Capon Method Research Articles

Evaluation of Norm-Constrained Capon Method on Improving Doppler Peak Localization of Antenna-Arrayed High-Frequency Coastal Radar

Abstract Antenna-arrayed high-frequency coastal radar is widely used to monitor the ocean and obtain metocean parameters such as sea surface current, sea wave height, and surface wind. However, the accuracy of these parameters can be significantly influenced by the spectral width and Doppler velocity of the sea echo signals across azimuthal directions, and insufficient spectrum resolution increases uncertainties in the estimates of spectral width and Doppler velocity. To address this, we demonstrate an alternative approach to beamforming by utilizing the norm-constrained Capon (NC-Capon) method to enhance the Doppler spectral resolution and improve the localization accuracy of the spectral peaks. The efficacy of the NC-Capon method is exemplified through an application to a coastal radar dataset collected from 16 receiving channels, operated at a central frequency of 27.75 MHz. A comparative investigation of the NC-Capon beamforming method with the conventional Fourier beamforming method showed that the widths of the spectral peaks at different range cells and azimuthal angles are noticeably improved at lower signal-to-noise ratio (SNR) conditions. Given this, the NC-Capon beamforming method exhibits more robustness to noise and could effectively enhance the concentration of the radar sea echo signals in the Doppler frequency spectrum, thereby reducing the uncertainties of the spectral width and Doppler/radial velocity of the first-order sea echoes. These characteristics are substantiated by the comparative analysis of spectral parameters between the two beamforming methods across various ranges, beamforming angles, and SNR levels. Finally, the computed radial velocities are benchmarked against in situ measurements obtained from a bottom-mounted acoustic current profiler to confirm the validity of the NC-Capon method. Significance Statement We have recently implemented a high-frequency coastal radar equipped with an antenna array to monitor metocean variables within the offshore waters adjacent to Taichung Harbor in Taiwan. Our study focuses on enhancing the Doppler spectral resolution of radar sea echoes by employing an adaptive beamforming technique known as the norm-constrained Capon method. In comparison with the traditional linear beamforming approach, the norm-constrained Capon method demonstrates superior noise resilience. We anticipate that the norm-constrained Capon method holds promise as a dependable approach for refining the accuracy of metocean parameters obtained from antenna-arrayed high-frequency coastal radar systems.

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.

DIRECTION OF ARRIVAL USING PCA NEURALNETWORKS

This paper adapted the neural network for the estimating of the direction of arrival (DOA). It usesan unsupervised adaptive neural network with APEX algorithm to extract the principal componentsthat in turn, are used by Capon method to estimate the DOA, where by the PCA neural network wetake signal subspace only and use it in Capon (i.e. we will ignore the noise subspace, and take thesignal subspace only)

Spatial Filtering of Signals under Imprecise Calibration of Antenna Arrays

Introduction. Spatial filtering of signals is performed for the selection the signals of interest when the signals spectra overlap. The quality of spatial filtering depends on the accuracy of antenna array (AA) calibration, which allows estimation of the amplitude-phase distribution (APD) at all possible directions of arrival, thus ensuring the identity of reception paths. A mismatch between the actual and measured APD values leads to quality degradation in all spatial filtering methods.Aim. To develop a method for improving the quality of signal spatial filtering based on the estimates of the desired and interfering signal arrival directions formed by the MUSIC and ESPRIT algorithms under a priori uncertainty and imprecise AA calibration.Materials and methods. The quality of spatial filtering is improved by rejecting the interfering signals unsuppressed due to imprecisely measured APD of an AA. Statistical simulation modeling was carried out in the MATLAB environment; the data obtained experimentally were analyzed.Results. A method for spatial filtering based on MUSIC and ESPRIT completed with an additional rejection of unsuppressed interfering signals due to imprecise AA calibration is developed. An algorithm for basis construction for rejection under of a priori uncertainty of the signal-interference environment is substantiated. The results of statistical simulation modeling and experimental data processing have shown the feasibility of additional rejection applied to the selected signals by spatial filtering.Conclusion. The developed method for spatial filtering under the conditions of a priori uncertainty of the signal-interference situation and imprecise calibration of AA and reception paths ensures high quality characteristics across a wide dynamic range of desired and interfering signals. Whereas the Capon's method, which requires a priori knowledge of the arrival direction of the desired signal or its estimation, is capable of selecting only weak signals and suppressing strong ones under the conditions of imprecise APD.

