak noise tolerance due to the inherent property of rotational invariance. A hyperbolic-valued Hopfield neural network (HHNN) resolves rotational invariance and improves the noise tolerance. A rotor Hopfield neural network (RHNN) is an extension of CHNN and the weights are represented by matrices. It provides excellent noise tolerance by resolving the rotational invariance. However, an RHNN needs double weight parameters of a CHNN, unlike an HHNN. In this work, we propose a diagonal RHNN (DRHNN), which restricts the weights of RHNN to diagonal matrices and reduces the number of weight parameters. The number of weight parameters in a DRHNN, an HHNN, and a CHNN is same. In addition, a DRHNN resolves the rotational invariance and provides excellent noise tolerance like an RHNN.

In this paper, a fast adaptive Principal Component Analysis (PCA) based scheme is proposed to estimate and track the channel state information (CSI) of two dimensional (2D) massive multiple-input and multiple-output (M-MIMO) systems with uniform rectangular array (URA). First, the signals received online at the base station (BS) are used to estimate and track the principal components. Then, based on the estimated signal eigenvectors, a 2D unitary estimating signal parameters via rotational invariance technique (ESPRIT) algorithm is introduced to jointly estimate and track the channel coefficients which include the direction of arrival (DoA) of elevation and azimuth angles and the channel gain corresponding to each resolvable path of the channel. In order to improve the tracking speed, an optimal step size is derived which can accelerate the convergence speed of channel tracking significantly. Since the 2D unitary ESPRIT algorithm is applied, the proposed method can reduce computational complexity by converting the complex data matrix to the real one. Simulation results are provided to verify the estimation and tracking accuracy of the proposed scheme.

System inertia plays a vital role in controlling the angular stability of the system during a disturbance. Due to increased penetration of power electronic interfaced sources, such as Solar Photovoltaic (SPV) source, the overall system inertia reduces and varies depending on their operating conditions. In this paper, an approach for online inertia estimation in the power system network with SPV sources is proposed, using the synchronized measurements from Phasor Measurement Units (PMUs). An equivalent swing equation is used to emulate the network dynamics. A relationship between the inertia constant and the roots of this equation is determined. In order to numerically obtain the roots, the Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) method is first used to find the modes present in the frequency signal. A new formulation is proposed to extract an equivalent mode from all the obtained modes. Also, to avoid phase step error, Rate Of Change Of Frequency (ROCOF) is estimated from the equivalent mode of the frequency signal. Results obtained for the 39 bus New England system for various test cases, using Real-Time Digital Simulator (RTDS), prove the efficacy and superiority of the proposed approach over the existing approaches in the literature.

This paper has made proposition of a nested array and an estimation algorithm for direction-of-arrival (DOA) of two-dimensional (2D) coherently distributed (CD) sources. According to the difference coarray concept, double parallel hole-free virtual uniform linear arrays are generated by virtue of vectorization operation on cross-correlation matrices of subarrays. Sensor coordinates of virtual arrays are derived. Rational invariance relationships of virtual arrays are derived. According to the rotational invariance relationships, matrices satisfying rotation invariance are constructed by extracting and regrouping the receive vectors of the virtual arrays, and then an estimation of signal parameters via rotational invariance techniques- (ESPRIT-) like framework on matrix reconstruction is deduced. Optimal configuration of the nested array as well as computational complexity are analyzed. Without pair matching, the proposed method can resolve more sources than the sensor number. Simulation outcomes indicate that the proposed method tends to have a better performance as compared to the traditional uniform arrays that have similar number of sensors.

To exploit the information from two-dimensional structured data, two-dimensional principal component analysis (2-DPCA) has been widely used for dimensionality reduction and feature extraction. However, 2-DPCA is sensitive to outliers which are common in real applications. Therefore, many robust 2-DPCA methods have been proposed to improve the robustness of 2-DPCA. But existing robust 2-DPCAs have several weaknesses. First, these methods cannot be robust enough to outliers. Second, to center a sample set mixed with outliers using the L2-norm distance is usually biased. Third, most methods do not preserve the nice property of 2-DPCA (rotational invariance), which is important for learning algorithm. To alleviate these issues, we present a generalized robust 2-DPCA, which is named as 2-DPCA with $$\ell _{2,p}$$ -norm minimization ( $$\ell _{2,p}$$ -2-DPCA), for image representation and recognition. In $$\ell _{2,p}$$ -2-DPCA, $$\ell _{2,p}$$ -norm is employed as the distance metric to measure the reconstruction error, which can alleviate the effect of outliers. Therefore, the proposed method is robust to outliers and preserves the desirable property of 2-DPCA which is invariant to rotational and well characterizes the geometric structure of samples. Moreover, most existing robust PCA methods estimate sample mean from database with outliers by averaging, which is usually biased. Sample mean are treated as an unknown variable to remedy the bias of computing sample mean in $$\ell _{2,p}$$ -2-DPCA. To solve $$\ell _{2,p}$$ -2-DPCA, we propose an iterative algorithm, which has a closed-form solution in each iteration. Experimental results on several benchmark databases demonstrate the effectiveness and advantages of our method.

