Spatial Spectrum Research Articles

Space Target Tracking with the HRRP Characteristic-Aided Filter via Space-Based Radar

Approaching space target tracking is a typical and challenging mission in the space situational awareness (SSA) field. As the space-based radar is able to monitor the space targets of interest full-weather all-time, the space-based radar system is utilized in this paper. However, most multi-target tracking (MTT) filters in target tracking studies merely utilize the location or narrow measurements, and many potentially valuable electromagnetic scattering characteristics are missed, which leads to space target false tracking problems. The space-based radar transmits a wide-band signal, and the measured high-resolution range profile (HRRP) information is an effective characteristic for different target discrimination. Therefore, the HRRP characteristics of space targets are implemented into the update recursion of the MTT filter, which can be utilized to improve the tracking performance. Then, to predict the target HRRP sequence, the geometrical theory of diffraction (GTD) model is utilized. Additionally, a modified spatial spectrum method with a novel covariance matrix is designed to improve the scattering parameter estimation accuracy. Finally, an adapting threshold is devised for merging the Gaussian mixture (GM) components weights. The proposed threshold is on the basis of the proposed HRRP characteristic-aided probability hypothesis density (PHD) filter, and it can tackle the problem of space target discrimination. Simulation results validate the effectiveness and robustness of the proposed probability hypothesis density (HGI-PHD) filter aided by HRRP information and improved with GM weights.

Algorithmic Hallucinations of Near-Surface Winds: Statistical Downscaling with Generative Adversarial Networks to Convection-Permitting Scales

Abstract This paper explores the application of emerging machine learning methods from image super resolution (SR) to the task of statistical downscaling. We specifically focus on convolutional neural network–based generative adversarial networks (GANs). Our GANs are conditioned on low-resolution (LR) inputs to generate high-resolution (HR) surface winds emulating Weather Research and Forecasting (WRF) Model simulations over North America. Unlike traditional SR models, where LR inputs are idealized coarsened versions of the HR images, WRF emulation involves using nonidealized LR and HR pairs, resulting in shared-scale mismatches due to internal variability. Our study builds upon current SR-based statistical downscaling by experimenting with a novel frequency-separation (FS) approach from the computer vision field. To assess the skill of SR models, we carefully select evaluation metrics and focus on performance measures based on spatial power spectra. Our analyses reveal how GAN configurations influence spatial structures in the generated fields, particularly biases in spatial variability spectra. Using power spectra to evaluate the FS experiments reveals that successful applications of FS in computer vision do not translate to climate fields. However, the FS experiments demonstrate the sensitivity of power spectra to a commonly used GAN-based SR objective function, which helps interpret and understand its role in determining spatial structures. This result motivates the development of a novel partial frequency-separation scheme as a promising configuration option. We also quantify the influence on GAN performance of nonidealized LR fields resulting from internal variability. Furthermore, we conduct a spectrum-based feature-importance experiment, allowing us to explore the dependence of the spatial structure of generated fields on different physically relevant LR covariates. Significance Statement We use artificial intelligence algorithms to mimic wind patterns from high-resolution climate models, offering a faster alternative to running these models directly. Unlike many similar approaches, we use datasets that acknowledge the essentially stochastic nature of the downscaling problem. Drawing inspiration from computer vision studies, we design several experiments to explore how different configurations impact our results. We find evaluation methods based on spatial frequencies in the climate fields to be quite effective at understanding how algorithms behave. Our results provide valuable insights into and interpretations of the methods for future research in this field.

