Capon Algorithm Research Articles

Signal Positioning of Lightning Detection and Warning System Combining Direction of Arrival Algorithm and Capon Algorithm

Aiming at the poor warning effect and slightly low precision of signal positioning in the traditional lightning detection and warning system, the research utilizes the artificial intelligence approach to signal positioning in the lightning detection and warning system for performance improvement. The study first digitized the lightning signal using the arrival direction algorithm and then used the Capon algorithm based on the digitized processing to reduce the interference and improve the accuracy of lightning positioning. The results indicated that the root mean square error value and positioning angle error of lightning warning signal positioning data processing by hybrid algorithm were 6.72% and 5.93%, respectively. Meanwhile, the percentage of detection efficiency and real time was 96.36% and 95.16%, respectively, and the anti-interference ability was 94.02%. Moreover, the average value of time-consuming lightning warning positioning and the positioning error were 2.39 s and 2.69%, respectively. Moreover, the performance of all the comparison indexes was better than that of the comparison methods. This indicates that the method not only improves the precision of lightning signal positioning but also enhances the stability and real-time performance of the system. It has significant application potential in the field of lightning detection and warning and can effectively improve the precision and timeliness of lightning warning.

Quantitative assessment of the effectiveness of adaptive spatial processing algorithms in searching for low-noise underwater vehicles in surface shipping conditions of different density

The article describes the methodology and provides the results of a model quantitative assessment of the effectiveness of solving the problem of detecting and tracking a low-noise underwater object using three algorithms for spatial signal processing at the output of a multi-element antenna — the non-adaptive Bartlett algorithm, the Capon algorithm, and the Capon algorithm combined with a projection procedure limiting the signal power of strong local sources.

Sound Source Identification of Vehicle Noise Based on a Microphone Array With a Modified Multiple Signal Classification Algorithm

In this paper, a modified multiple signal classification (MUSIC) algorithm tailored for sound source identification (SSI) of vehicle noise is introduced and experimentally validated. A uniform planar microphone array (UPMA) is formulated for mathematical modeling, with its SSI-oriented parameters selected based on the primary frequency spectrum of vehicle noise. Simulations are conducted to compare the SSI accuracy of two conventional spatial spectra estimation (SSE) algorithms: the Capon algorithm and the MUSIC algorithm. The results demonstrate that the MUSIC algorithm, which relies on the eigenvalues of a covariance matrix to estimate signal direction, exhibits superior SSI resolution under low signal-to-noise ratio (SNR) conditions. However, it faces challenges in distinguishing between coherent or closely spaced signals. To address this, a modified MUSIC algorithm is proposed by reconstructing the covariance matrix of received signals and the SSE function. Simulation outcomes indicate that the modified MUSIC significantly outperforms the conventional version, owing to its enhanced SSI resolution. The accuracy of the SSI system, incorporating the UPMA and the modified MUSIC, is verified using a low-frequency volume source. Ultimately, the devised SSI system is successfully deployed to identify noise sources in a vehicle at different operational conditions, further validating the efficacy of the modified MUSIC. The UPMA and the modified MUSIC presented in this study have direct applicability in vehicle noise source identification and may be extended to other sound-related engineering fields for SSI purposes.

High-resolution 2D-DoA sequential algorithm of azimuth and elevation estimation in automotive distributed system of coherent MIMO radars