The prevalent imaging method in inverse synthetic aperture radar (ISAR) system is range-Doppler (RD) method, which is implemented by the fast Fourier transformation (FFT). FFT is computationally efficient, but it comes with a price – the problems of wide main-lobes and high side-lobes, especially under the sparse apertures condition. In addition, the resolution of RD method is determined by the radar parameters, which poses limitation to super-resolution imaging, multi-tasking and cognitive reconfigurable applications. In this study, the authors propose a novel super-resolution ISAR imaging method based on the total least squares-estimation of signal parameters via rotational invariance technique (TLS-ESPRIT). The locations and intensities of the scatterers are obtained by employing the ESPRIT algorithm and the least squares technique. Then the ISAR image is formulated, having circumvented all of the above-mentioned limitations. Experiments based on simulated and real measured data validate the effectiveness of the proposed method.

Multiple-input multiple-output (MIMO) is a technical hotspot in physical layer with numerous applications in wireless communications, radars, sonars, and well beyond. In this paper, we focus on the multi-dimensional angle estimation problem in a bistatic electromagnetic vector sensors (EMVS) MIMO system. Namely, we need to simultaneously estimate two-dimensional (2D) direction-of-arrival (DOA), 2D direction-of-departure (DOD), 2D receive polarization angle (RPA) and 2D transmit polarization angle (TPA). To tackle this issue, a parallel factor (PARAFAC) analysis-based estimator is proposed. Firstly, a third-order PARAFAC analysis data model is established, which can efficiently exploit the tensor structure of the array measurement. After performing PARAFAC decomposition on the tensor measurement, the factor matrices are achieved. By combining the estimation method of signal parameters via rotational invariance technique (ESPRIT) with the vector cross-product method, joint estimates of 2D-DOD, 2D-DOA, 2D-TPA and 2D-RPA are obtained without further pairing calculation. Compared with the state-of-the-art ESPRIT-Like approach, the proposed method can achieve better performance by enforcing the third-order structure information, and it is suitable for arbitrary array manifolds. Theoretical analyses are given and numerical results corroborate our analysis.

Based on the optimized coprime array (OpCA), we propose a real-valued Toeplitz matrix method. This article analyzes the feasibility of converting the manifold matrix of a virtual domain constructed from a physical array into a real-valued matrix, and the unitary estimation of signal parameters via rotational invariance technique is introduced to transform the equivalent received signal rearranged Toeplitz matrix into a real-valued matrix and obtain directions of arrival (DOAs). Moreover, the proposed method offers higher estimation accuracy. Simulations are demonstrated to prove the validity of this method.