Two-dimensional vector field of the phase energy spectrum application for motion identification

In the tasks of determining the location of objects and identifying movement, it is important to use the phase information contained in the phase-frequency spatial spectrum. In these problems, the phase-energy spectrum can be applied, which combines the advantages of the energy and phase spectra. A frame of a video sequence can be associated with a discrete vector field of the phase-energy spectrum; its components are located throughout the image. No less informative, but much simpler for analysis, is the discrete vector field of phase-energy characteristics. Its components are formed by the amplitudes of the harmonics of the phase-energy spectrum of a two-dimensional frame. To use the vector field of phase-energy characteristics in algorithms for identifying dynamic objects, information about interframe changes in its components is important. In this paper, the features of the change in the components of the vector field for the cases of horizontal and vertical movement of a rectangular object of constant brightness against a homogeneous background are investigated. Graphical representations of scalar fields of phase-energy functions are given. Characteristic regions are identified and their projections onto the coordinate plane are made. It is shown that two characteristic areas are the near and far hills, by analyzing which it is possible to determine the spatial coordinates of the object before the start of movement and the value of the object's inter-frame shift. The special areas of scalar fields of phase-energy functions are determined for the case of object motion in an arbitrary direction. It has been established that the presence of extended extrema in the graphs of phase-energy functions indicates a strictly vertical or horizontal movement of the object, and the presence of point extrema indicates the movement of the object “at an angle”, and the boundaries of the moving object and the magnitude of its displacement horizontally and vertically are completely determined by the coordinates of the point extrema. A number of options for finding the parameters of objects by extremums and/or by the boundaries of characteristic regions of phase-energy functions are proposed. The "boundary" and "extreme" approaches can be applied in vision systems as both an additional and a main tool for motion identification.

Investigating Spatial and Temporal Structuring of E‐Region Coherent Scattering Regions Over Northern Norway

AbstractRecently, it has been shown that the Spread Spectrum Interferometric Multistatic meteor radar Observing Network radar system located in northern Norway is capable of measuring ionospheric E‐region coherent scatter with spatial and temporal resolutions on the order of 1.5 km and 2 s, respectively. Four different events from June and July of 2022 are examined in the present study, where the coherent scatter measurements are used as a tracer for large‐scale ionospheric phenomena such as plasma density enhancements and ionospheric electric fields. By applying a two‐dimensional Fourier analysis to range‐time‐intensity data, we perform a multi‐scale spatial and temporal investigation to determine the change in range over time of large‐scale ionospheric structures (>3 km) which are compared with line‐of‐sight velocities of the small scale structures (∼5 m) determined from the Doppler shift of the coherent scatter. The spectral characteristics of the large‐scale structures are also investigated and logarithmic spectral slopes for scale sizes of 100–10 km were found to be between −3.0 and −1.5. This agrees with much of the previous work on the spatial spectra scaling for ionospheric electric fields. This analysis aids in characterizing the source of the plasma turbulence and provides crucial information about how energy is redistributed from large to small scales in the E‐region ionosphere.

Periodic Variation of Mesoscale Ultraviolet Contrast at the Cloud Top of Venus

AbstractImages of Venusian clouds taken at ultraviolet (UV) wavelengths frequently exhibit mesoscale cellular structures at low latitudes. To obtain clues regarding the origin of these structures, we studied the temporal variation of the mesoscale UV contrast using 283‐ and 365‐nm images taken by the ultraviolet imager (UVI) onboard the Akatsuki spacecraft. The 283‐nm channel is mostly affected by SO2 at the cloud top and the 365‐nm channel is mostly affected by an unknown absorber, though both absorbers are thought to influence both wavelengths. We defined the mesoscale as a spatial scale roughly below 1,000 km, where the effect of large‐scale streaky patterns is not significant according to the spatial spectra of 283‐nm images taken by UVI and 2.02‐μm images taken by the near‐infrared camera (IR2) onboard Akatsuki. We found that the temporal variation of the standard deviation of the mesoscale UV contrast is dominated by quasi‐periodic oscillations with amplitudes of 30%–50% relative to the mean value and periods of around 4–5 Earth days. Oscillations of the planetary‐scale UV contrast with similar periods were also observed, suggesting that the mesoscale structures are influenced by planetary‐scale waves. The mesoscale contrast tends to be enhanced when the background albedo decreases in the course of the propagation of planetary‐scale waves. This correlation suggests that the solar heating near the cloud top level feeds the mesoscale dynamics. An enhancement of the mesoscale contrast in the afternoon was seen at a wavelength of 365 nm.

