Showing papers on "Spectral density estimation published in 2021"

Rank Minimization-Based Toeplitz Reconstruction for DoA Estimation Using Coprime Array

Abstract: In this letter, we address the problem of direction finding using coprime array, which is one of the most preferred sparse array configurations. Motivated by the fact that non-uniform element spacing hinders full utilization of the underlying information in the receive signals, we propose a direction-of-arrival (DoA) estimation algorithm based on low-rank reconstruction of the Toeplitz covariance matrix. The atomic-norm representation of the measurements from the interpolated virtual array is considered, and the equivalent dual-variable rank minimization problem is formulated and solved using a cyclic optimization approach. The recovered covariance matrix enables the application of conventional subspace-based spectral estimation algorithms, such as MUSIC, to achieve enhanced DoA estimation performance. The estimation performance of the proposed approach, in terms of the degrees-of-freedom and spatial resolution, is examined. We also show the superiority of the proposed method over the competitive approaches in the root-mean-square error sense.

A Multi-Taper S-Transform Method for Spectral Estimation of Stationary Processes

Abstract: The S-transform (ST) is a method of time-frequency analysis of time series. We develop here the Multi-taper S-transform (MTST) for spectral estimation of multi-variate stationary processes through replacing the scalable Gaussian window of the ST with scalable, adjustable orthogonal time-frequency Hermite functions. The MTST is shown to reduce bias and variance of power spectral density (PSD) estimates and coherence over the entire frequency domain and compares favourably with the estimates obtained with the Welch and Multi-taper methods. The MTST method has been successfully applied to data from two anemometers in Hong Kong, during Typhoon Mangkhut, for the estimation of PSD and coherence.

A Theory of Computational Resolution Limit for Line Spectral Estimation

Abstract: Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the theoretical understanding of this problem is still elusive. In this paper, we introduce and quantitatively characterize the two resolution limits for the line spectral estimation problem under deterministic noise: one is the minimum separation distance between the line spectra that is required for exact detection of their number, and the other is the minimum separation distance between the line spectra that is required for a stable recovery of their supports. The quantitative results imply a phase transition phenomenon in each of the two recovery problems, and also the subtle difference between the two. We further propose a sweeping singular-value-thresholding algorithm for the number detection problem and conduct numerical experiments. The numerical results confirm the phase transition phenomenon in the number detection problem.

M$^2$ Spectral Estimation: A Flexible Approach Ensuring Rational Solutions

Abstract: This paper concerns a spectral estimation problem for multivariate (i.e., vector-valued) signals defined on a multidimensional domain, abbreviated as M$^2$. The problem is posed as solving a finite...

A Spectral Model of Grid Frequency for Assessing the Impact of Inertia Response on Wind Turbine Dynamics

Abstract: The recent developments in renewable energy have led to a higher proportion of converter-connected power generation sources in the grid. Operating a high renewable energy penetration power system and ensuring the frequency stability could be challenging due to the reduced system inertia, which is usually provided by the conventional synchronous generators. Previous studies have shown the potential of wind turbines to provide an inertia response to the grid based on the measured rate of change of the grid frequency. This is achieved by controlling the kinetic energy extraction from the rotating parts by its converters. In this paper, we derive a spectral-based model of the grid frequency by analyzing historical measurements. The spectral model is then used to generate realistic, generic, and stochastic signals of the grid frequency for typical aero-elastic simulations of wind turbines. The spectral model enables the direct assessment of the additional impact of the inertia response control on wind turbines: the spectra of wind turbine output signals such as generator speed, tower base bending moment, and shaft torsional moment are calculated directly from the developed spectral model of the grid frequency and a commonly used spectral model of the turbulent wind. The calculation of output spectra is verified with non-linear time-domain simulations and spectral estimation. Based on this analysis, a notch filter is designed to significantly alleviate the negative impact on wind turbine’s structural loads due to the inertia response with only a small reduction on the grid support.

