A Uniform Funnel Array for DOA Estimation in FANET Using Fibonacci Sampling

The Flying Ad-Hoc Network (FANET) is an important component of the 6G communication system. In order to achieve the precise positioning of unmanned aerial vehicle (UAV) nodes in a FANET when satellite navigation signals are unavailable, simple and accurate direction-of-arrival (DOA) estimation methods are required. In this paper, we propose an improved correlative interferometer method to estimate the DOAs of the UAVs in a FANET. This method adopts a uniform funnel array (UFA) configuration, which consists of a uniform circular array (UCA) and an additional element located above the center. This configuration improves the estimation accuracy for DOAs with large polar angles because it utilizes the degree of freedom in the vertical aperture. In addition, the Fibonacci sampling strategy is employed to overcome the polar clustering phenomenon exhibited by latitude-longitude sampling. Furthermore, in the interferometer, only partial phase differences are used to reduce the storage burden. When calculating the similarity function, we adopt the triangular function instead of the cosine function to improve computational efficiency. The simulation results show that the proposed UFA improves the DOA estimation accuracy by 65.56% over the planar UCA for signals with large polar angles. Moreover, Fibonacci sampling improves the DOA estimation accuracy by 11.54% as compared to the latitude-longitude sampling.

An Underwater Velocity-Independent DOA Estimation Based on Improved Toeplitz Matrix Reconstruction

Conventional acoustic velocity-independent direction of arrival (DOA) estimation models have limited measurement ranges and low degrees of freedom. This paper proposes an omnidirectional DOA estimation model based on improved Toeplitz matrix reconstruction to address these issues. The proposed method focuses on the Toeplitz matrix reconstruction method for sparse arrays to enhance the degree of freedom of the arrays. The method employs an expanding coprime array with a larger aperture, eliminating the acoustic velocity factor through geometric relationships and constructing a larger-size Toeplitz matrix. In addition, the concept of "low-rank matrix reconstruction" is introduced to fill the vacant terms in the Toeplitz matrix. Finally, the simulation experiments demonstrate the effectiveness of the proposed algorithm in improving the estimation accuracy.

Height Measurement Method for Meter-Wave Multiple Input Multiple Output Radar Based on Transmitted Signals and Receive Filter Design

To address the issue of low-elevation target height measurement in the Multiple Input Multiple Output (MIMO) radar, this paper proposes a height measurement method for meter-wave MIMO radar based on transmitted signals and receive filter design, integrating beamforming technology and cognitive processing methods. According to the characteristics of beamforming technology forming nulls at interference locations, we assume that the direct wave and reflected wave act as interference signals and hypothesize a direction for a hypothetical target. Then, the data received are processed to obtain the height of low-elevation-angle targets using a cognitive approach that jointly optimizes the transmitted signal and receive filter. Firstly, a signal model for the meter-wave MIMO radar based on the transmit weight matrix is established under low-elevation scenarios. Secondly, the signal model is analyzed and transformed. Thirdly, the beamforming algorithm that jointly optimizes the transmitted signals and receive filter is derived and analyzed. The algorithm maximizes the output Signal-to-Interference-plus-Noise ratio (SINR) of the receiver by designing the transmit weight matrix and receive filter. The optimization problem based on the SINR criterion is non-convex and difficult to solve. We transformed it into two sub-optimization problems and approximated the optimal solution through an alternating iteration algorithm. Finally, the proposed height measurement algorithm is compared with the Generalized Multiple Signal Classification (GMUSIC) and Maximum Likelihood (ML) height measurement algorithms. Simulation results show that the proposed algorithm can realize the height measurement of low-elevation targets. Compared to the GMUSIC and ML algorithms, it demonstrates superior performance in terms of computational complexity and multi-target elevation estimation.

Satellite Interference Source Direction of Arrival (DOA) Estimation Based on Frequency Domain Covariance Matrix Reconstruction

Direction of arrival (DOA) estimation is an effective method for detecting various active interference signals during the satellite navigation process. It can be utilized for both interference detection and anti-interference applications. This paper proposes a DOA estimation algorithm for satellite interference sources based on frequency domain covariance matrix reconstruction (FDCMR) to address various types of active interference that may occur in the satellite navigation positioning process. This algorithm can estimate the DOA of coherent signals from multiple frequency points under low signal-to-noise ratio (SNR) conditions. The signals received from the array are transformed from the time domain to the frequency domain using a fast Fourier transform (FFT). The data corresponding to the frequency point of the target signal is extracted from the signal in the frequency domain. The frequency domain covariance matrix of the received array signals is reconstructed by utilizing its covariance matrix property. The spatial spectrum search method is used for the final DOA estimation. Simulation experiments have shown that the proposed algorithm performs well in the DOA estimation under low SNR conditions and also resolves coherency. Moreover, the algorithm's effectiveness is verified through comparison with three other algorithms. Finally, the algorithm's applicability is validated through simulations of various interference scenarios.