Identification of spectrum of secondary acoustic-gravity waves in the middle and upper atmosphere in a high-resolution numerical model

Considerable attention has recently been paid to the study of so-called “secondary” acoustic-gravity waves (AGWs) that arise as a result of instability and nonlinear interactions of “primary” wave modes propagating from atmospheric sources, among themselves, and with the mean flow. In this paper, for the first time, the horizontal spatial spectra of primary and secondary AGWs are separated at fixed altitude levels in the middle and upper atmosphere at different time moments, which are simulated using a three-dimensional nonlinear high-resolution model AtmoSym. It is shown that in a short time after switching on the plane wave source at the lower boundary of the model, the spectrum consists of a peak corresponding to primary AGW and quasi-white noise generated by random atmospheric disturbances and the numerical model. Later, secondary peaks appear in the spectra at horizontal wave numbers, which are multiples of the wave numbers of primary AGW. The proposed separation of the spectra of primary and secondary AGWs makes it possible to estimate the relative contribution of secondary AGW at different altitudes, at different times, and with different stability of background temperature and wind profiles in the atmosphere.

Выделение спектра вторичных акустико-гравитационных волн в средней и верхней атмосфере в численной модели высокого разрешения

Considerable attention has recently been paid to the study of so-called “secondary” acoustic-gravity waves (AGWs) that arise as a result of instability and nonlinear interactions of “primary” wave modes propagating from atmospheric sources, among themselves, and with the mean flow. In this paper, for the first time, the horizontal spatial spectra of primary and secondary AGWs are separated at fixed altitude levels in the middle and upper atmosphere at different time moments, which are simulated using a three-dimensional nonlinear high-resolution model AtmoSym. It is shown that in a short time after switching on the plane wave source at the lower boundary of the model, the spectrum consists of a peak corresponding to primary AGW and quasi-white noise generated by random atmospheric disturbances and the numerical model. Later, secondary peaks appear in the spectra at horizontal wave numbers, which are multiples of the wave numbers of primary AGW. The proposed separation of the spectra of primary and secondary AGWs makes it possible to estimate the relative contribution of secondary AGW at different altitudes, at different times, and with different stability of background temperature and wind profiles in the atmosphere.

Structural design of an improved SPIDER optical system based on a multimode interference coupler.

The Segmented Planar Imaging Detector for Electro-Optical Reconnaissance (SPIDER) is a small volume, lightweight, low energy consumption, and high-resolution system expected to replace traditional large aperture telescopes for long-distance detection. In this paper, an improved SPIDER system is proposed, which uses a multimode interference (MMI) coupler instead of an orthogonal detector, and successfully doubles the space spectrum coverage. We present a three-point configuring method to configure lenslets, calculate spatial spectrum values from the output currents obtained by MMI. By comparing the performance of the MMI-SPIDER and SPIDER systems through simulations, we demonstrate that the former has more complete spatial spectrum coverage, resulting in better image restoration quality.

Brief Adaptation to Astigmatism Reduces Meridional Anisotropy in Contrast Sensitivity.