An Effective Array Beamforming Scheme Based on Branch-and-Bound Algorithm

In this paper, we propose an effective full array and sparse array adaptive beamforming scheme that can be applied for multiple desired signals based on the branch-and-bound algorithm. Adaptive beamforming for the multiple desired signals is realized by the improved Capon method. At the same time, the sidelobe constraint is added to reduce the sidelobe level. To reduce the pointing errors of multiple desired signals, the array response phase of the desired signal is firstly optimized by using auxilary variables while keeping the response amplitude unchanged. The whole design is formulated as a convex optimization problem solved by the branch-and-bound algorithm. In addition, the beamformer weight vector is penalized with the modified reweighted ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -norm to achieve sparsity. Theoretical analysis and simulation results show that the proposed algorithm has lower sidelobe level, higher SINR, and less pointing error than the state-of-the-art methods in the case of a single expected signal and multiple desired signals.

Lamb wave based damage imaging using an adaptive Capon method

As plate-like structures are widely used in railway vehicle systems, structural health monitoring and nondestructive testing of those structures are important. The Lamb wave, as an ultrasonic guided wave propagating in plate-like structures, is an effective tool for fault diagnosis. The Capon method is widely used in Lamb wave based damage imaging due to its superior performance in suppressing background noise compared with the conventional delay-and-sum method. As the conventional Capon method is sensitive to modeling errors like the inaccuracy of the look-direction, diagonal loading is usually adopted to regularize the inverse of the covariance matrix. However, the degree of diagonal loading is related to the accuracy of the given look-direction and is hard to determine accurately. Aimed at improving the imaging quality of the conventional Capon method, an adaptive Capon method with adaptive diagonal loading is proposed. In the proposed method, the dispersion and the amplitude caused by wave diffusion are first compensated for each imaging point using the virtual time reversal technique. The correlations among the compensated waveforms after windowing are used to determine the degree of diagonal loading. In the process of regularizing the inverse of the covariance matrix, a large diagonal loading factor will be applied when the correlations among the compensated waveforms are large. As correlations are closely related to the signal phase, both the amplitude and the phase of scattering signals are utilized in the proposed method. The numerical and experimental validations on an aluminum plate are carried out to verify the effectiveness of the proposed method. The results show that compared with the conventional Capon method, the proposed method can obtain images with higher imaging quality, fewer artifacts, and lower noise.

Fast Adaptive Beamforming for Weather Observations with Convolutional Neural Networks

Polarimetric phased array radar (PAR) can achieve high temporal resolutions for improved meteorological observations with digital beamforming (DBF). The Fourier method performs DBF deterministically, and produces antenna radiation patterns with fixed sidelobe levels and angular resolution by pre-computing the beamforming weights based on the geometry of receivers. In contrast, the Capon method performs DBF adaptively in response to the changing environment by computing the beamforming weights from the received signals at multiple channels. However, it becomes computationally expensive as the number of receivers grows. This paper presents computationally efficient adaptive beamforming with an application of convolutional neural networks, named ABCNN. ABCNN is trained with the phase and amplitude of complex-valued time-series IQ signals and the Capon beamforming weights as input and output. ABCNN is tested and evaluated using simulated time-series data from both point targets and weather scatterers for a planar of fully digital PAR architecture. The preliminary results show that ABCNN lowers computation time by a factor of three, compared to the Capon method, for a phased array antenna with 1024 elements, while mitigating the contamination from sidelobes by placing nulls at the location of the clutter. Furthermore, ABCNN produces antenna patterns similar to those from the Capon method, which shows that it has successfully learned the data.