Objectives. One of the main tasks of radiolocation involves the problem of increasing spatial resolution of the targets in the case of limited aperture of the radar antenna array and short length of time samples (snapshots). Algorithms must be developed to provide high angular resolution and low computational complexity. In order to conform with the existing Advanced Driver Assistance Systems requirements, modern cars are equipped with more than one radar having a common signal processing scheme to improve performance during target detection, positioning, and recognition as compared to a single radar. The present study aims to develop a two-dimensional Direction-of-Arrival algorithm with low computation complexity as part of distributed coherent automotive radar system for cases involving short time samples (snapshots).Methods. A virtual antenna array formation algorithm is formulated according to the two-dimensional Capon method. A proposed modification of two-dimensional Capon algorithm is based on sequentially estimating the directions of arrival for the distributed radar system. The Monte Carlo method is used to compare the effectiveness of the considered algorithms.Results. The 2D-DoA sequential algorithm of azimuth and elevation estimation is proposed. The comparative analysis results for the developed algorithm and classical 2D Capon method based on numerical simulation using Monte Carlo method are presented. The proposed scheme of DoA estimation for coherent signal processing of distributed radars is shown to lead to an improvement of the main considered metrics representing the probability of correctly estimating the number of targets, mean square error, and square error compared to a single radar system. The proposed low-computational algorithm shows the gain in complexity compared to full 2D Capon algorithm.Conclusions. The proposed two-stage algorithm for estimating the directions of arrival of signals in azimuth and elevation planes can be applied to the distributed system of coherent radars with several receiving and transmitting antennas representing multiple input multiple output (MIMO) radars. The algorithm is based on sequentially estimating the directions of arrival, implying estimation in the azimuthal plane at the first stage and estimation in the vertical plane at the second stage. The performance of a coherent radar system with limited antenna array configuration of separate radar is close in characteristics to a high-performance 4D-radar with a large antenna array system.

Improving the Accuracy of Direction of Arrival Estimation with Multiple Signal Inputs Using Deep Learning.

In this paper, an innovative cyclic noise reduction method and an improved CAPON algorithm (also the called minimum variance distortionless response (MVDR) algorithm) are proposed to improve the accuracy and reliability of DOA (direction of arrival) estimation. By processing the eigenvalues obtained from the covariance matrix of the received signal, the signal-to-noise ratio (SNR) can be increased by up to 5 dB by the cyclic noise reduction method, which will improve the DOA estimation accuracy. The improved CAPON algorithm has a convolution neural network (CNN) structure, whose input is the processed covariance matrix of the received signal, and the CAPON spectral value is used as the training label to obtain the estimated spatial spectrum. It retains the advantages of the CAPON algorithm, which can achieve blind source estimation, and simulations show that the proposed algorithm exhibits a better performance than the traditional algorithm in conditions of various SNRs and snapshot numbers. The simulation results show that, based on a certain SNR, the root mean square error (RMSE) of the improved CAPON algorithm can be reduced from 0.86° to 0.8° compared to traditional algorithms, and the angle estimation error can be decreased by up to about 0.3°. With the help of the cyclic noise reduction method, the angle estimation error decreases from 0.04° to 0.02°.

Snow profile reconstruction from tomographic UAV SAR

Snow profiles can provide reliable and detailed snow parameters for global change research, but it is still challenging to reconstruct large-scale spatiotemporally continuous snow profiles. Synthetic aperture radar (SAR) tomography (TomoSAR) has been proven to be a promising method for reconstructing the 3D structure of targets and has been used to reconstruct snow profiles from ground-based SAR. However, the experimental condition of ground-based SAR is ideal and the algorithms developed for ground-based SAR have some problems when applied to airborne and spaceborne sensors, such as large computational load and big angular diversity. In this paper, we first collected the Ku-band tomographic SAR dataset in the snow season of Altay, China using the Unmanned Aerial Vehicle (UAV) platform. Then, we reconstructed the snow profile from the dataset using three spectral estimation-based focusing algorithms. According to the non-stationary characteristic of the UAV platform and the dense medium property of snow, phase calibration and medium correction were performed, respectively. Finally, we assessed the reconstruction accuracy of the snow profile and snow depth using the ground synchronous measurement data. The reconstruction accuracy of the three focusing algorithms from high to low is the MUSIC algorithm, the Capon algorithm, and the Beamforming algorithm. Among them, the average error of the MUSIC algorithm to reconstruct the snow profile is 1.13 cm, and the RMSE and MAE of the snow depth retrieval are 3.71 cm and 3.26 cm, respectively. Although TomoSAR is still widely unexplored for snow using air-based sensors, the results show that it has the ability to reconstruct snow profiles accurately, and the proposed method can provide reliable support for reconstructing the large-scale spatiotemporal continuous snow profiles from subsequent spaceborne SAR.

