Sparse Iterative Covariance-based Estimation Research Articles

An ADMM-qSPICE-Based Sparse DOA Estimation Method for MIMO Radar

In recent years, sparse direction-of-arrival (DOA) estimation for multiple-input multiple-output (MIMO) radar has attracted extensive attention and been extensively studied, especially the method based on the classic least absolute shrinkage and selection operator (LASSO) estimator. The alternating-direction method of multipliers (ADMM) is an effective method for solving this problem at the cost of introducing an additional user parameter. To avoid introducing an additional user parameter, this paper adopts an equivalent transformation in the form of the generalized SParse Iterative Covariance-based Estimation (qSPICE) cost function to obtain a mean squared minimized form of the cost function. Then, the problem is transformed into a sparse optimization problem in the form of a weighted LASSO. Next, this unconstrained optimization problem is decomposed into three subproblems, which are solved separately to reduce the dimension of each problem and thus reduce the overall computational complexity based on ADMM. Simulation results and measured data indicate that the proposed method significantly outperforms the traditional super-resolution DOA estimation method and ADMM-LASSO method and slightly outperforms qSPICE in terms of resolution and sidelobe suppression capability. In addition, the proposed method has a much lower computational complexity and substantially fewer iterations than qSPICE.

Low-Altitude Windshear Wind Speed Estimation Method Based on KASPICE-STAP

Aiming at the problem of low-altitude windshear wind speed estimation for airborne weather radar without independent identically distributed (IID) training samples, this paper proposes a low-altitude windshear wind speed estimation method based on knowledge-aided sparse iterative covariance-based estimation STAP (KASPICE-STAP). Firstly, a clutter dictionary composed of clutter space-time steering vectors is constructed using prior knowledge of the distribution position of ground clutter echo signals in the space-time spectrum. Secondly, the SPICE algorithm is used to obtain the clutter covariance matrix iteratively. Finally, the STAP processor is designed to eliminate the ground clutter echo signal, and the wind speed is estimated after eliminating the ground clutter echo signal. The simulation results show that the proposed method can accurately realize a low-altitude windshear wind speed estimation without IID training samples.

Angle-incremental range estimation for FDA-MIMO radar via hybrid sparse learning

In this paper, a target parameter estimation problem is addressed for the recently emerging frequency diverse array multiple-input multiple-output (FDA-MIMO) radar system, utilizing sparse learning. The scene is modeled as a two dimensional (2D) angle-incremental range grid. To solve the resulting sparse problem, the recently proposed user-parameter free algorithms including block sparse learning via iterative minimization (BSLIM), iterative adaptive approach (IAA), sparse iterative covariance-based estimation (SPICE), likelihood-based estimation of sparse parameters (LIKES), and orthogonal matching pursuit (OMP) are applied which achieve excellent parameter estimation performance. However, these algorithms do not exhibit a uniform performance under different scenarios such as the number of available snapshots and the number of present targets. In this paper, we propose a hybrid estimation approach which utilizes the model order selection (MOS), and automatically selects the best algorithm for the scenario under test. The performance analyses show that the proposed hybrid algorithm presents higher accuracy in terms of root mean square error (RMSE), as compared with the discussed sparse algorithms, and converges to the Cramér-Rao lower bound (CRLB).

Joint RFI mitigation and radar echo recovery for one-bit UWB radar

Radio frequency interference (RFI) mitigation and radar echo recovery are critically important for the proper functioning of ultra-wideband (UWB) radar systems using one-bit sampling techniques. We recently introduced a technique for one-bit UWB radar, which first uses a majorization-minimization method for RFI parameter estimation followed by a sparse method for radar echo recovery. However, this technique suffers from high computational complexity due to the need to estimate the parameters of each RFI source separately and iteratively. In this paper, we present a computationally efficient joint RFI mitigation and radar echo recovery framework to greatly reduce the computational cost. Specifically, we exploit the sparsity of RFI in the fast-frequency domain and the sparsity of radar echoes in the fast-time domain to design a one-bit weighted SPICE (SParse Iterative Covariance-based Estimation) based framework for the joint RFI mitigation and radar echo recovery of one-bit UWB radar. Both simulated and experimental results are presented to show that the proposed one-bit weighted SPICE framework can not only reduce the computational cost but also outperform the existing approach for decoupled RFI mitigation and radar echo recovery of one-bit UWB radar.