Advances in the Direct Spectral Estimation of Aeroacoustic Sources Using Continuous-Scan Phased Arrays

Abstract: Author(s): Morata Carranza, David | Advisor(s): Papamoschou, Dimitri | Abstract: The present study is related to the field of imaging of aeroacoustic noise sources. Traditional techniques include the use of phased microphone arrays and acoustic beamforming of the signals signals using algorithms such as the Delay-And-Sum (DAS). Over the last years, there has been an increasing interest in methods in which some of the sensors traverse in prescribed paths and motion. Some of the challenges of this approach include the treatment of the non-stationarity of the signal due to the motion of the microphone(s).An objective of this work is to review the methodology presented by D. Papamoschou, P. Shah and myself in the AIAA Journal "Inverse Acoustic Methodology for Continuous-Scan Phased Arrays" since it provides the building grounds for the thesis. The methodology accounts for the direct estimation of the spatio-spectral distribution of an acoustic source from microphone measurements that include fixed and continuously scanning sensors. The non-stationarity of the signal is addressed by means of the Wigner-Ville spectrum. Suppression of the non-stationary effects involves the division of the signal into blocks and the application of a frequency-dependent window within each block. The direct estimation approach involves the inversion of an integral that relates the modeled pressure field, the measured pressure field and the response of the array. A Bayesian-estimation that allows for efficient inversion of the integrals and performs similarly to the conjugate gradient method is reviewed.The coherence-based noise source distribution is studied in this work and the influence of the signal segmentation on its spatial resolution is analyzed. This thesis provides specific guidelines related to the signal processing. The signal is divided into blocks meeting a desired mathematical condition. A minimum and maximum size for the resulting blocks is proposed in this work, as well as a minimum and maximum block overlap. A safe region for the signal segmentation is presented as well.This work presents a methodology to synchronize the signals from the microphones (scanning or not) with the position of the scanning sensor. It also shows the methods to check the accuracy of the position scanning sensor.The methodology is applied to acoustic fields emitted by impinging jets approximating a point source and an overexpanded supersonic jet. Noise source maps that included the scanning sensor and a dense block distribution have increased spatial resolution and reduced sidelobes. The ability of the continuous scan paradigm to provide high-definition noise source maps with a lower sensor count is confirmed in this work as well. The effect of the proposed signal segmentation on sparse arrays is discussed.

Error Bounds for Dynamical Spectral Estimation.

Abstract: Dynamical spectral estimation is a well-established numerical approach for estimating eigenvalues and eigenfunctions of the Markov transition operator from trajectory data Although the approach ha

Bayesian spectral density estimation using P-splines with quantile-based knot placement

Abstract: This article proposes a Bayesian approach to estimating the spectral density of a stationary time series using a prior based on a mixture of P-spline distributions. Our proposal is motivated by the B-spline Dirichlet process prior of Edwards et al. (Stat Comput 29(1):67–78, 2019. https://doi.org/10.1007/s11222-017-9796-9 ) in combination with Whittle’s likelihood and aims at reducing the high computational complexity of its posterior computations. The strength of the B-spline Dirichlet process prior over the Bernstein–Dirichlet process prior of Choudhuri et al. (J Am Stat Assoc 99(468):1050–1059, 2004. https://doi.org/10.1198/016214504000000557 ) lies in its ability to estimate spectral densities with sharp peaks and abrupt changes due to the flexibility of B-splines with variable number and location of knots. Here, we suggest to use P-splines of Eilers and Marx (Stat Sci 11(2):89–121, 1996. https://doi.org/10.1214/ss/1038425655 ) that combine a B-spline basis with a discrete penalty on the basis coefficients. In addition to equidistant knots, a novel strategy for a more expedient placement of knots is proposed that makes use of the information provided by the periodogram about the steepness of the spectral power distribution. We demonstrate in a simulation study and two real case studies that this approach retains the flexibility of the B-splines, achieves similar ability to accurately estimate peaks due to the new data-driven knot allocation scheme but significantly reduces the computational costs.

Optimal Transport Between Gaussian Stationary Processes

Abstract: We consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is the variance of the filtered discrepancy process. The main contribution of this article is to show that the corresponding solution leads to a weighted Hellinger distance between multivariate power spectral densities. Then, we propose a spectral estimation approach in the case of indirect measurements, which is based on this distance.