Алгоритм оценки углов прихода сигналов в системе распределенных некогерентных автомобильных радаров

The present paper is focused on processing of signals from multiple sensors in non-coherent mode that provide improvement of angular resolution of close targets compared to single radar. The low-complexity technique of Direction-of-Arrival (DoA) estimation in Automotive Distributed Non-Coherent Multi-Radar Systems in the case of short length of snapshots is proposed. This technique consists of three main stages: beam-scanning procedure, transformation of the received signals of two radars to the unified coordinate system, and joint DoA estimation algorithm. The DoA method is represented by two approaches: (i) the Capon method modified for joint signal processing; (ii) low-complexity algorithm based on theory of auto-compensator. Performance of the system is investigated on the base of Monte-Carlo simulation. Current algorithm shows improvement of system performance of distributed non-coherent multi-radar systems compared to single radar.

Real-time cable force identification based on block recursive Capon spectral estimation method

Cables are critical force-bearing components of cable-supported structures that greatly influence structure security. The changes in cable forces can reflect the cable service state and provide an important basis for structural health assessment. This paper proposes a method for real-time cable force identification (CFI) to tracking its varying rules. First, a recursive Capon method based on block updating is derived to estimate the amplitude spectrum at each observation moment. Second, determine the natural frequency (and corresponding mode order) in the transformed frequency domain and calculate the cable tension according to related formulas. Proper algorithm optimization and parameter selection are studied to ensure that the calculation cost meets the real-time requirement of CFI. The proposed method is applied to an experimental cable and the cables of a half-through arch bridge for validation.

Adaptive Capon beamforming for lensless electron cyclotron emission imaging with high spatial resolution

Electron cyclotron emission (ECE) imaging diagnostics incorporating a lensless approach have been developed for measurements involving active spatial selectivity and direction-of-arrival estimation. The Capon method for adaptive-array analysis was proposed to improve the spatial resolution of the two-dimensional ECE imaging technique. Broadband noise source emissions were used to simulate the ECE to verify the practical effectiveness of the Capon method in the ECE imaging. Multiple noise source emission positions were properly estimated with a high spatial resolution using the Capon method.

Сравнительный анализ методов калибровки каналов сигналов антенн моноимпульсной радиолокации

Today, antenna arrays (ARs) are increasingly used as antennas in modern radio engineering systems. With the help of AR, you can control the shape of the radiation pattern (DN) and the position of its main lobe, called the beam of such an antenna system. Each AA channel contains microwave components for controlling the amplitude and phase of the signal passing through it. These components are characterized by errors in setting the amplitude and phase, which negatively affects the shape of the pattern and its characteristics. Therefore, to compensate for these errors, it is necessary to use the AP calibration at the production stage, and also during its operation. The paper presents various calibration methods; the most suitable and promising methods for AA calibration were determined; the principles of operation of these methods are considered, the advantages and disadvantages of the methods are identified, a comparative analysis of all methods is carried out, as well as the conditions under which it is more expedient to use one or another method. The following calibration methods are considered: Phaseless methods: (Rotating-Element Electric Field Vector method - REV method, Measurement of Two Elements method - MTE method, Sorace algorithm, Levita (Leavitt), Correlation algorithm Adaptive methods: (Music method, Capon method, SMI (Sample Matrix Inversion algorithm), least mean square error (LMS) algorithm, Quasi-Newton algorithm); Autocalibration methods: (Friedlander-Weiss method, Wang-Kedzou method, Estelie-Swindleharst-Otterson method), as well as the proposed two-phase AR calibration method. These methods are the most attractive from a practical point of view, since they can be used not only for factory calibration of the AA, but also during operation.

A Target Localization Method based on Optimized Newton Algorithm for MIMO Radar

Target localization is one of the fundamental research topics in multiple input multiple output (MIMO) radar systems. In this paper, we focus on the localization parameter estimation including direction of departure (DoD), direction of arrival (DoA) and radar cross section (RCS) coefficients in monostatic MIMO radar systems. An optimized Newton algorithm is proposed to jointly estimate DoAs/DoDs and RCS coefficients. Its angle estimation performance outperforms traditional Capon, MUSIC and ESPRIT methods. The proposed localization algorithm also has great RCS coefficient estimation performance. Moreover, the joint estimation performance of the proposed optimized Newton algorithm is superior even with unknown target numbers and low sampling numbers. Simulation results verify the effectiveness of the proposed optimized Newton algorithm.