Estimation of underwater acoustic direction-of-arrival using the probe beam deflection technique

This paper proposes a method of estimating the underwater acoustic direction-of-arrival using several laser beams impinging on a propagating underwater acoustic wave. The deflection of the laser beam caused by the spatial variation of the optical refractive index, which is further due to the modulation of the acoustic wave, reflects the information of direction-of-arrival and is sensed by the position sensitive detector (PSD). The sensing of the minute displacement on the PSD, in fact, introduces an extra dimension in the depth direction, which is a significant advantage over the conventional piezoelectric sensing regime. The employment of the extra sensing dimension can overcome several shortcomings, represented by spatial aliasing and phase ambiguity, existing in the current direction-of-arrival estimating methods. In addition, the ringing phenomenon of the piezoelectric effect is greatly reduced in the proposed laser-based sensing regime. By the flexibility of placing the laser beams, a prototype of the hydrophone is designed and manufactured, and a series of testing is performed. The results show that, benefiting from the probe beam deflection technique and combining the rough estimate and fine calculation, the resolution of the underwater acoustic direction-of-arrival can be improved to better than 0.016°, which can support and reform many underwater applications such as underwater acoustic communication, underwater detection, and ocean monitoring.

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

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

IWAVE-An adaptive filter approach to phase lock and the dynamic characterization of pseudo-harmonic waves

We present a novel adaptive filtering approach to the dynamic characterization of waves of varying frequencies and amplitudes embedded in arbitrary noise backgrounds. This method, known as IWAVE (Iterative Wave Action angle Variable Estimator), possesses critical advantages over conventional techniques, making it a useful new tool in the dynamic characterization of a wide range of data containing embedded oscillating signals. After a review of existing techniques, we present the IWAVE algorithm, derive its key characteristics, and provide tests of its performance using simulated and real world data.

Unfolded Coprime Linear Array with Three Subarrays for Non-Gaussian Signals: Configuration Design and DOA Estimation

In this paper, we investigate the problem of sparse array design for the direction of the arrival (DOA) of non-Gaussian signals and exploit the unfolded coprime linear array with three subarrays (UCLATS) to obtain physical sensors location. With the motivation from the large consecutive degree of freedom (DOF), we optimize the process of obtaining physical sensors location from two steps. Specifically, the first is to model the process of obtaining the longest consecutive virtual sum co-array from a given number of physical array elements into a global postage-stamp problem (GPSP), whose solution can be employed to determine the locations of the longest possible consecutive sum co-array (2-SC) and initial physical array. The second step is to multiply the location of the virtual sum co-array by appropriate coprime coefficients to generate UCLATS and then multiply the initial physical array position by the same corresponding coefficients to obtain physical sensors location. Besides, an algorithm is proposed to obtain DOA estimates, which employs the discrete Fourier transform (DFT) method and partial spectrum searching multiple signal classification (PSS-MUSIC) algorithm to obtain initial estimates and fine estimates, respectively, termed as the DFT-MUSIC method. Compared with the traditional total spectrum searching MUSIC (TSS-MUSIC) algorithm, the DFT-MUSIC method performs the same asymptotical performance of DOA estimation with less than 10% complex multiplication times, which can be verified by numerical simulations under the same condition.

Coherent, super-resolved radar beamforming using self-supervised learning

[Figure: see text].

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.

DOA Estimation Based on Weighted l1-norm Sparse Representation for Low SNR Scenarios

In this paper, a weighted l₁-norm is proposed in a l₁-norm-based singular value decomposition (L1-SVD) algorithm, which can suppress spurious peaks and improve accuracy of direction of arrival (DOA) estimation for the low signal-to-noise (SNR) scenarios. The weighted matrix is determined by optimizing the orthogonality of subspace, and the weighted l₁-norm is used as the minimum objective function to increase the signal sparsity. Thereby, the weighted matrix makes the l₁-norm approximate the original l₀-norm. Simulated results of orthogonal frequency division multiplexing (OFDM) signal demonstrate that the proposed algorithm has s narrower main lobe and lower side lobe with the characteristics of fewer snapshots and low sensitivity of misestimated signals, which can improve the resolution and accuracy of DOA estimation. Specifically, the proposed method exhibits a better performance than other works for the low SNR scenarios. Outdoor experimental results of OFDM signals show that the proposed algorithm is superior to other methods with a narrower main lobe and lower side lobe, which can be used for DOA estimation of UAV and pseudo base station.