High‐resolution time delay estimation via sparse parameter estimation methods

This study addresses the high-resolution time delay estimation (TDE) via sparse parameter estimation methods. Two representative algorithms, Sparse Asymptotic Minimum Variance (SAMV) and SParse Iterative Covariance-based Estimation are devised in both the time and frequency domains for application to the TDE of spread-spectrum signals and their performances are analysed in various multipath environments. The authors also proposes the combined approach of SAMV and weighted RELAX, referred to as SAMV-WRELAX, to reduce the computational load. Numerical examples demonstrate that the frequency-domain approaches with a proper type of snapshots not only outperform the corresponding time-domain approaches but also mitigate the problem of the noise correlation encountered in time-domain processing. They also show that the computational load of SAMV-WRELAX with a grid size of 0.1T c decreases up to a few tenths of that of SAMV with a fine grid, e.g. a size of 0.01T c , without any performance degradations.

SPICE-ML Algorithm for Direction-of-Arrival Estimation.

Sparse iterative covariance-based estimation, an iterative direction-of-arrival approach based on covariance fitting criterion, can simultaneously estimate the angle and power of incident signal. However, the signal power estimated by sparse iterative covariance-based estimation approach is inaccurate, and the estimation performance is limited to direction grid. To solve the problem above, an algorithm combing the sparse iterative covariance-based estimation approach and maximum likelihood estimation is proposed. The signal power estimated by sparse iterative covariance-based estimation approach is corrected by a new iterative process based on the asymptotically minimum variance criterion. In addition, a refinement procedure is derived by minimizing a maximum likelihood function to overcome the estimation accuracy limitation imposed by direction grid. Simulation results verify the effectiveness of the proposed algorithm. Compared with sparse iterative covariance-based estimation approach, the proposed algorithm can achieve more accurate signal power and improved estimation performance.

Fast implementation of sparse iterative covariance-based estimation for processing MST radar data

Doppler estimation is an essential problem for the mesosphere–stratosphere–troposphere (MST) radar data for estimation of atmospheric parameters. The Doppler is estimated by computing the power spectral density using either parametric or non-parametric method. A recent class of spectral estimation technique referred as Sparse Iterative Covariance Based Estimation (SPICE) is introduced in literature. SPICE is a sound, user-parameter free, good resolution, iterative and globally convergent method which exhibits the enhanced results than the current spectral estimation methods, at the high computational cost. This letter presents the fast implementation of the SPICE algorithm for the MST radar data and the estimation of various wind parameters at a lesser computational time and is validated with the radiosonde data.

Analysis and Evaluation of Data-Adaptive Spectral Estimation Algorithms for Processing MST Radar Data

The National Atmospheric Research Laboratory (NARL) situated at Gadanki, Andhra Pradesh, constitutes the primary source for Indian MST radar data (Mesosphere-Stratosphere-Troposphere). The primary purpose of the MST radar is to analyze and explore the atmospheric dynamics. The MST radar is developed with an array antenna in the active phase and consists of 1024 Yagi-Uda antennas being operated at a frequency of 53 MHz. The NARL provides atmospheric wind data by using MST radar. The wind speed parameters are calculated from the radar echo signals by using spectral estimation. In this paper, the analysis and evaluation of data-adaptive spectral estimation algorithms namely nonparametric iterative adaptive approach (IAA) and semiparametric methods—sparse learning via iterative minimization (SLIM) and sparse iterative covariance-based estimation (SPICE)—have been presented. These algorithms exhibit high resolution and low sidelobe levels. The detectability of the radar signals is improved at low signal-to-noise (SNR) conditions. The zonal speed (U), meridional speed (V) and wind speed (W) are computed and are validated using the Global Positioning System (GPS) radiosonde data. From the results, the SPICE algorithm outperforms the other two data-adaptive algorithms and the existing periodogram method.