International audience; The Canonical Polyadic (CP) tensor decomposition has become an attractive mathematical tool in several fields during the last ten years. This decomposition is very powerful for representing and analyzing multidimensional data. The most attractive feature of the CP decomposition is its uniqueness, contrary to rank-revealing matrix decompositions, where the problem of rotational invariance remains. This paper presents the performance analysis of iterative descent algorithms for calculating the CP decomposition of tensors when columns of factor matrices are almost collineari.e. swamp problems arise. We propose in this paper a new and efficient proximal algorithm based on the Forward Backward splitting method. More precisely, the existence of the best low-rank tensor approximation is ensured thanks to a coherence constraint implemented via a logarithmic regularized barrier. Computer experiments demonstrate the efficiency and stability of the proposed algorithm in comparison to other iterative algorithms in the literature for the normal case, and also producing significant results even in difficult situations.; La décomposition du tenseur polyadique canonique (CP) est devenue un outil mathématique intéressant dans plusieurs domaines au cours des dix dernières années. Cette décomposition est très puissante pour représenter et analyser des données multidimensionnelles. La caractéristique la plus attrayante de la décomposition CP est son caractère unique, contrairement aux décompositions matricielles, où le problème de l'invariance de rotation demeure. Cet article présente l'analyse des performances des algorithmes de descente itérative pour le calcul de la décomposition CP des tenseurs lorsque les colonnes des matrices de facteurs sont presque colinéaires, c'est-à-dire lorsque des problèmes de marais surviennent. Nous proposons dans cet article un nouveau algorithme proximal, basé sur la méthode de décomposition Avant et Arrière. Plus précisément, l'existence de la meilleure approximation des tenseurs de rang inférieur est assurée grâce à une contrainte de cohérence mise en œuvre via une barrière logarithmique régularisée. Les expériences réalisées sur ordinateur démontrent l'efficacité et la stabilité de l'algorithme proposé par rapport aux autres algorithmes itératifs de la littérature pour le cas normal, et produisant également des résultats significatifs même dans des situations difficiles.

Domain switching pathways in ferroelectric materials visualized by dynamic Piezoresponse Force Microscopy (PFM) are explored via variational autoencoder (VAE), which simplifies the elements of the observed domain structure, crucially allowing for rotational invariance, thereby reducing the variability of local polarization distributions to a small number of latent variables. For small sampling window sizes the latent space is degenerate, and variability is observed only in the direction of a single latent variable that can be identified with the presence of domain wall. For larger window sizes, the latent space is 2D, and the disentangled latent variables can be generally interpreted as the degree of switching and complexity of domain structure. Applied to multiple consecutive PFM images acquired while monitoring domain switching, the polarization switching mechanism can thus be visualized in the latent space, providing insight into domain evolution mechanisms and their correlation with the microstructure., The revised version

In this paper, we extend the coprime planar array to coprime cubic array and propose a three dimensional coprime array (TDCA) for two-dimensional direction of arrival (DOA) estimation, which possesses larger inter-element spacing so that the mutual coupling effects can be effectively relieved. Moreover, due to the larger array aperture, better DOA estimation performance can be achieved. To obtain more degrees of freedom (DOFs), a generalized TDCA (G-TDCA) configuration is proposed, which has a flexible array geometry and can extend the array aperture to obtain performance improvement. The principle for optimal array design of G-TDCA is derived to achieve the maximum DOF. And the Cramer–Rao Bounds which denotes as a theoretical benchmark for the lower bound of unbiased estimate are derived. Then we propose Khatri–Rao estimation signal parameters via rotational invariance techniques (KR-ESPRIT) algorithm and obtain the close-form expression. The algorithm can achieve angles with automatic pairing and doesn’t need spectrum peak searching. In order to decrease the computational complexity, we propose KR-Unitary ESPRIT algorithm, which can achieve approximate DOA estimation performance of the KR-ESPRIT algorithm with the lower computational complexity. Numerical simulation results verify the superiority of G-TDCA with proposed algorithms.

In this study, the authors propose a fast quadrilinear decomposition algorithm for estimation of the directions-of-arrival and polarisations of the incident sources via a uniform rectangular array of electromagnetic vector sensors (EMVSs). Conventional quadrilinear alternating least squares (QALS), involves computationally intensive Khatri-Rao products in each iteration, to update the parameter matrices (factors). Moreover, QALS is more likely to fall in a local minimum and tends to take more steps before an acceptable solution, which further slows down the convergence and often mis-converges, thereby yielding meaningless results. To preserve the quadrilinearity, they arrange the measurements as a four-dimensional (4D) data (fourth-order tensor), from which a third-order sub-tensor (3D slice) can be obtained by fixing one index along any dimension. These slices are used to create new cost functions that are alternately minimised while updating the factors until convergence. They show that the rows of parameter matrices form the diagonal elements of a tensor, which capture the internal quadrilinearity of data and significantly reduce the cost function in few iterations only. Simulation results verify that the authors' algorithm holds faster convergence, does not mis-converge, provides parameter estimation accuracy similarly to the QALS and superior of the Estimation of Signal Parameters via Rotational Invariance Technique and propagator method.