A Direction-of-Arrival Estimation Algorithm Based on Compressed Sensing and Density-Based Spatial Clustering and Its Application in Signal Processing of MEMS Vector Hydrophone

Direction of arrival (DOA) estimation has always been a hot topic for researchers. The complex and changeable environment makes it very challenging to estimate the DOA in a small snapshot and strong noise environment. The direction-of-arrival estimation method based on compressed sensing (CS) is a new method proposed in recent years. It has received widespread attention because it can realize the direction-of-arrival estimation under small snapshots. However, this method will cause serious distortion in a strong noise environment. To solve this problem, this paper proposes a DOA estimation algorithm based on the principle of CS and density-based spatial clustering (DBSCAN). First of all, in order to make the estimation accuracy higher, this paper selects a signal reconstruction strategy based on the basis pursuit de-noising (BPDN). In response to the challenge of the selection of regularization parameters in this strategy, the power spectrum entropy is proposed to characterize the noise intensity of the signal, so as to provide reasonable suggestions for the selection of regularization parameters; Then, this paper finds out that the DOA estimation based on the principle of CS will get a denser estimation near the real angle under the condition of small snapshots through analysis, so it is proposed to use a DBSCAN method to process the above data to obtain the final DOA estimate; Finally, calculate the cluster center value of each cluster, the number of clusters is the number of signal sources, and the cluster center value is the final DOA estimate. The proposed method is applied to the simulation experiment and the micro electro mechanical system (MEMS) vector hydrophone lake test experiment, and they are proved that the proposed method can obtain good results of DOA estimation under the conditions of small snapshots and low signal-to-noise ratio (SNR).

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

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

A Priori-Based Subarray Selection Algorithm for DOA Estimation

A finer direction-of-arrival (DOA) estimation result needs a large and dense array; it may, however, encounter the mutual coupling effect, which degrades the performance of DOA estimation. There is a new approach to mitigating this effect by using a nonuniform array to achieve DOA estimation. In this paper, we consider a priori DOA estimation, which is easily obtained from tracking results. The a priori DOA requires us to pay close attention to the high possibility of where the DOA will appear; then, a weight according to the prior probability distribution of DOA is added to each direction, which leads the sensing matrix of DOA estimation to be near low-rank. Thus, according to the low-rank matrix approximation theory, an optimal low-rank approximate matrix is obtained and an algorithm is proposed to select the elements of the original array according to right singular vectors of the approximate matrix. After that, the impacts of different weights are analyzed, and a mixed weight is presented which has flexibility for common use. Finally, a number of numerical simulations are carried out, and the results verify the effectiveness of the proposed methods.

TAM and MUSIC Approach for Impact-Source Localization under Deformation Conditions

As an impact-source-localization technique, Lamb waves are commonly used to detect low-velocity impact in composite structures. However, the performance of Lamb waves is susceptible under deformation conditions. In this paper, a novel approach combined the Toeplitz approximation method (TAM) and multiple-signal classification (MUSIC) (TAM-MUSIC) to improve impact-source-localization (angle and distance in polar coordinates) accuracy under deformation conditions. The method divided a two-dimensional search of direction and distance into two one-dimensional searches. The impact direction was calculated by the TAM, which was introduced into the steering vector of MUSIC to estimate the distance by scanning the whole monitoring area. An epoxy laminate plate experiment showed that the phase and amplitude of uniform linear-array signals had different average plate curvature that led to poor impact-source-localization accuracy using the MUSIC method. TAM provided high-resolution direction-finding capability, suitable for the pretreatment of Lamb waves. Results showed that the present method, with a small amount of computation and low memory requirement, had higher location-estimation accuracy than that of traditional methods under deformation conditions.

Acceleration Compensation for Estimation of Along-Track Velocity of Ground Moving Target from Single-Channel SAR SLC Data

Across-track acceleration is a major source of estimation error of along-track velocity in synthetic-aperture radar (SAR) ground moving-target indication (GMTI). This paper presents the theory and a method of compensating across-track acceleration to improve the accuracy of along-track velocity estimated from single-channel SAR single-look complex data. A unique feature of the proposed method is the utilisation of phase derivatives in the Doppler frequency domain, which is effective for azimuth-compressed signals. The performance of the method was evaluated through experimental data acquired by TerraSAR-X and speed-controlled and measured vehicles. The application results demonstrate a notable improvement in along-track velocity estimates. The amount of along-track velocity correction is particularly significant when a target has irregular motion with a low signal-to-clutter ratio. A discontinuous velocity jump rather than a constant acceleration was also observed and verified through comparison between actual data and simulations. By applying this method, the capability of single-channel SAR GMTI could be substantially improved in terms of accuracy of velocity, and moving direction. However, the method is effective only if the correlation between the actual Doppler phase derivatives and a model derived from the residual Doppler rate is sufficiently high. The proposed method will be applied to X-band SAR systems of KOMPSAT-5 and -6.