Array auto-calibration using a generalized least-squares method

This paper introduces a new class of auto-calibration algorithms, based on a generalized least-squares (GLS) cost function. This class supports both gain-phase calibration and mutual coupling calibration and it is independent of array shape. The GLS cost function is minimized cyclically with respect to the direction of arrivals (DOA) and calibration parameters. These two minimization steps are repeated until convergence. In the DOA estimation step, minimization leads to the SPICE (SParse Iterative Covariance-based Estimation) DOA estimation algorithm. In fact, the innovation of this paper mainly lies in the calibration step. In the DOA estimation step, a generalized form of the SPICE algorithm should be used in the coherent sources case. Consequently, the proposed auto-calibration algorithm is able to support coherent source cases. Moreover, the proposed algorithm does not need multi-dimensional search. The necessary condition for the existence of a solution is studied as well. Using simulations, the performance of the proposed algorithm is compared with several other auto-calibration algorithms. Simulation results show that the proposed algorithm is more robust than the other algorithms and usually has better performance.

RFI Mitigation for UWB Radar Via Hyperparameter-Free Sparse SPICE Methods

Radio frequency interference (RFI) causes serious problems to ultrawideband (UWB) radar operations due to severely degrading radar imaging capability and target detection performance. This paper formulates proper data models and proposes novel methods for effective RFI mitigation. We first apply the single-snapshot Sparse Iterative Covariance-based Estimation (SPICE) algorithm to data from each pulse repetition interval for RFI mitigation and discuss the connection of SPICE to the $l_{1}$ -penalized least absolute deviation ( $l_{1}$ -PLAD) approach. Then, we devise a modified group SPICE algorithm and we prove that it is equivalent to a special case of the $l_{1,2}$ -PLAD method. The modified group SPICE algorithm can be applied to data from a coherent processing interval for effective RFI mitigation. Both the single-snapshot SPICE and the modified group SPICE methods simultaneously exploit the sparsity properties of both RFI spectrum and UWB radar target echoes. Unlike the existing sparsity-based RFI suppression methods, such as the robust principal component analysis algorithm, the proposed methods are hyperparameter-free and therefore easier to use in practical applications. Furthermore, the fast implementation of the SPICE methods is considered by exploiting the special structures of both single-snapshot and multiple-snapshot covariance matrices. Finally, the results obtained from applying the SPICE methods to simulated data as well as measured data collected by the U.S. Army Research Laboratory synthetic aperture radar system are presented to demonstrate the effectiveness of the proposed methods.

A Frequency-Domain SPICE Approach to High-Resolution Time Delay Estimation

We propose a frequency-domain sparse iterative covariance-based estimation (FD-SPICE) approach for the high-resolution time delay estimation of spread spectrum signals. The conventional correlation method fails to resolve the signals in the case where they are spaced within a Rayleigh resolution limit and further processing should be applied to the correlation outputs in order to improve performance. SPICE is one of the most prominent candidates for further processing since it has various advantages over subspace-based approaches. SPICE is implemented normally in the time domain like other sparse signal reconstruction-based approaches. However, the time-domain SPICE (TD-SPICE) approach suffers from a severe performance degradation in coherent signal cases, as in direction-of-arrival estimation. We develop an FD-SPICE approach which makes use of the Fourier transform bins of the correlation output samples to form a sample covariance matrix. Numerical examples demonstrate the superiority of FD-SPICE over TD-SPICE, especially in coherent signal cases.