Source Localization in a Channel with a Rough Surface Using a Multi-Rank Capon Algorithm

Source Localization in a Channel with a Rough Surface Using a Multi-Rank Capon Algorithm

Nonhomogeneous Data-Based Direct Position Determination: The RD-DPD-Capon Algorithm

The accuracy of conventional two-step location methods is insufficient since the information loss problem in the parameter matching procedure. In this paper, we propose a Reduced Dimension Direct Position Determination with Capon (RD-DPD-Capon) algorithm. By introducing the idea of dimension reduction, the proposed algorithm avoids grid search along with the attenuation coefficient domain. Therefore, the RD-DPD-Capon algorithm has relatively low computational complexity. Meanwhile, the proposed algorithm inherits the high resolution and localization accuracy of the DPD-Capon algorithm. Numerical simulation verifies that the RD-DPD-Capon algorithm outperforms other conventional algorithms.

Assessment of underlying topography and forest height inversion based on TomoSAR methods

ABSTRACT Due to the strong penetrability, long-wavelength synthetic aperture radar (SAR) can provide an opportunity to reconstruct the three-dimensional structure of the penetrable media. SAR tomography (TomoSAR) technology can resynthesize aperture perpendicular to the slant-range direction and then obtain the tomographic profile consisting of power distribution of different heights, providing a powerful technical tool for reconstructing the three-dimensional structure of the penetrable ground objects. As an emerging technology, it is different from the traditional interferometric SAR (InSAR) technology and has advantages in reconstructing the three-dimensional structure of the illuminated media. Over the past two decades, many TomoSAR methods have been proposed to improve the vertical resolution, aiming to distinguish the locations of different scatters in the unit pixel. In order to cope with the forest mission of European Space Agency (ESA) that is designed to provide P-band SAR measurements to determine the amount of biomass and carbon stored in forests, it is necessary to systematically evaluate the performance of forest height and underlying topography inversion using TomoSAR technology. In this paper, we adopt three typical algorithms, namely, Capon, Multiple Signal Classification (MUSIC), and Compressed Sensing (CS), to evaluate the performance in forest height and underlying topography inversion. The P-band airborne full-polarization (FP) SAR data of Lopè National Park in the AfriSAR campaign implemented by ESA in 2016 is adopted to verify the experiment. Furthermore, we explore the effects of different baseline designs and filter methods on the reconstruction of the tomographic profile. The results show that a better tomographic profile can be obtained by using Hamming window filter and Capon algorithm in uniform baseline distribution and a certain number of acquisitions. Compared with LiDAR results, the root-mean-square error (RMSE) of forest height and underlying topography obtained by Capon algorithm is 2.17 m and 1.58 m, which performs the best among the three algorithms.

Parameter Estimation of Non-Gaussian Signals for Polarization-Sensitive Augmented Coprime Array: Fourth-Order Cumulant Reduced-Dimensional Capon Algorithm

In this paper, we investigate the problem of direction of arrival (DOA) and polarization estimation for non-Gaussian signal in polarization-sensitive augmented coprime array. Instead of the second-order cumulant statistics, the fourth-order cumulant statistics of the received signals are used for parameter estimation because they can detect more information of the non-Gaussian signal. First, polarization-sensitive augmented coprime array is designed, where each sensor element is equipped with a pair of orthogonal electric dipoles. Furthermore, a low-complexity reduced-dimensional Capon algorithm which uses the fourth-order cumulant of the received array signal is proposed for DOA and polarization estimation. Only one-dimensional peak search is required by reconstructing peak search function. Theoretical analysis has proven the effectiveness of the algorithm, and simulation results demonstrate that the proposed fourth-order cumulant reduced-dimensional Capon algorithm outperforms the other algorithms.

The Algorithm of Angular Superresolution Using the Cholesky Decomposition and its Implementation Based on Parallel Computing Technology

An algorithm of angular superresolution based on the Cholesky decomposition, which is a modification of the Capon algorithm, is proposed. It is shown that the proposed algorithm makes it possible to abandon the inversion of the covariance matrix of input signals. The proposed algorithm is compared with the Capon algorithm by the number of operations. It is established that the proposed algorithm, with a large dimension of the problem, provides some gain both when implemented on a single-threaded and multithreaded computer. Numerical estimates of the performance of the proposed and original algorithm using parallel computing technology CUDA NVidia are obtained. It is established that the proposed algorithm saves GPU computing resources and is able to solve the problem of constructing a spatial spectrum with an increase in the dimension of the covariance matrix of input signals by almost two times.

