Off-grid Targets Research Articles

Wideband off-grid direction-of-arrival estimation based on the improved finite rate of innovation method.

Off-grid direction-of-arrival estimation is a crucial research area in multi-sensor array signal processing to achieve accurate estimation in a finite sparse grid. However, current off-grid estimation methods primarily focus on narrowband processing, which may not be suitable for practical passive estimation scenarios where the targets of interest are wideband signals with various steering vectors and varying signal-to-noise ratios across frequency bins. First, we propose an improved weighting-based wideband joint finite rate of innovation algorithm to address this limitation. This algorithm extends the narrowband approach by approximating the wideband array data as multiple observations at the difference frequency using extended frequency difference weighting. Additionally, we propose an estimation method under non-ideal weighting conditions to mitigate bias caused by deviations in initial weight values through linear fitting of multiple estimation results obtained on a sparse grid. Simulation results demonstrate that our proposed algorithm outperforms existing methods by providing more accurate estimates and lower computational complexity for wideband off-grid multi-targets at low signal-to-noise ratio while unrestricted by grid limitations. Furthermore, experimental data collected from the South China Sea validate our proposed algorithm's effectiveness and superior performance for direction-of-arrival estimation of wideband off-grid targets.

A Novel Method for Airborne Array-InSAR Tomography Based on Off-grid Target Modeling and Group Sparsity

A Novel Method for Airborne Array-InSAR Tomography Based on Off-grid Target Modeling and Group Sparsity

On the False Alarm Probability of the Normalized Matched Filter for Off-Grid Targets: A Geometrical Approach and Its Validity Conditions

On the False Alarm Probability of the Normalized Matched Filter for Off-Grid Targets: A Geometrical Approach and Its Validity Conditions

A Vortex Electromagnetic Imaging Method Based on Two-Dimensional Matrix Compensation for Off-Grid Targets

Vortex electromagnetic (EM) wave has shown great potential in the field of radar imaging. Under the assumption that the target is located at the grid point, the compressed sensing (CS) algorithm is applied to vortex EM imaging and achieves high imaging quality. However, the off-grid target in the actual scene deviates from the grid points, resulting in the basis mismatch problem. This problem will lead to the mismatch between the assumed measurement matrix and the real echo signal and the degradation of the CS imaging performance. In order to solve this problem, a novel two-dimensional (2-D) joint off-grid imaging method is proposed by considering the gridding error as a multiplicative matrix and separating it via series expansion. This method compensates for errors in 2-D matrix directly instead of converting the 2-D matrix into the 1-D vector, which can not only solve the off-grid problem, but also reduce the storage of data acquisition and processing. Furthermore, the 2-D iterative adaptive algorithm (2DIAA) for the 2-D model is adopted to achieve better reconstruction performance and lower computational complexity. Finally, Simulation results show the effectiveness and robustness of the algorithm.

An Improved OMP-GA Combined Algorithm for Off-grid DOA Estimation

DOA (Direction of Arrival) is used to determine the direction of the targets and is one of the important technologies in array signal processing. To ensure the accuracy of traditional OMP-based DOA estimation algorithm, the over-complete dictionary needs to contain grids that match the real incident angles. However, for off-grid targets, the estimation accuracy will decrease. In this paper, we propose an improved OMP-based DOA estimation algorithm with genetic algorithm (GA), in which GA is introduced to search incident angle of the off-grid target directly, the subsequent traditional OMP steps are remained and the result got by which is used to filter out the false estimation results that deviate from the true target obtained by GA. Compared with the traditional OMP-based DOA estimation algorithm, this proposed algorithm could achieve higher accuracy. Simulation results verify the effectiveness of this proposed algorithm in the case of low signal-to-noise ratio (SNR) and low number of snapshots.

One bit compressive sensing with off-grid targets

The compressive sensing theory enables reconstruction of sparse or compressible signals at reduced sampling rate. Recent studies have shown that stable signal reconstruction is possible even if each measurement is quantized to one bit. In conventional compressive sensing framework, the signal can be sparsely represented by some discrete atoms. In many applications however, signals are sparse in a continuous parameter space, e.g., radar imaging. A commonly used method is to discretize the continuous parameter into grid points and build a dictionary to characterize the sparsity. However, the true targets may not coincide with the predefined grid points. This off-grid problem always leads to a mismatched basis matrix, which results in degradation of the performance. In this paper, a parameter perturbation method, based on 1-bit compressive sensing is proposed to deal with the off-grid problem. Especially for adjacent targets in the adjoining grids, a self-checking mechanism is proposed to further discriminate the adjacent targets located within the proximity of adjoining grids. In the proposed algorithm, the available grid points in the dictionary are adaptively updated to approach the true targets. The convergence of the algorithm can be theoretically guaranteed, and numerical experiments demonstrate that the proposed algorithm can be effectively applied to range profile and synthetic aperture radar imaging. Simulations indicate that the proposed algorithm outperforms the state-of-the-art techniques over a wide range of signal-to-noise ratio levels.