Sparse iterative covariance-based estimation approach for processing atmospheric radar data

The Doppler estimation is an important problem for Mesosphere–Stratosphere–Troposphere (MST) Radar data for detection and estimation of the weather parameters like turbulence intensity, mean radial velocity, humidity, temperature, wind speed. For Doppler estimation, one has to compute the Power Spectral Density (PSD). Various parametric and nonparametric methods have been developed. Recently, a new category of spectrum estimation method called Sparse Iterative Covariance Based Estimation (SPICE) is also developed. SPICE is a robust, user parameter-free, high resolution, iterative and globally convergent estimation algorithm. In this paper, the simple gradient approach is used for minimization of the weighted covariance estimation analyzing the data collected from the Indian MST radar at Gadanki (13.5°N, 79.2°E). The same method is applied for radar data to estimate the power spectrum and Doppler frequency. The zonal (U), meridional (V), wind speed (W) are calculated and the results have been validated using simultaneous Global Positioning System (GPS) Sonde data.

Stokes parameters and 2-D DOAs estimation of polarized sources with an L-shaped coprime array

In this paper, a sparse reconstruction based approach to estimate Stokes parameters and 2-D DOAs of polarized sources is proposed in case of unknown number of sources. An L-shaped coprime array composed of dipole-dipole pairs, where a dipole in the dipole-dipole pair is placed on x-axis and the other is placed on z-axis, is used to reduce the mutual coupling across two dipoles in the dipole-dipole pair. In order to estimate the elevation of polarized sources, an orthogonal matching pursuit algorithm with the identification of the sources' number (OMP-isn) is proposed. In our proposed approach, the quasi deterministic maximum likelihood (qDML) test step is added in each iteration of algorithm. In addition, a refining grid step is also added in each iteration to reduce the estimation error incurred by the grid mismatch. The OMP algorithm and sparse iterative covariance-based estimation (SPICE) method are employed to estimate the azimuth of polarized sources. In order to pari the azimuth with the elevation, a pair-matching method is proposed based on the l2-norm and l1-norm (l2/l1) minimization. Based on the pairing azimuth and elevation, Stokes parameters of polarized sources are estimated by using Least Squares (LS) or Total Least Squares (TLS). The stochastic CRB is derived for the 2-D DOAs and Stokes parameters of polarized sources. Simulations are used to verify the performance of the proposed approach.

Wideband Sparse Reconstruction for Scanning Radar

Recently, the generalized sparse iterative covariance-based estimation algorithm was extended to allow for varying norm constraints in scanning radar applications. In this paper, further to this development, we introduce a wideband dictionary framework which can provide a computationally efficient estimation of sparse signals. The technique is formed by initially introducing a coarse grid dictionary constructed from integrating elements, spanning bands of the considered parameter space. After forming estimates of the initially activated bands, these are retained and refined, whereas nonactivated bands are discarded from the further optimization, resulting in a smaller and zoomed dictionary with a finer grid. Implementing this scheme allows for reliable sparse signal reconstruction, at a much lower computational cost as compared to directly forming a larger dictionary spanning the whole parameter space. Simulation and real data processing results demonstrate that the proposed wideband estimator offers significant computational savings, without noticeable loss of performance.

Direction-Of-Arrival Estimation and Tracking Based on a Sequential Implementation of C-SPICE with an Off-Grid Model.

This paper focuses on the problem of estimating and tracking time-varying direction-of-arrivals (DoAs) with an antenna array. A sequential DoA estimation method is proposed by extending the capon and sparse iterative covariance-based estimation (C-SPICE) method, which is an iterative off-grid method for estimating constant DoAs. Then, a moving average initialization technique is introduced such that the spatial spectrum information estimated in this snapshot can be utilized in the next one. In uniform linear arrays (ULAs), we replace the uniform grid in direction domain with that in a “frequency” domain, to improve estimation accuracy without additional complexity in practical applications. The validity and efficiency of the proposed methods are demonstrated through numerical experiments.