Reconstruction of Mercury's internal magnetic field beyond the octupole

Abstract. The reconstruction of Mercury's internal magnetic field enables us to take a look into the inner heart of Mercury. In view of the BepiColombo mission, Mercury's magnetosphere is simulated using a hybrid plasma code, and the multipoles of the internal magnetic field are estimated from the virtual spacecraft data using three distinct reconstruction methods: the truncated singular value decomposition, the Tikhonov regularization and Capon's minimum variance projection. The study shows that a precise determination of Mercury's internal field beyond the octupole up to the dotriacontapole is possible and that Capon's method provides the same high performance as the Tikhonov regularization, which is superior to the performance of the truncated singular value decomposition.

High‐resolution angle estimation method in partly calibrated subarray‐based bistatic multiple‐input multiple‐output radar with unknown non‐uniform noise

Uniformly distributed white noise is often the desirable noise assumption for partly calibrated subarray-based radar systems. However, this assumption may practically not always be guaranteed. In this study, the angle estimation problem of the partly calibrated multi-subarray-based bistatic multiple-input multiple-output radar, where intersubarray calibration errors and non-uniform noise coexist, is considered. In addition, an inverse transformation-based enhanced Capon method is proposed to adapt to such a challenging situation. First, the noise-free covariance matrix of each subarray is obtained by formulating an imaginary selecting matrix following a covariance matrix invariance approach which performs an inverse transformation of the matrix. Thus, the noise identities at the different antennas of the subarray are estimated as nuisance parameters at the expense of the target signals. Second, assuming that the calibration within each subarray is well configured such that the steering vector of a subarray is known, knowledge is required of the intersubarray calibration mismatches. To this, a high-resolution Capon estimator which applies a combination of root and local searching orientation of the antenna arrays is implemented. The proposed approach resolves the intersubarray calibration errors and ultimately leads to obtaining the joint direction of departure and direction of arrival estimation of the target. Evidence of the proposed algorithm's validity and effectiveness over existing methods is demonstrated in numerical simulations under varying conditions.

Forest Height and Underlying Topography Inversion Using Polarimetric SAR Tomography Based on SKP Decomposition and Maximum Likelihood Estimation

The key point of forest height and underlying topography inversion using synthetic aperture radar tomography (TomoSAR) depends on the accurate positioning of the phase centers of different scattering mechanisms. The traditional nonparametric spectrum analysis methods (such as beamforming and Capon) have limited vertical resolution and cannot accurately distinguish closely spaced scatterers. In addition, it is very difficult to accurately estimate the ground or canopy heights with single polarimetric SAR images because there is no guarantee that the vertical profile will generate two clear and separate peaks for all resolution cells. A polarimetric TomoSAR method based on SKP (sum of Kronecker products) decomposition and iterative maximum likelihood estimation is proposed in this paper. On the one hand, the iterative maximum likelihood TomoSAR method has a higher vertical resolution than that of the traditional methods. On the other hand, the separation of the canopy scattering mechanism and the ground scattering mechanism is conducive to the positioning of the phase centers. This method was applied to the inversion of forest height and underlying topography in a tropical forest over the TropiSAR2009 test site in Paracou, French Guiana with six passes of polarimetric SAR images. The inversion accuracy of underlying topography of the proposed method was up to 1.489 m and the inversion accuracy of forest height was up to 1.765 m. Compared with the traditional polarimetric beamforming and polarimetric capon methods, the proposed method greatly improved the inversion accuracy of forest height and underlying topography.