Frequency-selective harmonic retrieval for Schottky mass spectrometry

Nuclear mass measurements by means of Schottky mass spectrometry critically rely on an accurate determination of revolution frequencies of the circulating ions in a storage ring. Such a harmonic retrieval problem is conventionally tackled via the periodogram of the Schottky data, where the ion peaks are identified and their spectral locations are obtained by fittings. However, the discrete frequency grid of the periodogram has unfortunately hampered a fine resolution of two closely spaced harmonics. We thereby propose a method based on the state space representation in the frequency domain to overcome this limit. Moreover, its frequency-selective merit has allowed the method to focus only on a narrow band and thus greatly reduced the computational cost while still retaining superb accuracy. With the real Schottky data from an isochronous-Schottky beam time at the experimental cooler-storage ring in Lanzhou, the accuracy of the retrieved harmonics is demonstrated to be around 1 ppm, as limited by the anisochronism effect of the ion optics.

A Novel Real-Valued DOA Algorithm Based on Eigenvalue

To solve the high complexity of the subspace-based direction-of-arrival (DOA) estimation algorithm, a super-resolution DOA algorithm is built in this paper. However, in this method, matrix decomposition is required for each search angle. Therefore, in this paper, real-valued processing is used to reduce the scanning range by half, which is less effective in algorithm complexity. The super-resolution algorithm mainly uses the conservation of energy. By exploring the relationship between the covariance matrix and its complex conjugate, we constructed the real-valued matrix and introduced a real-valued searching source to make the operation of the matrix real-valued. Finally, the simulation experiments show that the proposed algorithm not only reduces the spectral search range by half but also has a higher angular resolution than the traditional algorithm.

High Accuracy Power Quality Evaluation under a Colored Noisy Condition by Filter Bank ESPRIT

Due to the highly increasing integration of renewable energy sources with the power grid and their fluctuations, besides the recent growth of new power electronics equipment, the noise in power systems has become colored. The colored noise affects the methodologies for power quality parameters’ estimation, such as harmonic and interharmonic components. Estimation of signal parameters via rotational invariance techniques (ESPRIT) as a parametric technique with high resolution has proven its efficiency in the estimation of power signal components’ frequencies, amplitudes, and phases for quality analysis, under the assumption of white Gaussian noise. Since ESPRIT suffers from high computational effort, filter bank ESPRIT (FB-ESPRIT) was suggested for mitigation of the complexity. This manuscript suggests FB-ESPRIT as well for accurate and robust estimation of power signal components’ parameters in the presence of the colored noise. Even though the parametric techniques depend on the Gaussianity of contaminating noise to perform properly, FB-ESPRIT performs well in colored noise. The FB-ESPRIT superiority compared with the conventional ESPRIT and MUSIC techniques was demonstrated through many simulations runs on synthetic power signals with multiple harmonics, interharmonics, and subharmonic components in the presence of noises of different colors and different SNR levels. FB-ESPRIT had a significant efficiency superiority in power quality analysis with a wide gap distance from the other estimators, especially under the high level of colored noise.

Gridless Sparse Direction Finding Method for Correlated Signals with Gain-Phase Errors

In practical array systems, the gain-phase errors among antennas degrade the performance of direction finding significantly. In this paper, a novel sparse system model for direction of arrival (DOA) estimation in the scenario with gain-phase errors is proposed by exploiting the signal sparsity in the spatial domain. In contrast to the existing sparse-based methods using the grids to construct the dictionary matrix, a novel gridless method based on atomic norm and convex optimization is proposed, where the gain-phase errors are described by a diagonal matrix. With the Schur complement, a semidefinite programming is formulated from the optimization problem, and can be solved efficiently. With the gain-phase errors, the corresponding Cram’er-Rao lower bound (CRLB) of direction finding is derived as an estimation benchmark. Simulation results show that the proposed method performs better than the state-of-the-art methods in the scenario with correlated signals and gain-phase errors.

Compressed Sensing-Based DOA Estimation With Antenna Phase Errors

In array signal processing, the direction of arrivals (DOAs) of the received signals are estimatedby measuring the relative phases among antennas; hence, the estimation performance is reducedby the inconsistency among antennas. In this paper, the DOA estimation problem of the uniformlinear array (ULA) is investigated in the scenario with phase errors among the antennas, and adiagonal matrix composed of phase errors is used to formulate the system model. Then, by using thecompressed sensing (CS) theory, we convert the DOA estimation problem into a sparse reconstructionproblem. A novel reconstruction method is proposed to estimate both the DOA and the unknownphase errors, iteratively. The phase errors are calculated by a gradient descent method with thetheoretical expressions. Simulation results show that the proposed method is cost-efficient andoutperforms state-of-the-art methods regarding the DOA estimation with unknown phase errors.