The problem of direction-of-arrival (DOA) estimation in partially calibrated arrays composed of multiple uniform linear arrays is studied. We assume that each subarray is calibrated well, so that the steering vectors of all subarrays are exactly known. However, the intersubarray calibration errors are unknown. The proposed method first obtains a set of initial DOA results by employing a rotational invariance property between two sets of received data, and then more accurate DOA estimation and self-calibration are performed by using the MUSIC-based method through a local searching algorithm. We also derive the corresponding stochastic Cramer-Rao bound to which we compare the performance of the proposed estimator.

In the present paper, we describe a new simple stereological method of estimating volume tensors in 3D from vertical sections. The volume tensors provide information about particle shape in 3D. In a model-based setting, the method requires that the particle distribution is invariant under rotations around the vertical axis. In a design-based approach, where the vertical section is uniformly rotated around the vertical axis, the method provides information about an index of elongation of the particles in the direction of the vertical axis. The method has been implemented on human brain tissue for the analysis of neurons in layer III of the medial frontal gyrus of Brodmann Area 46. In the actual implementation, the new estimator shows similar precision as an earlier estimator, based on an optical rotator design, but it is a factor 3 faster to collect the measurements for the new estimator. Furthermore, the calculations needed for determining the new estimator are much simpler. Lay Description A new method is described for estimating volume tensors in 3 dimensions based on the stereological method: planar rotator. In general, volume tensors may provide information about particle volume, shape and direction. The new estimator was implemented on human brain tissue for the analysis of neurons in layer III of the medial frontal gyrus on Brodmann Area 46 and compared to a previous published method, based on an optical rotator design. The new estimator shows similar precision as the earlier estimator, but it is a factor 3 faster to collect the measurements. Besides, the calculations behind the new estimator are simpler and easier to implement to a software program.

We consider the problem of sampling binary phase shift keying (BPSK) signals, which are widely used in communications and radar systems. Although sub-Nyquist sampling of such signals has been treated in various works, giant samples were needed. In this brief, a new sub-Nyquist sampling method based on a multichannel feedback structure is proposed for BPSK signals, which requires fewer samples. BPSK signals can be characterized by a finite number of parameters, namely, the carrier frequency, amplitude, locations of discontinuities, and phase of each symbol. Our feedback structure consists of a main channel and a feedback channel. The carrier frequency and amplitude can be estimated by the estimation of signal parameters by a rotational invariance technique algorithm in the main channel, while the phases and locations of discontinuities can be estimated by the annihilating filter in the feedback channel. The effectiveness of the proposed method is verified via simulations. In a noiseless situation, for a seven-segment BPSK signal lasting $1~{\mu } {s}$ with a 500-MHz carrier frequency, the equivalent sampling rate of the proposed method is only 3.8% of the carrier frequency, and much less than the Nyquist sampling rate of the signal. Finally, we analyze the effect of noise and present a robust reconstruction algorithm. Simulation results show that the proposed method exhibits better noise robustness than previous approaches.

Distributed sources can be regarded as an assembly of point sources within a spatial distribution. In this paper, we explore the estimation of the two-dimensional incoherently distributed sources using double L-shape arrays. The rotational invariance properties of the nominal elevation and nominal elevation are firstly obtained by taking first-order Taylor series expansions with regard to the generalized steering vectors of two pairs of parallel subarrays. The rotation operators can be solved based on signal subspace. Then the nominal elevation and nominal elevation can be obtained from parameters matching method. Estimation of direction of arrival can be used in multi-source scenario and needn't peak-finding search. Lastly the angular spreads can be solved through two-dimensional Capon search based on nominal angles. The simulation experiments show that the proposed method has good performance on the estimation of two-dimensional incoherently distributed sources. Investigating different experimental conditions, sources with different angular spreads, simulations are conducted to validate better estimation accuracy of the proposed method.

The presence of fault antennas in bistatic multiple-input–multiple-output (MIMO) radar causes a significant degradation of angle estimation performance. In this study, the authors present a signal-processing scheme for bistatic MIMO radar with impaired receive array including array diagnosis as well as angle estimation. The damaged antenna in the receiver, which is incapable of receiving the target signals and leaves only the thermal noise generated within the receiver itself, leads to a decrease in the entropy of its received data. The dissimilarity of the entropy values between the damaged and normal receive antennas is used for array diagnosis. Thereafter, the useless noise data of the detected fault antennas is removed in the receive signal matrix, so that the successive data missing occurs along the row directions of the signal subspace matrix. A low-rank block-Hankel structured matrix is constructed from the incomplete signal subspace matrix, which can facilitate the exploitation of the matrix completion technique to recover that successive missing data. On the basis of the restored rotational invariance structure of the complete signal subspace, the estimation of signal parameters via rotational invariance technique can then be applied for angle estimation. Simulation results confirm the validity of the proposed methods.