Estimation of noise radiance point sources multichannel direction finding systems resolution by linear prediction method

The resolution of multichannel direction finding systems of independent noise radiance point sources is estimated quantitatively under a limited learning sample on the basis of a linear prediction methods “bank” and modified Capon algorithms.

Comparison of density and positioning accuracy of PS extracted from super-resolution PSI with those from traditional PSI

In the application of persistent scatterer interferometry (PSI), deformation information is extracted from persistent scatterer (PS) points. Thus, the density and position of PS points are critical for PSI. To increase the PS density, a time-series In-SAR chain termed as "super-resolution persistent scatterer interferometry" (SR-PSI) is proposed. In this study, we investigate certain important properties of SR-PSI. First, we review the main workflow and dataflow of SR-PSI. It is shown that in the implementation of the Capon algorithm, the diagonal loading (DL) approach should be only used when the condition number of the covariance matrix is sufficiently high to reduce the discontinuities between the joint images. We then discuss the density and positioning accuracy of PS when compared with traditional PSI. The theory and experimental results indicate that SR-PSI can increase the PS density in urban areas. However, it is ineffective for the rural areas, which should be an important consideration for the engineering application of SR-PSI. Furthermore, we validate that the positioning accuracy of PS can be improved by SR-PSI via simulations.

Source Localization in a Randomly Inhomogeneous Channel Using the Multirank Capon Algorithm

Source Localization in a Randomly Inhomogeneous Channel Using the Multirank Capon Algorithm

Features of implementation of adaptive signals processing for a cylindrical antenna array with a horizontal generatrix

The ways of overcoming the problems caused by the specific asymmetry of the side lobes of the channels formed at the output of cylindrical antenna arrays with a horizontal generatrix, which are relevant for underwater robots, are considered. An algorithmic solution is proposed based on the use of adaptive signal power limitation for solving detection-direction finding problems in combination with non-adaptive reception or the diagonal loading Capon algorithm for assessing the spectral and correlation characteristics of strong signals.

Adaptive Spectral Doppler Estimation Based on the Modified Amplitude Spectrum Capon.

In conventional ultrasound systems, the compromise between frequency and temporal resolution limits the quality of the spectrograms and the ability to track fast blood flows. The main objective of this study was to identify a method that could reduce spectral broadening over time by reducing the observations and improving the spectral resolution and contrast. This problem is more pronounced in the process of imaging at higher blood velocities when using a short Doppler signal observation window (OW) in adaptive methods. The proposed adaptive technique, which is based on the covariance matrix Eigen space and the amplitude spectrum Capon (ASC) algorithm, managed to improve the spectral resolution and contrast compared with other adaptive algorithms within a shorter observation time, and it offered a narrower power spectrum and a more accurate spectrogram over time in combination with a coherence-based post filter. All methods were tested through various simulations. First, an analysis was carried out by simulating the femoral artery flow and the time-independent parabolic flow using the Field II simulator. Then, the performance of the proposed method was evaluated under more realistic conditions using a computational fluid dynamics simulation of complex flow fields in a carotid bifurcation model. Afterward, in vivo clinical data on the hepatic vein were used to validate the proposed method. Finally, the accuracy of the velocity estimated by different methods was evaluated through a mean-square-error assessment. Not only could the proposed method show significant improvements using extreme small OWs, N=[2, 4] , in the simulated data in terms of frequency resolution and contrast, but it also managed to offer an improvement of 74%, 73.3%, 22.2%, and 50% in frequency resolution, and an increase of 96.5, 90.2, 49, and 31.5 dB in contrast using in vivo clinical data compared with the Capon, amplitude and phase estimation (APES), projection-based Capon, and projection-based APES, respectively, for the OW of N=4 .

Persistent Scatterer Densification Through Capon-Based SAR Reprocessing for Sentinel-1 TOPS Data

Several researchers have shown that the Capon algorithm can be applied to reprocess SAR images, resulting in super-resolution reconstructed scenes with lower sidelobe levels. Thus by employing the Capon-based reprocessed images in Persistent Scatterer Interferometry (PSI), the persistent scatterer (PS) density can be increased. In this letter, we exploit the Capon-based PS densification method for Sentinel-1 (S-1)Terrain Observation by Progressive Scans(TOPS) data. We propose a revised robust approach of the Capon algorithm, which applies the automatic diagonal loading (DL) method when the condition number of the covariance matrix is big enough. The proposed approach is robust and can avoid spurious persistent scatterer candidate (PSC) points introduced by DL approaches. We also consider and analyze the spectral property caused by the scanning mode of TOPS in the reprocessing. We applied the revised-robust-Capon-based reprocessing algorithm to a stack of real-life S-1 data and selected PSCs from them. The final result shows that the number of PSs increases by approximately 30% with respect to the original stack.