To investigate the effect of visual adaptation to orientation-dependent optical blur on meridional contrast sensitivity function in artificially imposed astigmatism. The study adopted a top-up adapt-test paradigm. During the blur adaptation process, the 18 non-astigmatic young adult participants were briefly presented with natural scene images (first trial, 10minutes; subsequent trials, 6 seconds). Contrast sensitivities for horizontal and vertical gratings at spatial frequencies ranging from 1 to 8 cycles per degree (cpd) were measured immediately before and after adaptation to +3.00 diopters cylinder (DC) with-the-rule or against-the-rule astigmatism. Meridional anisotropy was measured to quantify the contrast sensitivity difference between the two grating orientations. Adapting to astigmatic blur enhanced contrast sensitivity at the blurred power meridian but reduced contrast sensitivity at the least affected axis meridian. In with-the-rule conditions, contrast sensitivity for horizontal gratings was significantly increased, whereas that for vertical gratings was significantly decreased. Similarly, in against-the-rule conditions, contrast sensitivity for vertical gratings was significantly increased, whereas that for horizontal gratings was significantly decreased. These two factors together resulted in a substantial systematic reduction, averaging 34%, in meridional anisotropy of contrast sensitivity across the spatial frequency spectrum. Astigmatism adaptation occurs in natural scene viewing. Brief exposure to astigmatic blur altered contrast sensitivity in the opposite direction at the two principal meridians, indicating that the mature visual system possesses functional plasticity to recalibrate the response characteristics of orientationally tuned cortical filters and thus promote substantial reductions of meridional anisotropy in astigmatic vision, to some extent counterbalancing the elongated oval shape of astigmatic blur.

MIMO-SA-Based 3-D Image Reconstruction of Targets Under Illumination of Terahertz Gaussian Beam—Theory and Experiment

For the 3-D terahertz (THz) holographic imaging, this work proposes an extended phase-shift migration (PSM) reconstruction algorithm based on multiple-input-multiple-output (MIMO) array with an orthogonal synthetic aperture (SA). For this MIMO-SA-based imaging mechanism, the accurate expression of the signal spatial spectrum can also be obtained by utilizing the method of stationary phase (MSP). Meanwhile, the analytical expression of the reconstructed 3-D point-spread function (PSF) for target under the illumination of MIMO-SA-based THz Gaussian beam is derived to provide the theoretical spatial resolutions quantitatively. A serial of simulation results with fairly good agreement were given to verify the accuracy of the proposed MIMO-SA-based PSM reconstruction algorithm. Meanwhile, due to the PSM’s characteristic of phase shift compensation along the range direction, the image reconstruction process can also be implemented and accelerated by a GPU solution. Finally, two types of MIMO-SA-based prototype imagers are applied for the proof-of-principle experiments. The first prototype imager is configured with one transmitter and two receivers in 0.3-THz band. The MIMO linear array including arbitrary number of transmitters/receivers can be realized by controlling their positions in a low-cost way with the help of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$</tex-math> </inline-formula> -axis of a 2-D scanner. The second prototype imager is configured with eight transmitters and eight receivers in 0.2-THz band. The experimental results from the two prototype imagers can validate the effectiveness on image reconstruction quality.

SWASH FLOWS GENERATED BY A TRAIN OF SOLITARY WAVES ON A PLANAR SLOPE

The objective of this study is to gain insights of the swash flows generated by a train of solitary waves on a planar beach and the corresponding turbulence structure. Two dimensional velocity measurements are made using a 1000-Hz high speed particle image velocimetry (HSPIV). The turbulence characteristics in terms of the temporal and spatial evolution of the turbulent kinetic energy (TKE), TKE spatial spectra, and turbulence length scales are examined.

Acceleration and Reynolds effects of crosswind flow fields in gorge terrains

A significant acceleration generated in the gorge terrain poses a serious threat to the operational safety of the transportation facilities downstream of the gorge. To determine the formation mechanism of the acceleration effect, this paper compares the results of wind tunnel tests with the improved delayed detached eddy simulation in terms of the spatial distribution, turbulence, and spectrum of the flow field on the gorge topography under crosswinds. The effect of the Reynolds number on the results is discussed in terms of the characteristic wind speed of flow field and the scaling ratio. Recurrent neural networks are used to attempt to get signals from unknown measurement points and to repair damaged signals. The results show that when the mountain spacing in the experimental and the computational fluid dynamics models is zero, the most dramatic acceleration reaches 1.28–1.4 times the incoming wind speed. In the wind tunnel tests, the peak of the power spectra density (1.065 × 10−2) at the downstream of the center of the gorge with a mountain spacing of zero is 3.37 and 14.77 times higher than the corresponding values (3.16 × 10−3 and 7.21 × 10−4) in the gorge topography with the mountain spacing of 0.01 and 0.02 m, respectively. The maximum difference of mean wind velocities in the leeward of the gorge is 6.4% when the Reynolds number ranges from 2.03 × 105 to 1.03 × 107. The results are expected to provide a reference for the design of windproof facilities in gorge terrains.