Fast and accurate spectral-estimation axial super-resolution optical coherence tomography

Abstract: Spectral-estimation OCT (SE-OCT) is a computational method to enhance the axial resolution beyond the traditional bandwidth limit. However, it has not yet been used widely due to its high computational load, dependency on user-optimized parameters, and inaccuracy in intensity reconstruction. In this study, we implement SE-OCT using a fast implementation of the iterative adaptive approach (IAA). This non-parametric spectral estimation method is optimized for use on OCT data. Both in simulations and experiments we show an axial resolution improvement with a factor between 2 and 10 compared to standard discrete Fourier transform. Contrary to parametric methods, IAA gives consistent peak intensity and speckle statistics. Using a recursive and fast reconstruction scheme the computation time is brought to the sub-second level for a 2D scan. Our work shows that SE-OCT can be used for volumetric OCT imaging in a reasonable computation time, thus paving the way for wide-scale implementation of super-resolution OCT.

Optimized light source spectral power distribution for RGB camera based spectral reflectance recovery

Abstract: The accuracy of recovered spectra from camera responses mainly depends on the spectral estimation algorithm used, the camera and filters selected, and the light source used to illuminate the object. We present and compare different light source spectrum optimization methods together with different spectral estimation algorithms applied to reflectance recovery. These optimization methods include the Monte Carlo (MC) method, particle swarm optimization (PSO) and multi-population genetic algorithm (MPGA). Optimized SPDs are compared with D65, D50 A and three LED light sources in simulation and reality. Results obtained show us that MPGA has superior performance, and optimized light source spectra along with better spectral estimation algorithm can provide a more accurate spectral reflectance estimation of an object surface. Meanwhile, it is found that camera spectral sensitivities weighted by optimized SPDs tend to be mutually orthogonal.

Sea Spectral Estimation Using ARMA Models.

Abstract: This paper deals with the spectral estimation of sea wave elevation time series by means of ARMA models. To start, the procedure to estimate the ARMA coefficients, based on the use of the Prony’s method applied to the auto-covariance series, is presented. Afterwards, an analysis on how the parameters involved in the ARMA reconstruction procedure—for example, the signal time length, the number of poles and data used—affect the spectral estimates is carried out, providing evidence on their effect on the accuracy of results. This allowed us to provide guidelines on how to set these parameters in order to make the ARMA model as accurate as possible. The paper focuses on mono-modal sea states. Nevertheless, examples also related to bi-modal sea states are discussed.

Doubly-Toeplitz-Based Interpolation for Joint DoA-Range Estimation Using Coprime FDA

Abstract: The concept of coprime frequency diverse array (FDA) has attracted much attention in the recent years. For it reaps the benefits of coprime sampling and frequency diversity, improved degrees-of-freedom (DoF) and spatial resolution can be achieved. However, existing works adopt on-grid methods in the joint direction-of-arrival (DoA)-range estimation and, thus, a compromise between the off-grid error and the computational cost is needed. In this paper, a doubly-Toeplitz-based estimation algorithm is proposed to achieve the coarray interpolation and off-grid estimation for coprime FDA. A positive semi-definite optimization problem is formulated based on atomic-norm minimization, and the joint DoA-range estimation can be achieved by applying well-established subspace-based spectral estimation algorithm to the optimized covariance matrix. The effectiveness of proposed method is validated by numerical simulations.

Bayesian Reconstruction of Fourier Pairs

Abstract: In a number of data-driven applications such as detection of arrhythmia, interferometry or audio compression, observations are acquired indistinctly in the time or frequency domains: temporal observations allow us to study the spectral content of signals (e.g., audio), while frequency-domain observations are used to reconstruct temporal/spatial data (e.g., MRI). Classical approaches for spectral analysis rely either on i) a discretisation of the time and frequency domains, where the fast Fourier transform stands out as the de facto off-the-shelf resource, or ii) stringent parametric models with closed-form spectra. However, the general literature fails to cater for missing observations and noise-corrupted data. Our aim is to address the lack of a principled treatment of data acquired indistinctly in the temporal and frequency domains in a way that is robust to missing or noisy observations, and that at the same time models uncertainty effectively. To achieve this aim, we first define a joint probabilistic model for the temporal and spectral representations of signals, to then perform a Bayesian model update in the light of observations, thus jointly reconstructing the complete (latent) time and frequency representations. The proposed model is analysed from a classical spectral analysis perspective, and its implementation is illustrated through intuitive examples. Lastly, we show that the proposed model is able to perform joint time and frequency reconstruction of real-world audio, healthcare and astronomy signals, while successfully dealing with missing data and handling uncertainty (noise) naturally against both classical and modern approaches for spectral estimation.