Coding Prony's method in MATLAB and applying it to biomedical signal filtering

BACKGROUND

The response of many biomedical systems can be modelled using a linear combination of damped exponential functions. The approximation parameters, based on equally spaced samples, can be obtained using Prony's method and its variants (e.g. the matrix pencil method). This paper provides a tutorial on the main polynomial Prony and matrix pencil methods and their implementation in MATLAB and analyses how they perform with synthetic and multifocal visual-evoked potential (mfVEP) signals. This paper briefly describes the theoretical basis of four polynomial Prony approximation methods: classic, least squares (LS), total least squares (TLS) and matrix pencil method (MPM). In each of these cases, implementation uses general MATLAB functions. The features of the various options are tested by approximating a set of synthetic mathematical functions and evaluating filtering performance in the Prony domain when applied to mfVEP signals to improve diagnosis of patients with multiple sclerosis (MS).

RESULTS

The code implemented does not achieve 100%-correct signal approximation and, of the methods tested, LS and MPM perform best. When filtering mfVEP records in the Prony domain, the value of the area under the receiver-operating-characteristic (ROC) curve is 0.7055 compared with 0.6538 obtained with the usual filtering method used for this type of signal (discrete Fourier transform low-pass filter with a cut-off frequency of 35 Hz).

CONCLUSIONS

This paper reviews Prony's method in relation to signal filtering and approximation, provides the MATLAB code needed to implement the classic, LS, TLS and MPM methods, and tests their performance in biomedical signal filtering and function approximation. It emphasizes the importance of improving the computational methods used to implement the various methods described above.

An Improved Method for Discerning Broken Rotor Bar Fault and Load Oscillation in Induction Motors

A few methods for discerning broken rotor bar (BRB) fault and load oscillation in induction motors have been reported in the literature. However, they all perhaps inevitably fail in adverse cases in which these two phenomena are simultaneously present. To tackle this problem, an improved method for discerning BRB fault and load oscillation is proposed in this paper based on the following work. On the one hand, the theoretical basis is analytically extended to include such an adverse case, yielding some important findings on the spectra of the instantaneous reactive and active powers. A novel strategy is thus outlined to correctly discern BRB fault and load oscillation even when simultaneously present. On the other hand, Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) is adopted as the spectral analysis technique to deal with the instantaneous reactive and active powers, yielding a certain improvement compared to the existing methods, adopting Fast Fourier Transform (FFT). Simulation and experimental results demonstrate that the proposed method can correctly discern BRB fault and load oscillation even when simultaneously present.

DOA Estimation for Coprime Linear Array Based on MI-ESPRIT and Lookup Table

In order to improve the angle measurement performance of a coprime linear array, this paper proposes a novel direction-of-arrival (DOA) estimation algorithm for a coprime linear array based on the multiple invariance estimation of signal parameters via rotational invariance techniques (MI-ESPRIT) and a lookup table method. The proposed algorithm does not require a spatial spectrum search and uses a lookup table to solve ambiguity, which reduces the computational complexity. To fully use the subarray elements, the DOA estimation precision is higher compared with existing algorithms. Moreover, the algorithm avoids the matching error when multiple signals exist by using the relationship between the signal subspace of two subarrays. Simulation results verify the effectiveness of the proposed algorithm.

Parameter Estimation of Electromechanical Oscillation Based on a Constrained EKF with C&I-PSO

By combining together the extended Kalman filter with a newly developed C&I particle swarm optimization algorithm (C&I-PSO), a novel estimation method is proposed for parameter estimation of electromechanical oscillation, in which critical physical constraints on the parameters are taken into account. Based on the extended Kalman filtering algorithm, the constrained parameter estimation problem is formulated via the projection method. Then, by utilizing the penalty function method, the obtained constrained optimization problem could be converted into an equivalent unconstrained optimization problem; finally, the C&I-PSO algorithm is developed to address the unconstrained optimization problem. Therefore, the parameters of electromechanical oscillation with physical constraints can be successfully estimated and better performed. Finally, the effectiveness of the obtained results has been illustrated by several test systems.

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.

Estimating SpO2 via Time-Efficient High-Resolution Harmonics Analysis and Maximum Likelihood Tracking

The accuracy of noninvasive oxygen saturation (SpO₂), which is defined by the measurements based on photoplethysmographic (PPG) signals, is intensively affected by motion artifacts (MAs) and low perfusion. This study introduces a novel approach called ESPRIT-MLT to measure SpO₂ when such interferences are present. In contrast to previous studies, the work focuses on the harmonic model of the PPG signal and the probability model of results from harmonic analysis. The optimized parametric ESPRIT method is applied to improve the accuracy of harmonic power estimation, and the maximum likelihood SpO₂ tracking (MLT) technique is proposed to track the most probable uncontaminated harmonic of heart rate frequency. We construct an evaluation platform for testing the proposed method via generated signals and subject tests. Compared with the nonparametric periodogram method, the probability of correct harmonics being found is improved by 18.7% or 19.7%, when the signal is contaminated by motion artifacts or affected by low perfusion, respectively. In comparison with the reference methods, the proposed ESPRIT-MLT method exhibits a lower average root mean square error (RMSE) (1.17%) in the simulation using an MA-contaminated PPG signal, and a lower RMSE (2.70%) in the simulation using an extremely low (0.05%) perfusion index. A comprehensive subject test that consists of 4 activities and 20 subjects shows an average RMSE of 0.84% ( 0.44%). Furthermore, the time-efficiency is optimized to be adaptable with wearable devices. Therefore, the proposed method has potential in enhancing the performance of clinical pulse oximetry and wearable SpO₂ measurement devices for daily use.