A New GRACE Filtering Approach Based on Iterative Image Convolution

AbstractThe Gravity Recovery and Climate Experiment (GRACE) mission and its successor GRACE Follow‐On (GRACE‐FO) mission provide humans with a unique perspective on mass distribution through accurate temporal gravity field models. However, these models suffer from unavoidable stripe errors in the spatial domain. A new approach based on image processing has been developed for filtering GRACE and GRACE‐FO spherical harmonic solutions. In this approach, the gravity fields are treated as noise‐contaminated images, and the stripe errors are expected to be suppressed by convolving the input with an appropriate kernel. To verify the effectiveness of the proposed approach, a closed‐loop simulation environment over the nominal mission lifetime of 5 years is designed. Image processing indicators and geophysical information evaluation results demonstrate the superior performance of the new approach in suppressing stripe errors. In the context of real GRACE data processing, our new approach still yields better results as follows: (a) The comprehensive ability of de‐striping and retaining details has slight advantages over some commonly used filters, as demonstrated through spatial distributions, amplitude spectra, and coefficient spectra. (b) The equivalent water height time series at the basin scale is comparable to the results derived from other filters or Level‐3 products. (c) The estimated signal amplitude of the Mw9.1 2004 Sumatra earthquake co‐seismic gravity change is 52.7% larger than that derived from the Gaussian 300 km filter, which is much closer to the theoretical value derived from the dislocation theory.

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.

Retracted: A Spatial Spectrum Estimation Method for Optimization and Improvement of Resource Allocation and Management of Public Sport and Health Facilities.

[This retracts the article DOI: 10.1155/2022/3800237.].

Joint Direction of Arrival-Polarization Parameter Tracking Algorithm Based on Multi-Target Multi-Bernoulli Filter

This paper presents a tracking algorithm for joint estimation of direction of arrival (DOA) and polarization parameters, which exhibit dynamic behavior due to the movement of signal source carriers. The proposed algorithm addresses the challenge of real-time estimation in multi-target scenarios with an unknown number. This algorithm is built upon the Multi-target Multi-Bernoulli (MeMBer) filter algorithm, which makes use of a sensor array called Circular Orthogonal Double-Dipole (CODD). The algorithm begins by constructing a Minimum Description Length (MDL) principle, taking advantage of the characteristics of the polarization-sensitive array. This allows for adaptive estimation of the number of signal sources and facilitates the separation of the noise subspace. Subsequently, the joint parameter Multiple Signal Classification (MUSIC) spatial spectrum function is employed as the pseudo-likelihood function, overcoming the limitations imposed by unknown prior information constraints. To approximate the posterior distribution of MeMBer filters, Sequential Monte Carlo (SMC) method is utilized. The simulation results demonstrate that the proposed algorithm achieves excellent tracking accuracy in joint DOA-polarization parameter estimation, whether in scenarios with known or unknown numbers of signal sources. Moreover, the algorithm demonstrates robust tracking convergence even under low Signal-to-Noise Ratio (SNR) conditions.

Wideband optical edge detection based on dielectric metasurface

Optical image edge detection manifests itself as the advantages of fast speed, low energy consumption, parallel operation, and large information capacity, playing a crucial role in object and image recognition in the realms of biology, medicine, and artificial intelligence. In this paper, a dielectric metasurface that can achieve object edge detection in the full visible band is proposed. By combining two optical differential methods referring to spatial spectrum-dependent transmission function and 4f system-based spatial spectrum phase shift, a tetratomic macropixel metasurface that enables polarization-correlated interference based on dual geometric phase modulation is designed, which can achieve object edge detection under 473, 530, and 633 nm wavelengths, and even under white light conditions. This coherent filtering metasurface operator provides a flexible approach for achieving wideband two-dimensional edge detection.