Gridless variational Bayesian inference of line spectral from quantized samples

Abstract: Efficient estimation of line spectral from quantized samples is of significant importance in information theory and signal processing, e.g., channel estimation in energy efficient massive MIMO systems and direction of arrival estimation. The goal of this paper is to recover the line spectral as well as its corresponding parameters including the model order, frequencies and amplitudes from heavily quantized samples. To this end, we propose an efficient grid-less Bayesian algorithm named VALSE-EP, which is a combination of the high resolution and low complexity gridless variational line spectral estimation (VALSE) and expectation propagation (EP). The basic idea of VALSE-EP is to iteratively approximate the challenging quantized model of line spectral estimation as a sequence of simple pseudo unquantized models, where VALSE is applied. Moreover, to obtain a benchmark of the performance of the proposed algorithm, the Cramer Rao bound (CRB) is derived. Finally, numerical experiments on both synthetic and real data are performed, demonstrating the near CRB performance of the proposed VALSE-EP for line spectral estimation from quantized samples.

Gridless Variational Direction-of-Arrival Estimation in Heteroscedastic Noise Environment

Abstract: Horizontal line arrays are often employed in underwater environments to estimate the direction of arrival (DOA) of a weak signal. Conventional beamforming is robust but has wide beamwidths and high-level sidelobes. High-resolution methods, such as minimum-variance distortionless response and subspace-based MUSIC algorithm, produce low sidelobe levels and narrow beamwidths, but are sensitive to signal mismatch, and require many snapshots and the knowledge of number of sources. In addition, heteroscedastic noise (HN) where the variance varies across observations and sensors due to nonstationary environments degrades the conventional methods significantly. This article studies DOA in an HN environment, where the variance of noise is varied across the snapshots and the antennas. By treating the DOAs as random variables and the nuisance parameters of the noise variance different across the snapshots and the antennas, multisnapshot variational line spectral estimation dealing with HN (MVHN) is proposed, which automatically estimates the noise variance, nuisance parameters of the prior distribution, and number of sources, and provides the uncertain degrees of DOA estimates. When the noise variance only varies across the snapshots or the antennas, the variants of MVHN, i.e., MVHN-S and MVHN-A, can be naturally developed. Finally, substantial numerical experiments are conducted to illustrate the proposed algorithms’ performance, including a real data set in a DOA application.

Forward-Backward Hankel Matrix Fitting for Spectral Super-Resolution

Abstract: Hankel-based approaches form an important class of methods for line spectral estimation within the recent spectral super-resolution framework. However, they suffer from the fundamental limitation that their estimated signal poles do not lie on the unit circle in general, causing difficulties of physical interpretation and performance loss. In this paper, we present a modified Hankel approach called forward-backward Hankel matrix fitting (FB-Hankel) that can be implemented by simply modifying the existing algorithms. We show analytically that the new approach has great potential to restrict the estimated poles on the unit circle. Numerical results are provided that corroborate our analysis and demonstrate the advantage of FB-Hankel in improving the estimation accuracy. 1

Robust and Efficient Parametric Spectral Density Estimation for High-Throughput Data

Abstract: Modern scientific instruments readily record various dynamical phenomena at high frequency and for extended durations Spanning timescales across several orders of magnitude, such “high-throughput”

Spectral estimation for detecting low-dimensional structure in networks using arbitrary null models.