Analysis of weighted subspace fitting and subspace-based eigenvector techniques for frequency estimation for the coherent Doppler lidar

Since the periodogram maximum (PM) algorithm fails to provide consistent estimates, more robust techniques are developed, especially in a low signal-to-noise ratio (SNR) regime. The methods are formulated in a subspace fitting-based framework, such as the eigenvector (EV) method and the proposed weighted subspace fitting (WSF) method by introducing an optimal weighting matrix, which exploits the low-rank properties of the covariance matrix of the coherent Doppler lidar echo data. Simulation results reveal that the number of the reliable estimates by the WSF method is more than the other two methods, and the standard deviation is the smallest. Furthermore, the predicted best-fit Gaussian model for the probability density function of the estimates has a narrower spectral width than that of PM and EV methods. Experimental results also validate the simulation results, which show that the WSF approach outperforms the PM and EV algorithms in the furthest detectable range. The proposed method improves the detection range approximately up to 14.2% and 26.6% when compared to the EV method and the PM method, respectively. In conclusion, the proposed method can reduce the statistical uncertainties and enhance the accuracy in wind estimation specifically for a low SNR regime.

Super-Resolved Nuclear Magnetic Resonance Spectroscopy

We present a novel method that breaks the resolution barrier in nuclear magnetic resonance (NMR) spectroscopy, allowing one to accurately estimate the chemical shift values of highly overlapping or broadened peaks. This problem is routinely encountered in NMR when peaks have large linewidths due to rapidly decaying signals, hindering its application. We address this problem based on the notion of finite-rate-of-innovation (FRI) sampling, which is based on the premise that signals such as the NMR signal, can be accurately reconstructed using fewer measurements than that required by existing approaches. The FRI approach leads to super-resolution, beyond the limits of contemporary NMR techniques. Using this method, we could measure for the first time small changes in chemical shifts during the formation of a Gold nanorod-protein complex, facilitating the quantification of the strength of such interactions. The method thus opens up new possibilities for the application and acceleration of multidimensional NMR spectroscopy across a wide range of systems.

Direction-of-arrival estimation of multipath signals using independent component analysis and compressive sensing

Multipath signal is often considered an interference that must be removed. The coherence between multipath and direct component makes it difficult to use conventional direction-of-arrival (DOA) estimation methods in a smart antenna system. This study demonstrates a new multipath signal DOA estimation technique. Unlike the common methods, without decoherence preprocessing, the proposed algorithm first apply a complex fast independent component analysis (cFastICA) algorithm to obtain the steering vectors with multipath information that corresponds to each source signal. Then, according to the special structure of the obtained steering vectors and spatial sparsity of the multipath signal components, the algorithm uses the solution of the sparse signal reconstruction problem in the compressive sensing (CS) theory, and the DOA estimation of the multipath signal is translated into an l1 norm minimization problem. Finally, we search the space spectrums to acquire the DOAs for each direct component and multipath component. Comparative simulation tests and analysis prove the effectiveness of the proposed algorithm in estimation accuracy in underdetermined conditions.

Underdetermined DOA Estimation of Quasi-Stationary Signals Using a Partly-Calibrated Array

Quasi-stationary signals have been widely found in practical applications, which have time-varying second-order statistics while staying static within local time frames. In this paper, we develop a robust direction-of-arrival (DOA) estimation algorithm for quasi-stationary signals based on the Khatri-Rao (KR) subspace approach. A partly-calibrated array is considered, in which some of the sensors have an inaccurate knowledge of the gain and phase. In detail, we first develop a closed-form solution to estimate the unknown sensor gains and phases. The array is then calibrated using the estimated sensor gains and phases which enables the improved DOA estimation. To reduce the computational complexity, we also proposed a reduced-dimensional method for DOA estimation. The exploitation of the KR subspace approach enables the proposed method to achieve a larger number of degrees-of-freedom, i.e., more sources than sensors can be estimated. The unique identification condition for the proposed method is also derived. Simulation results demonstrate the effectiveness of the proposed underdetermined DOA estimation algorithm for quasi-stationary signals.