Phase-coherence of signals in different sub-bands is a prerequisite for multiband fusion radar imaging. Here, a mutual-coherence compensation method based on valid dominant poles and phase autofocusing is proposed to compensate for the incoherent phases (ICPs) between sub-bands in multiband fusion inverse synthetic aperture radar (ISAR) imaging. In the proposed method, the linear ICP compensation and fixed ICP compensation are decoupled rather than the ICPs being compensated pulse by pulse as in traditional methods. In this method, the valid dominant poles that correspond to strong scatterers in the estimated poles of each sub-band are first extracted to estimate the linear ICP. Then, phase autofocusing technology based on the same rotation centre is applied to multiple pulses in each sub-band in the ISAR coherently processing time to jointly compensate for all the fixed ICPs at once. Furthermore, a unitary estimation of signal parameters via the rotational invariance techniques (U-ESPRIT) method, which can exploit considerable information from the measured data, is utilised to estimate the poles of the sub-bands to improve the accuracy of the estimation of the linear ICP between sub-bands. The effectiveness and robustness of the method were verified experimentally based on both numerical simulations and real data.

In this paper, the topic of coherent two-dimensional direction of arrival (2D-DOA) estimation is investigated. Our study jointly utilizes the compressed sensing (CS) technique and the parallel profiles with linear dependencies (PARALIND) model and presents a 2D-DOA estimation algorithm for coherent sources with the uniform rectangular array. Compared to the traditional PARALIND decomposition, the proposed algorithm owns lower computational complexity and smaller data storage capacity due to the process of compression. Besides, the proposed algorithm can obtain autopaired azimuth angles and elevation angles and can achieve the same estimation performance as the traditional PARALIND, which outperforms some familiar algorithms presented for coherent sources such as the forward backward spatial smoothing-estimating signal parameters via rotational invariance techniques (FBSS-ESPRIT) and forward backward spatial smoothing-propagator method (FBSS-PM). Extensive simulations are provided to validate the effectiveness of the proposed CS-PARALIND algorithm.

Spatially confined magnetic inhomogeneities were revealed by measuring nuclear forward scattering time spectra on the same sample in two different geometric arrangements. They differ by 180° rotation of the sample around one of the polarization axes. A basic theoretical description of this phenomenon and its relation to a spatial distribution of nuclei featuring different magnetic moments is provided. From an experimental point of view, the violation of rotational invariance was observed for an inhomogeneous Fe81Mo8Cu1B10 metallic glass. The development of magnetic inhomogeneities and their relation to the evolution of time spectra was studied during thermal annealing.

Several techniques exist to estimate the directions of arrival (DOAs) of sound sources captured with a spherical microphone array. The eigenbeam rotational invariance technique (EB-ESPRIT) uses recurrence relations of spherical harmonics to estimate the DOAs. In this letter, we propose a new EB-ESPRIT method which uses three recurrence relations and a joint-diagonalization procedure to estimate the unit-vectors pointing to the source DOAs. We evaluate the angular estimation errors of the proposed method under noisy and reverberant conditions and compare it to existing EB-ESPRIT methods. We find that our proposed method can estimate the source DOAs with higher accuracy compared to the discussed existing EB-ESPRIT methods, and the estimation accuracy does not depend on the source DOAs.

We construct a set of special complex-valued integral images and an algorithm that allows to calculate Zernike moments fast, namely in constant time. The technique is suitable for dense detection procedures, where the image is scanned by a sliding window at multiple scales, and where rotational invariance is required at the level of each window. We assume no preliminary image segmentation. Owing to the proposed integral images and binomial expansions, the extraction of each feature does not depend on the number of pixels in the window and thereby is an $O(1)$ calculation. We analyze algorithmic properties of the proposition, such as: number of needed integral images, complex-conjugacy of integral images, number of operations involved in feature extraction, speed-up possibilities based on lookup tables. We also point out connections between Zernike and orthogonal Fourier–Mellin moments in the context of computations backed with integral images. Finally, we demonstrate three examples of detection tasks of varying difficulty. Detectors are trained on the proposed features by the RealBoost algorithm. When learning, the classifiers get acquainted only with examples of target objects in their upright position or rotated within a limited range. At the testing stage, generalization onto the full $360^\circ$ angle takes place automatically.