Abstract: Discovering low-dimensional structure in real-world networks requires a suitable null model that defines the absence of meaningful structure. Here we introduce a spectral approach for detecting a network’s low-dimensional structure, and the nodes that participate in it, using any null model. We use generative models to estimate the expected eigenvalue distribution under a specified null model, and then detect where the data network’s eigenspectra exceed the estimated bounds. On synthetic networks, this spectral estimation approach cleanly detects transitions between random and community structure, recovers the number and membership of communities, and removes noise nodes. On real networks spectral estimation finds either a significant fraction of noise nodes or no departure from a null model, in stark contrast to traditional community detection methods. Across all analyses, we find the choice of null model can strongly alter conclusions about the presence of network structure. Our spectral estimation approach is therefore a promising basis for detecting low-dimensional structure in real-world networks, or lack thereof.

\(\kappa \)-Circulant Maximum Variance Bases

Abstract: Principal component analysis (PCA), a well-known technique in machine learning and statistics, is typically applied to time-independent data, as it is based on point-wise correlations. Dynamic PCA (DPCA) handles this issue by augmenting the data set with lagged versions of itself. In this paper, we show that both, PCA and DPCA, are a special case of \(\kappa \)-circulant maximum variance bases. We formulate the constrained linear optimization problem of finding such \(\kappa \)-circulant bases and present a closed-form solution that allows further interpretation and significant speed-up for DPCA. Furthermore, the relation of the proposed bases to the discrete Fourier transform, finite impulse response filters as well as spectral density estimation is pointed out.

Missing data filling based on the spectral analysis and the Long Short- Term Memory network

Abstract: A combined missing data filling approach based on the spectral analysis and the Long Short-Term Memory (LSTM) network is put forward in this paper to solve the data missing problem in wind speed. Firstly, the periodicity of wind speed data is determined by the periodogram and spectral density estimation results. Then two periodicity-related prediction filling strategies named the forward periodic prediction filling and the inverse periodic prediction filling are designed and realized through LSTM networks along with a non-periodicity-related sequence prediction filling strategy called the sequence prediction filling. Finally, the results of the three prediction filling models are combined according to the best weight vector obtained by the parameter optimization algorithm. Error comparison results demonstrate that the proposed approach performs well in wind speed missing data filling.

Resolution Enhancement of Spatial Parametric Methods via Regularization

Abstract: The spatial spectral estimation problem has applications in a variety of fields, including radar, telecommunications, and biomedical engineering. Among the different approaches for estimating the spatial spectral pattern, there are several parametric methods, as the well-known multiple signal classification (MUSIC). Parametric methods like MUSIC are reduced to the problem of selecting an integer-valued parameter [so-called model order (MO)], which describes the number of signals impinging on the sensors array. Commonly, the best MO corresponds to the actual number of targets, nonetheless, relatively large model orders also retrieve good-fitted responses when the data generating mechanism is more complex than the models used to fit it. Most commonly employed MO selection (MOS) tools are based on information theoretic criteria (e.g., Akaike information criterion, minimum description length and efficient detection criterion). Normally, the implementation of these tools involves the eigenvalues decomposition of the data covariance matrix. A major drawback of such parametric methods (together with certain MOS tool) is the drastic accuracy decrease in adverse scenarios, particularly, with low signal-to-noise ratio, since the separation of the signal and noise subspaces becomes more difficult to achieve. Consequently, with the aim of refining the responses attained by parametric techniques like MUSIC, this article suggests utilizing regularization as a postprocessing step. Furthermore, as an alternative, this article also explores the possibility of selecting a single relatively large MO (rather than using MOS tools) and enhancing via regularization, the solutions retrieved by the treated parametric methods. In order to demonstrate the capabilities of this novel strategy, synthetic aperture radar tomography is considered as application.

Effects of Cosine Tapering Window on Quantum Phase Estimation

Abstract: We provide a modification to the quantum phase estimation algorithm (QPEA) inspired on classical windowing methods for spectral density estimation. From this modification we obtain an upper bound in the cost that implies a cubic improvement with respect to the algorithm's error rate. Numerical evaluation of the costs also demonstrates an improvement. Moreover, with similar techniques, we detail an iterative projective measurement method for ground state preparation that gives an exponential improvement over previous bounds using QPEA. Numerical tests that confirm the expected scaling behavior are also obtained. For these numerical tests we have used a Lattice Thirring model as testing ground. Using well-known perturbation theory results, we also show how to more appropriately estimate the cost scaling with respect to state error instead of evolution operator error.