Estimation of Cardiopulmonary Parameters From Ultra Wideband Radar Measurements Using the State Space Method

Ultra wideband (UWB) Doppler radar has many biomedical applications, including remote diagnosis of cardiovascular disease, triage and real-time personnel tracking in rescue missions. It uses narrow pulses to probe the human body and detect tiny cardiopulmonary movements by spectral analysis of the backscattered electromagnetic (EM) field. With the help of super-resolution spectral algorithms, UWB radar is capable of increased accuracy for estimating vital signs such as heart and respiration rates in adverse signal-to-noise conditions. A major challenge for biomedical radar systems is detecting the heartbeat of a subject with high accuracy, because of minute thorax motion (less than 0.5 mm) caused by the heartbeat. The problem becomes compounded by EM clutter and noise in the environment. In this paper, we introduce a new algorithm based on the state space method (SSM) for the extraction of cardiac and respiration rates from UWB radar measurements. SSM produces range-dependent system poles that can be classified parametrically with spectral peaks at the cardiac and respiratory frequencies. It is shown that SSM produces accurate estimates of the vital signs without producing harmonics and inter-modulation products that plague signal resolution in widely used FFT spectrograms.

Compressed Symmetric Nested Arrays and Their Application for Direction-of-Arrival Estimation of Near-Field Sources

In this paper, a new sensor array geometry, called a compressed symmetric nested array (CSNA), is designed to increase the degrees of freedom in the near field. As its name suggests, a CSNA is constructed by getting rid of some elements from two identical nested arrays. The closed form expressions are also presented for the sensor locations and the largest degrees of freedom obtainable as a function of the total number of sensors. Furthermore, a novel DOA estimation method is proposed by utilizing the CSNA in the near field. By employing this new array geometry, our method can identify more sources than sensors. Compared with other existing methods, the proposed method achieves higher resolution because of increased array aperture. Simulation results are demonstrated to verify the effectiveness of the proposed method.

Active tuning of stroke-induced vibrations by tennis players

This paper investigates how tennis players control stroke-induced vibration. Its aim is to characterise how a tennis player deals with entering vibration waves or how he/she has the ability to finely adjust them. A specific experimental procedure was designed, based on simultaneously collecting sets of kinematic, vibration and electromyographic data during forehand strokes using various commercial rackets and stroke intensities. Using 14 expert players, a wide range of excitations at spectral and temporal levels were investigated. Energetic and spectral descriptors of stroke-induced vibration occurring at the racket handle and at the player's wrist and elbow were computed. Results indicated that vibrational characteristics are strongly governed by grip force and to a lower extent by the racket properties. Grip force management drives the amount of energy, as well as its distribution, into the forearm. Furthermore, hand-grip can be assimilated to an adaptive filter which can significantly modify the spectral parameters propagating into the player's upper limb. A significant outcome is that these spectral characteristics are as much dependent on the player as on the racket. This contribution opens up new perspectives in equipment manufacture by underlining the need to account for player/racket interaction in the design process.

The effects of player grip on the dynamic behaviour of a tennis racket

The aim of this article is to characterise the extent to which the dynamic behaviour of a tennis racket is dependent on its mechanical characteristics and the modulation of the player's grip force. This problem is addressed through steps involving both experiment and modelling. The first step was a free boundary condition modal analysis on five commercial rackets. Operational modal analyses were carried out under "slight", "medium" and "strong" grip force conditions. Modal frequencies and damping factors were then obtained using a high-resolution method. Results indicated that the dynamic behaviour of a racket is not only determined by its mechanical characteristics, but is also highly dependent on the player's grip force. Depending on the grip force intensity, the first two bending modes and the first torsional mode frequencies respectively decreased and increased while damping factors increased. The second step considered the design of a phenomenological hand-gripped racket model. This model is fruitful in that it easily predicts the potential variations in a racket's dynamic behaviour according to the player's grip force. These results provide a new perspective on the player/racket interaction optimisation by revealing how grip force can drive racket dynamic behaviour, and hence underlining the necessity of taking the player into account in the racket design process.

An efficient algorithm for direction finding against unknown mutual coupling

In this paper, an algorithm of direction finding is proposed in the presence of unknown mutual coupling. The preliminary direction of arrival (DOA) is estimated using the whole array for high resolution. Further refinement can then be conducted by estimating the angularly dependent coefficients (ADCs) with the subspace theory. The mutual coupling coefficients are finally determined by solving the least squares problem with all of the ADCs utilized without discarding any. Simulation results show that the proposed method can achieve better performance at a low signal-to-noise ratio (SNR) with a small-sized array and is more robust, compared with the similar processes employing the initial DOA estimation and further improvement iteratively.