Inspired by the importance of preserve the robustness of algorithm, in this paper, a simple and effective underwater target recognition algorithm called robust principal component analysis network (RPCANet) is established, which has further enhanced the operational ability of unmanned underwater vehicle (UUV) with optical vision systems. Several advantages of RPCANet are summarized as follows. First, RPCANet is superior to traditional underwater target recognition methods, such as principal component analysis (PCA), because it is not sensitive to severe outliers. Second, RPCANet employs .... F p .... -norm as the distance metric for obtaining a filter. The proposed method retains the desirable properties of the PCA, which includes a solution related to the covariance matrix and rotational invariance. In addition, RPCANet is a simple deep learning network used for image recognition and classification. Finally, the performance of the proposed method is illustrated by video image data collected by the optical vision system of the UUV. The experimental results show the advantages and effectiveness of proposed recognition scheme.

In electronic countermeasures and reconnaissance, unmanned aerial vehicle (UAV) has played a more and more significant role. Usually when UAV conducts low altitude reconnaissance, due to the complicated environment, the reflected signals of the same source through different propagation paths will produce multipath signals. In this paper, we construct the received multipath signals of UAV with antennas array as coherently distributed (CD) sources model and propose a successive distributed signal parameter estimation (S-DSPE) algorithm to estimate its nominal direction of arrival (DOA) and angular spread. The proposed algorithm simplifies two-dimensional (2D) spectral peak searching within the conventional DSPE algorithm to one-dimensional spectral peak searching, which remarkably reduces the computational complexity of conventional DSPE algorithm. Furthermore, the parameters estimation performance of the proposed algorithm is close to the conventional DSPE algorithm, and outperforms the estimation of signal parameters via rotational invariance technique (ESPIRT) algorithm and propagator method (PM). The simulations results verify the usefulness of the proposed algorithm.

In estimating the two-dimensional (2D) direction-of-arrival (DOA) using a coprime planar array, there are problems of the limited degree of freedom (DOF) and high complexity caused by the spectral peak search. We utilize the time-domain characteristics of signals and present a high DOF algorithm with low complexity based on the noncircular signals. The paper first analyzes the covariance matrix and ellipse covariance matrix of the received signals, vectorizes these matrices, and then constructs the received data of a virtual uniform rectangular array (URA). 2D spatial smoothing processing is applied to calculate the covariance of the virtual URA. Finally, the paper presents an algorithm using 2D multiple signal classification and an improved algorithm using unitary estimating signal parameters via rotational invariance techniques, where the latter solves the closed-form solutions of DOAs replacing the spectral peak search to reduce the complexity. The simulation experiments demonstrate that the proposed algorithms obtain the high DOF and enable to estimate the underdetermined signals. Furthermore, both two proposed algorithms can acquire the high accuracy.

This study presents a minimum distance-based direction-of-arrival (DOA) estimation algorithm for coprime electromagnetic vector sensor (EMVS) arrays. The idea is to split-up the coprime array into two uniform linear arrays (ULAs) of vector sensors and arrange the received ULA data in the form of a three-way array suitable for parallel factor (PARAFAC) analysis, which fits least-square models to the received source signal mixtures of ULAs and thus enables to retrieve the model matrices corresponding to each ULA. Nevertheless, because of the array splitting the estimated DOAs from these matrices are not unique. To uniquely determine the DOA, the authors state and prove a theorem which is fundamental to the proposed algorithm and provides a means to find an estimate based on the minimum distance criterion. Efficacy of the proposed algorithm is demonstrated through performance comparison with other existing algorithms such as Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), long vector MUltiple SIgnal Classification (MUSIC), conventional PARAFAC and the propagator method being simulated for an equivalent element ULA of EMVS and spaced half a wavelength apart. Numerical simulations reveal that the proposed algorithm outperforms the others.