Comparison of Two Hyperparameter-Free Sparse Signal Processing Methods for Direction-of-Arrival Tracking in the HF97 Ocean Acoustic Experiment

In this paper, we review and compare the performance of two recently introduced hyperparameter-free sparse signal processing methods namely, the sparse iterative covariance-based estimation method and the sparse Bayesian learning-based relevance vector machine method, for direction-of-arrival (DOA) tracking of multiple signals using an array of sensors. The methods are presented to the readers, in a tutorial style for easy understanding. Hyperparameter-free sparsity-based methods are attractive in practice since tuning of regularization parameters (hyperparameters) is not necessary as they are automatically estimated from the data. The DOA tracking problem is formulated as a snapshot-by-snapshot estimation problem and the implementation of the methods are discussed in detail. A simulation study using a uniform-linear-array is carried out to evaluate the performance of the methods in terms of the root-mean-squared error of the DOA estimates and the probability of resolution with the goal of determining when one is to be preferred over the other. The algorithms are also applied on passive sonar data from the 1997 High-Frequency (HF $\mathbf {97}$ ) ocean acoustic experiment to demonstrate their usability in a real underwater scenario, as well as their robustness to the modeling assumptions made. We draw new conclusions about the main features of these methods that are important to the underwater acoustic practitioners.

High-Resolution Imaging for Impulse-Based Forward-Looking Ground Penetrating Radar

Forward-Looking Ground Penetrating Radar (FLGPR) has multiple applications, one of which includes its use for detecting landmines and other buried improvised explosive devices (IEDs). The standard method for generating synthetic aperture radar (SAR) images for this radar is the backprojection (BP) algorithm, which has poor resolution and high sidelobe problems. In this paper, we consider using the Sparse Iterative Covariance-based Estimation (SPICE) algorithm and the Spare Learning via Iterative Minimization (SLIM) algorithm for generating sparse high-resolution images for FLGPR. A pre-processing step, which involves an orthogonal projection of the received data onto a subspace related to the region of interest is performed, for decreasing the dimension of the data and for clutter reduction. The SLIM and SPICE algorithms are user-parameter free, and are capable of providing SAR images with improved resolution. We also use the well-known CLEAN approach for imaging based on a proposed signal model in the time domain. We show using simulated data that the SPICE and SLIM algorithms provide higher resolution than CLEAN and the standard BP. Imaging using real data collected via the Synchronous Impulse Reconstruction (SIRE) radar, a multiple-input multiple-output (MIMO) FLGPR radar developed by the Army Research Laboratory (ARL), is also presented and used for analysis.

Training data selection method for adaptive beamforming

A method for adaptively selecting training data is proposed to improve the performance of adaptive beamforming. The method first measures the contribution of each snapshot to the covariance matrix required by the beamforming using the sparse iterative covariance-based estimation technique. Then, those snapshots making larger contributions are selected as the final training samples. The homogeneity of training samples can be improved significantly, and thus results in an evident performance improvement in adaptive beamforming. Simulation results demonstrate the effectiveness of the proposed method.

Connection between SPICE and Square-Root LASSO for sparse parameter estimation

In this note we show that the sparse estimation technique named Square-Root LASSO (SR-LASSO) is connected to a previously introduced method named SPICE. More concretely we prove that the SR-LASSO with a unit weighting factor is identical to SPICE. Furthermore we show via numerical simulations that the performance of the SR-LASSO changes insignificantly when the weighting factor is varied. SPICE stands for sparse iterative covariance-based estimation and LASSO for least absolute shrinkage and selection operator.

Fast implementation of sparse iterative covariance-based estimation for source localization

Fast implementations of the sparse iterative covariance-based estimation (SPICE) algorithm are presented for source localization with a uniform linear array (ULA). SPICE is a robust, user parameter-free, high-resolution, iterative, and globally convergent estimation algorithm for array processing. SPICE offers superior resolution and lower sidelobe levels for source localization compared to the conventional delay-and-sum beamforming method; however, a traditional SPICE implementation has a higher computational complexity (which is exacerbated in higher dimensional data). It is shown that the computational complexity of the SPICE algorithm can be mitigated by exploiting the Toeplitz structure of the array output covariance matrix using Gohberg-Semencul factorization. The SPICE algorithm is also extended to the acoustic vector-sensor ULA scenario with a specific nonuniform white noise assumption, and the fast implementation is developed based on the block Toeplitz properties of the array output covariance matrix. Finally, numerical simulations illustrate the computational gains of the proposed methods.