A Maximum Likelihood Method for Joint DOA and Polarization Estimation Based on Manifold Separation

The use of the polarization diversity of a target signal at a polarization-sensitive antenna array can enhance the target detection and tracking capabilities of a radar. In this article, the manifold separation steering vector modeling technique is used to develop a maximum likelihood method for joint direction of arrival (DOA) and polarization estimation. Manifold separation can incorporate antenna array nonideal characteristics (e.g., cross polarization, mutual coupling) into the estimation algorithm using array calibration measurements. In the proposed technique, the estimation problem is formulated as a generalized Rayleigh quotient minimization problem that is transformed into a determinant minimization problem. Both the azimuth and elevation angles are estimated using the fast Fourier transform. Unlike the existing manifold separation based polarimetric element space (PES) multiple signal classification method and the PES Capon method, the proposed method can obtain DOA and polarization estimates based on very small-size primary data samples, even with a single sample, which makes the proposed method more suitable for nonstationary target polarization. The performance of the proposed method is demonstrated through simulations. The Cramer-Rao lower bound for joint DOA and polarization is also used for comparison with empirical errors.

A Modified Capon Method for SAR Tomography Over Forest

The 3-D structure of forests is an important indicator for evaluating forest health and can provide data support for ecological monitoring and protection. Synthetic aperture radar (SAR) tomography (TomoSAR) is an important technology for forest structure estimation using the multibaseline (MB) SAR data stacks. The spectral estimators, such as the Capon method, are usually used to estimate the 3-D reflectivity along elevation direction. In this letter, a modified Capon (M-Capon) method is proposed to improve the estimated profiles of ground and canopy scatterers in the elevation direction, including the estimation accuracy and resolution. This method combines the ideas of the CLEAN algorithm with the Capon method and uses iteration to improve the resolution and accuracy of the estimation. The effectiveness of the M-Capon method is demonstrated using the simulated data and the MB SAR data acquired by the P-band airborne SAR system over the Saihanba Forest Farm in Hebei, China.

The Performance of Relative Height Metrics for Estimation of Forest Above-Ground Biomass Using L- and X-Bands TomoSAR Data

Both synthetic aperture radar tomography (TomoSAR) profiles and light detection and ranging (LiDAR) waveforms are the responses of a 3-D canopy structure. Relative height (RH) metrics are extensively applied for forest biophysical parameters [i.e., the forest height and above-ground biomass (AGB)] estimation in full-waveform LiDAR studies. However, the use of RH metrics to forest biophysical estimation with TomoSAR profiles is limited due to the estimation error in the ground peak. To overcome this problem, RH metrics were redefined to avoid directly estimating the ground peak in this article. The redefined RH metrics were examined based on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> - and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -bands multibaseline (MB) SAR data simulated by LandSAR, which was a coherent backscattering model of 3-D forest canopies with the capability of MB data simulation at a landscape scale. First, the performance of LandSAR in modeling the tomographic features was verified over mountainous areas using the reference DSM and LiDAR digital terrain model acquired in 2012 in the frame of the Daxinganling campaign. Subsequently, the tomographic profiles were retrieved from the simulated MB data by using the Capon method. Additionally, redefined RH metrics were derived and then applied for retrieving the forest height. The highest performance corresponded to the combination of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> -band redefined RH metrics, with a correlation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.863. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -band redefined RH metrics performed worst due to limited penetration. Finally, the estimated forest height was used for the AGB retrieval with a height-to-biomass allometry. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and root-mean-square error of the forest AGB estimated using the combined model were 0.814 and 28.566 t/ha, respectively, compared with the reference forest AGB. All findings demonstrated that the redefined RH metrics had the potential of forest height and AGB retrieval using low frequencies TomoSAR data.

Mathematical foundation of Capon's method for planetary magnetic field analysis

Abstract. Minimum variance distortionless projection, the so-called Capon method, serves as a powerful and robust data analysis tool when working on various kinds of ill-posed inverse problems. The method has not only successfully been applied to multipoint wave and turbulence studies in the context of space plasma physics, but it is also currently being considered as a technique to perform the multipole expansion of planetary magnetic fields from a limited data set, such as Mercury's magnetic field analysis. The practical application and limits of the Capon method are discussed in a rigorous fashion by formulating its linear algebraic derivation in view of planetary magnetic field studies. Furthermore, the optimization of Capon's method by making use of diagonal loading is considered.

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.