In this paper, a two-stage mode identification algorithm including preprocessing and identification steps is introduced to solve the problems of measuring noise and inaccurate mode identification in the analysis of low-frequency oscillation (LFO) in a wide area measurement systems (WAMSs). S-G filter de-noising is utilized for the preprocessing. An adaptive total least squares-estimation of signal parameters via rotational invariance techniques (TLS-ESPRIT) algorithm with the order setting of the singular value accumulation percentage adjacency increment ratio (SVAPAIR) is utilized for the identifying stage. The S-G filter is used to mitigate the measuring of LFO noise of the system. Furthermore, the SVAPAIR is adopted to achieve an adaptive and precise determination of the LFO order, and then LFO parameters are extracted by the adaptive TLS-ESPRIT algorithm. The proposed algorithm has been tested and verified using the IEEE four-generator two-area system and the actual measured data of the LFO accident in the North American power grid. The simulation and experimental result showed that the proposed algorithm has better adaptability, anti-noise characteristic, and robustness compared to those of the conventional Prony, matrix pencil (MP), and TLS-ESPRIT algorithms.

Inspired by the importance of distance metrics and the structure-preserving ability of features, a novel recognition method for underwater targets, called generalized robust principal component analysis (GRPCA), is proposed in this paper. Several advantages of GRPCA are summarized as follows. First, GRPCA employs the l2,p-norm as the distance metric for calculating the reconstruction error and variance of projected data and attempts to minimize the sum of the ratios between the reconstruction error and the variance for each data sample. This approach allows it to extract the feature information of an image more accurately, which is important for recognition and representation. Second, the proposed GRPCA algorithm not only is robust but also retains the desirable properties of PCA, such as rotational invariance. Moreover, we present a simple yet efficient iterative update algorithm to solve the GRPCA problem. Finally, on the basis of GRPCA, underwater target recognition technology is developed. The extensive experiments on several underwater optical image databases show that our method is more effective and advantageous than other subspace learning algorithms are.

Direction-of-arrival (DOA) estimation in coprime array involves the problem that there is the coexistence of both uncorrelated signals and coherent signals in the multipath environment. An approach to estimate DOA of uncorrelated and coherent signals separately, based on the coprime linear array and coprime planar array, is proposed in this paper. The uncorrelated signals are estimated first, where the root multiple signal classification (root-MUSIC) is applied in the coprime linear array and unitary estimating signal parameters via rotational invariance techniques (Unitary-ESPRIT) is utilized in the coprime planar array. Those subspace algorithms are of low complexity compared with the spectral peak search method. We then eliminate the components of noises and uncorrelated signals and reconstruct a covariance matrix of coherent signals. Finally, we use the root-MUSIC or Unitary-ESPRIT to resolve the one-dimensional or two-dimensional DOAs of coherent signals, respectively. The simulation results demonstrate the computational efficiency and high accuracy of the proposed algorithm. The results also prove that this algorithm can estimate the number of signals more than that of subarray sensors and separate two signals from the same angle.

In this paper, we investigated into the problem of target location in a bistatic multiple-input multiple-output (MIMO), whose transmit antennas and receive antennas are electromagnetic vector sensors (EMVS). Unlike the traditional linear scaler-sensor array, a linear EMVS array can offer two-diemensional (2D) direction estimation, thus a bistatic EMVS-MIMO radar provides (2D) direction-of-arrival and 2D direction-of-departure estimation. Besides, it is able to estimate 2D transmit/receive polarization angles of the targets. An propagator method (PM)-based estimator is proposed. Firstly, it estimate the propagator from the covariance matrix. The parameters are achieved via utilizing the estimation method of signal parameters via rotational invariance technique (ESPRIT) and the vector cross-product technique. The proposed estimator is computationally friendly since it does not involving eigendecomposition of high-dimensional data. Also, it may has similar (or even better) parameter estimation accuracy than the current EPSRIT-Like algorithm. Simulation results verify the effectiveness of the proposed PM estimator.

Dipole antenna elements whose physical length L is greater than or equal to one-tenth of the wavelength λ are generally denoted as long dipoles. Such radiators are more useful in practical polarization sensitive arrays (PSAs) for electromagnetic sensing applications because their radiation efficiency is greater than that of short dipole radiators for which L

Simultaneous localization and communication (SLAC) is a desirable feature of 5G and beyond 5G wireless networks. To be able to implement SLAC, efficient high dimensional channel estimation methods are critical. This work presents a low-complexity multidimensional channel parameter estimation via rotational invariance techniques (MD-ESPRIT). We use both the spatial smoothing and forward-backward averaging techniques to further explore data samples to extract multipath components (MPCs). We propose a one-dimensional Fast-Fourier-Transform- (FFT) and inverse-FFT-based approach to obtain the signal subspaces for angular frequency estimation. The geometry relationship between MPCs and positions is utilized for simultaneous positioning and mapping. Numerical results demonstrate the improved identifiability and low complexity performance of the proposed scheme.