Deep learning self-image update procedure in a wavefront sensor based on the Talbot phenomenon under Gaussian illumination

A feature-based image update procedure using machine learning is proposed to use in preprocessing of self-images in a Talbot wavefront sensor. A variant of the recurrent neural network with backpropagation, which is one of most widely applied machine learning tools, is utilized to stabilize intensity distribution in self-images in the case of an optical beam with a Gaussian profile. Once well trained, the neural network can decrease pit image shifts caused by beam intensity distribution in the case of a cosine-like grating. It is shown that based on the proposed recurrent neural network, it is possible to decrease the shift error caused by the Gaussian beam up to nine times depending on the aberration order and value. Despite the decreasing shift error, the value of the error of the restored aberration coefficient does not decrease significantly because of the feature-vector extraction method. It is shown additionally that due to the spatial spectrum wideness, the proposed self-image procedure is not applicable to binary gratings on the example of binary gratings with square pits. Adequate simulations are implemented to demonstrate the effectiveness and accuracy of the proposed approach.

Molecular hydrodynamic theory of the velocity autocorrelation function.

The velocity autocorrelation function (VACF) encapsulates extensive information about a fluid's molecular-structural and hydrodynamic properties. We address the following fundamental question: How well can a purely hydrodynamic description recover the molecular features of a fluid as exhibited by the VACF? To this end, we formulate a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes and tagged-particle self-motion are modeled by linear hydrodynamic equations; the fluid's spatial velocity power spectrum is identified as a necessary initial condition for the momentum current correlation. This formulation leads to a natural physical interpretation of the VACF as a superposition of products of quasinormal hydrodynamic modes weighted commensurately with the spatial velocity power spectrum, the latter of which appears to physically bridge continuum hydrodynamical behavior and discrete-particle kinetics. The methodology yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals. Furthermore, we obtain a new, hydrodynamic form of the self-intermediate scattering function whose description has been extended to low densities where the Schmidt number is of order unity; various calculations are performed for gaseous and supercritical argon to support the general validity of the theory. Excellent quantitative agreement is obtained with recent MD calculations for a dense supercritical Lennard-Jones fluid.

Joint Range and Angle Estimation by FDA-MIMO Radar With Unknown Mutual Coupling

Frequency diverse array-multiple-input multiple-output (FDA-MIMO) radar is characterized by a range-angle-dependent transmit antenna beampattern, where both range and angle of the target can be jointly estimated. However, the performance of existing estimation algorithms degrades in the presence of mutual coupling effect. To overcome this drawback, this paper deals with the problem of joint range and angle estimation by FDA-MIMO radar with unknown mutual coupling. At the design stage, the mutual coupling matrices (MCM) are constructed in both transmit and receive arrays, exploiting the banded symmetric Toeplitz structure, where the mutual coupling effect is eliminated by transforming the MCM into a diagonal matrix with a selection matrix. Subsequently, the range ambiguity is resolved by setting two linear coprime frequency increments, which locates the true target at the overlap of the peaks corresponding to the two spatial spectra. Furthermore, to reduce the computational cost resulted from the two-dimensional (2-D) grid search, an iterative procedure based on the coordinate descent (CD) algorithm is considered by alternating between the optimization over one variable keeping the other fixed. At the analysis stage, the closed-form solutions of the mutual coupling coefficients are given by utilizing the estimated range and angle. Moreover, a comparison in terms of estimation performance in different coupling scenarios is carried out, where the Cramér-Rao lower bound is provided as the benchmark. Numerical results verify the effectiveness of the considered estimation strategy in multiple simulated scenarios.