UAVSAR Tomography for Vertical Profile Generation of Tropical Forest of Mondah National Park, Gabon

AbstractPolarimetric synthetic‐aperture radar (SAR) remote sensing has been widely used for structural and biophysical parameters retrieval of forest vegetation. It has been found that the combination of polarimetric properties and interferometric characteristics of SAR remote sensing provides the capacity to retrieve forest height. The prime objective of this research was to investigate the potential of Polarimetric Synthetic Aperture Radar Tomography (PolTomSAR) for the forested and river region of Mondah National Park, Gabon. SAR tomography is an improved method for acquiring the height of geographical features. UAVSAR L‐band fully polarimetric multibaseline data have been used in this research (1.275 GHz). SAR data and ground data over the area have been collected in the year 2016. With the superresolution‐based Capon algorithm, multiple scatterers located at a different vertical position in the same azimuth range cell has been resolved and reconstructed. This work provides a framework for Capon‐based tomographic processing of multibaseline UAVSAR data for vertical profile retrieval of forest vegetation. The height profile of the forest patch having sparse, as well as dense vegetation, were retrieved. The vertical profile for a single azimuthal bin was obtained in range direction. The tomographic profile obtained was cross‐checked with the field‐measured forest height for the 16 locations in Mondah National Park, Gabon. To check the accuracy of the applied method, the statistical method of R2 and root‐mean‐square error (RMSE) is employed. The obtained RMSE of the result is 4.21 m and R2 is 0.92. The obtained results were concluded to find the potential of the Capon algorithm for the tomographic reconstruction of UAVSAR data.

An Implementation Scheme of Range and Angular Measurements for FMCW MIMO Radar via Sparse Spectrum Fitting

The work presented in this paper is about implementing a frequency-modulated continuous wave (FMCW) multiple-input multiple-output (MIMO) positioning radar and a sparse spectrum fitting (SpSF) algorithm for range and angular measurements. First, we designed a coherent FMCW MIMO radar system working in the S-band with low power consumption that consists of four transmitter and four receiver antennas and has the ability to extend its virtual aperture; thus, this system can achieve a higher resolution than conventional phased array radars. Then, the SpSF algorithm was designed for estimating the distance and angle of the targets in the FMCW MIMO radar. Due to the fact that the SpSF algorithm can exploit the spatial sparsity diversity of a signal, the SpSF algorithm that is applied in the designed MIMO radar system can achieve a better estimation performance than the multiple signal classification (MUSIC) and Capon algorithms, especially in the context of small snapshots and low signal-to-noise ratios (SNRs). The simulated and experimental results are used to prove the effectiveness of the designed MIMO radar and the superior performance of the algorithm.

Meteor observations using radar imaging techniques and norm-constrained Capon method

Multifrequency and multireceiver techniques were employed simultaneously to examine the meteor echoes for the first time. A high-power-large-aperture radar−the Middle and Upper (MU) atmosphere radar (34.85oN, 136.10° E) was used in observation, with the radar beam directed to the geographic north and at 51° zenith. Receiving was done using 20 receivers and 5 carrier frequencies (46.250, 46.375, 46.500, 46.625, 46.750 ​MHz) for executing angular and range imaging of the meteor echoes, respectively. In addition to the conventional Capon and Fourier imaging methods, a norm-constrained Capon algorithm was also employed to improve the imaging results. Both meteor head echoes and long-duration range spread trail echoes (RSTEs, also known as non-specular meteor echoes) were observed simultaneously. It is demonstrated that range imaging is capable of resolving the evolution of RSTEs in the radar volume clearly, in which the branched RSTEs could be evidence of meteoroid fragmentation. On the other hand, angular imaging with single point of raw data (0.015s time resolution) can identify the multiple echo centers of meteor head echoes, which is also related to meteoroid fragmentation.