The detection and localization of multiple targets is a fundamental research area for multiple input multiple output (MIMO) radar. In many civilian applications of MIMO technology, for example, automotive radar, high resolution direction of arrival (DOA) estimation is required. In this paper, a novel DOA estimation algorithm based on tensor decomposition is proposed for collocated transmit beamspace MIMO radar. First, we introduce the flipped-conjugate version of the transmit beamspace matrix, which focuses the transmit energy into fixed region. This can increase the signal to noise ratio (SNR) of targets. Then we reshape the received data into a tensor form, the structure of which provides the estimations of the transmit and receive steering matrices. The alternating least squares (ALS) algorithm is applied to find the tensor components. The DOA estimation is conducted in transmitters via the rotational invariance property achieved by beamspace matrix. It is proved that at most M−2 grating lobes exist during the process of DOA estimation, where M is the number of the transmitters. These grating lobes can be eliminated by finite trials of spectrum search. The performance of our proposed DOA estimation method surpasses several conventional algorithms in terms of accuracy and resolution.

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.

Multistate Hopfield models, such as complex-valued Hopfield neural networks (CHNNs), have been used as multistate neural associative memories. Quaternion-valued Hopfield neural networks (QHNNs) reduce the number of weight parameters of CHNNs. The CHNNs and QHNNs have weak noise tolerance by the inherent property of rotational invariance. Klein Hopfield neural networks (KHNNs) improve the noise tolerance by resolving rotational invariance. However, the KHNNs have another disadvantage of self-feedback, a major factor of deterioration in noise tolerance. In this work, the stability conditions of KHNNs are extended. Moreover, the projection rule for KHNNs is modified using the extended conditions. The proposed projection rule improves the noise tolerance by a reduction in self-feedback. Computer simulations support that the proposed projection rule improves the noise tolerance of KHNNs.

Signal estimation at the antenna is a major challenge of the antenna array structure because the received signals have different directions. Therefore, in this paper, a Genetic Algorithm (GA) is applied to the uniform circular array for the optimization of array structure in regard to its geometry. On the optimized array structure, four different algorithms (Estimation of Signal Parameter via Rotational Invariance Technique – ESPRIT, First Order Forward Prediction - FOFP, Beamscan, and Multiple Signal Classification - MUSIC) have been implemented in order to estimate the signal direction accurately with quick estimation time. The accuracy has been calculated with Root Mean Square Error (RMSE) indices. From the experimental analysis, it has been found that the performance of the ESPRIT algorithm is better than the others in terms of accuracy and estimation time.

This paper proposes a robust WKNN-TLS-ESPRIT algorithm that takes into account the effect of the unavailability of phasor measurement unit (PMU) data for identifying the low-frequency oscillatory modes in power systems. The main contribution of the proposed work is to create an enhanced autocorrelation matrix using a weighted K nearest neighbours (WKNN)-based predictive model to deal with such issues. In the present work, a Bayesian approach is utilized to determine the empirical number of neighbourhood parameters. The improved autocorrelation matrix is then used by total least square estimation of signal parameters via rotational invariance technique (TLS-ESPRIT) algorithm to provide a robust estimate of the modes. Robustness of the proposed method over the other methods is validated with a simulated test signal with missing data through Monte Carlo simulations at different SNRs. The effectiveness of the proposed approach is further verified on real data derived from PMU located in Western Electricity Coordinating Council grid.

In this paper we propose a method of localize a mobile robot along a route by processing spherical images. A spherical camera is mounted on a mobile robot. The route is sampled by discrete points which correspond to the places to be localized. Then, the localization problem is formulated as a classification problem, in which a place (a sampling point along a route) corresponds to a class. Since a spherical image has rotational invariance, the content of a spherical image is independent of camera rotation. Since a route is sampled as discrete points at space, the discrete points have a unique label the scenes at the points are different to each other. As shown in the preliminary experimental results, the proposed method achieves a very high accuracy for the localization of a wheelchair robot.