Predicting the decay time of solid body electric guitar tones

Although it can be transformed by various electronic devices, the sound of the solid body electric guitar originates from, and is strongly linked with, the string vibration. The coupling of the string with the guitar alters its vibration and can lead to decay time inhomogeneities. This paper implements and justifies a framework for the study of decay times of electric guitar tones. Two damping mechanisms are theoretically and experimentally identified: the string intrinsic damping and the damping due to mechanical coupling with the neck of the guitar. The electromagnetic pickup is shown to not provide any additional damping to the string. The pickup is also shown to be far more sensitive to the out-of-plane polarization of the string. Finally, an accurate prediction of the decay time of electric guitar tones is made possible, whose only requirements are the knowledge of the isolated string dampings and the out-of-plane conductance at the neck of the guitar. This prediction can be of great help for instrument makers and manufacturers.

Incident signal power comparison for localization of concurrent multiple acoustic sources

In this paper, a method to solve the localization of concurrent multiple acoustic sources in large open spaces is presented. The problem of the multisource localization in far-field conditions is to correctly associate the direction of arrival (DOA) estimated by a network array system to the same source. The use of systems implementing a Bayesian filter is a traditional approach to address the problem of localization in multisource acoustic scenario. However, in a real noisy open space the acoustic sources are often discontinuous with numerous short-duration events and thus the filtering methods may have difficulty to track the multiple sources. Incident signal power comparison (ISPC) is proposed to compute DOAs association. ISPC is based on identifying the incident signal power (ISP) of the sources on a microphone array using beamforming methods and comparing the ISP between different arrays using spectral distance (SD) measurement techniques. This method solves the ambiguities, due to the presence of simultaneous sources, by identifying sounds through a minimization of an error criterion on SD measures of DOA combinations. The experimental results were conducted in an outdoor real noisy environment and the ISPC performance is reported using different beamforming techniques and SD functions.

Decimative Spectral Estimation with Unconstrained Model Order

This paper presents a new state-space method for spectral estimation that performs decimation by any factor, it makes use of the full set of data and brings further apart the poles under consideration, while imposing almost no constraints to the size of the Hankel matrix (model order), as decimation increases. It is compared against two previously proposed techniques for spectral estimation (along with derived decimative versions), that lie among the most promising methods in the field of spectroscopy, where accuracy of parameter estimation is of utmost importance. Moreover, it is compared against a state-of-the-art purely decimative method proposed in literature. Experiments performed on simulated NMR signals prove the new method to be more robust, especially for low signal-to-noise ratio.

Sensitivity analysis of solutions of the harmonic inversion problem: are all data points created equal?

We consider the harmonic inversion problem, and the associated spectral estimation problem, both of which are key numerical problems in NMR data analysis. Under certain conditions (in particular, in exact arithmetic) these problems have unique solutions. Therefore, these solutions must not depend on the inversion algorithm, as long as it is exact in principle. In this paper, we are not concerned with the algorithmic aspects of harmonic inversion, but rather with the sensitivity of the solutions of the problem to perturbations of the time-domain data. A sensitivity analysis was performed and the counterintuitive results call into question the common assumption made in "super-resolution" methods using non-uniform data sampling, namely, that the data should be sampled more often where the time signal has the largest signal-to-noise ratio. The numerical analysis herein demonstrates that the spectral parameters (such as the peak positions and amplitudes) resulting from the solution of the harmonic inversion problem are least susceptible to the perturbations in the values of data points at the edges of the time interval and most susceptible to the perturbations in the values at intermediate times.

Iterative high-resolution wavenumber inversion applied to broadband acoustic data

This paper presents the results of an iterative high-resolution wavenumber inversion algorithm applied to acoustic waveguides in which wave propagation is described by propagating modes. Following work on the first description of the inversion algorithm, a generalization to broadband signals is performed and experimental data are investigated. The algorithm leads to dispersion curves for propagating modes in the case of an ultrasonic waveguide and an elastic plate. Results are compared with spatial-temporal Fourier transforms.

Prostate cancer spectral multifeature analysis using TRUS images

This paper focuses on extracting and analyzing different spectral features from transrectal ultrasound (TRUS) images for prostate cancer recognition. First, the information about the images' frequency domain features and spatial domain features are combined using a Gabor filter and then integrated with the expert radiologist's information to identify the highly suspicious regions of interest (ROIs). The next stage of the proposed algorithm is to scan each identified region in order to generate the corresponding 1-D signal that represents each region. For each ROI, possible spectral feature sets are constructed using different new geometrical features extracted from the power spectrum density (PSD) of each region's signal. Next, a classifier-based algorithm for feature selection using particle swarm optimization (PSO) is adopted and used to select the optimal feature subset from the constructed feature sets. A new spectral feature set for the TRUS images using estimation of signal parameters via rotational invariance technique (ESPRIT) is also constructed, and its ability to represent tissue texture is compared to the PSD-based spectral feature sets using the support vector machines (SVMs) classifier. The accuracy obtained ranges from 72.2% to 94.4%, with the best accuracy achieved by the ESPRIT feature set.