Underdetermined wideband DOA estimation for off‐grid targets: a computationally efficient sparse Bayesian learning approach

Underdetermined wideband direction of arrival (DOA) estimation based on the sparse array is studied here and a novel algorithm is developed to improve the estimation performance of off-grid targets in the framework of sparse Bayesian learning. First, the narrowband off-grid model is extended to a wideband case and the sparse Bayesian model containing off-grid biases is deduced. Then, a sequential solution is proposed to obtain the estimation, where the fast sparse Bayesian learning strategy is employed to improve the computational efficiency. The estimation accuracy is improved significantly through off-grid compensation and the computational complexity is reduced remarkably. Simulation results verify the effectiveness of the proposed method.

A New Computing Paradigm for Off-Grid Direction of Arrival Estimation Using Compressive Sensing

In this paper, a method for solving grid mismatch or off-grid target is presented for direction of arrival (DOA) estimation problem using compressive sensing (CS) technique. Location of the sources are at few angles as compare to the entire angle domain, i.e., spatially sparse sources, and their location can be estimated using CS methods with ability of achieving super resolution and estimation with a smaller number of samples. Due to grid mismatch in CS techniques, the source energy is distributed among the adjacent grids. Therefore, a fitness function is introduced which is based on the difference of the source energy among the adjacent grids. This function provides the best discretization value for the grid through iterative grid refinement. The effectiveness of the proposed scheme is verified through extensive simulations for different number of sources.

Off-Grid Aware Channel and Covariance Estimation in mmWave Networks

The spectrum scarcity at sub-6 GHz spectrum has made millimeter-wave (mmWave) frequency band a key component of the next-generation wireless networks. While mmWave spectrum offers extremely large transmission bandwidths to accommodate ever-increasing data rates, unique characteristics of this new spectrum need special consideration to achieve the promised network throughput. In this work, we consider the off-grid targets (basis mismatch) problem for mmWave communications. The off-grid effect naturally appears in compressed sensing (CS) techniques adopting a discretization approach for representing the angular domain. This approach yields a finite set of discrete angle points, which are an approximation to the continuous angular space, and hence degrade the accuracy of related parameter estimation. In order to cope with the off-grid effect, we present a novel parameter-perturbation framework to efficiently estimate the channel and the covariance for mmWave networks. The proposed algorithms employ a smart perturbation mechanism in conjunction with a low-complexity greedy framework of simultaneous orthogonal matching pursuit (SOMP), and jointly solve for the off-grid parameters and weights. Numerical results show a significant performance improvement through our novel framework as a result of handling the off-grid effects, which is totally ignored in the conventional sparse mmWave channel or covariance estimation algorithms.

Direction of arrival estimation with off-grid target based on sparse reconstruction in impulsive noise

This paper proposes a direction of arrival estimation based on sparse signal reconstruction in the presence of alpha noise by the off-grid orthogonal matching pursuit algorithm. Assuming Gaussian distribution as the noise model, the previous sparse reconstruction enhances robustness by utilizing the least square criterion-based direction of arrival estimation algorithms. However, they severely degrade, even invalid, when there is thick trailing and large impulse in the noise molded by [Formula: see text] stable distribution. In addition, due to the discretization of the potential angle space, the accuracy of these methods will be reduced when the target is not completely on the divided mesh exactly. Increasing the grid density to improve estimation effect will increase the computation burden. The compressed sensing signal model is reconstructed by reshaping the fractional lower order covariance matrix of the sensor array received signal. Based on the reshaped signal model, the novel reshaped orthogonal matching pursuit algorithm and reshaped off-grid orthogonal matching pursuit algorithm are derived. Compared to the least square criterion method with Gaussian distribution assumption, the proposed algorithm obtains high-resolution direction of arrival estimation in [Formula: see text] noise. Moreover, the reshaped off-grid orthogonal matching pursuit algorithm improves the direction of arrival estimation accuracy with off-grid target. Numerical simulation results demonstrate the effectiveness of proposed method in direction of arrival estimation with off-grid targets in [Formula: see text] noise.

MIMO Radar Imaging With Multiple Probing Pulses for 2D Off-Grid Targets via Variational Sparse Bayesian Learning

Spatial sparsity of the target space has been successfully exploited to provide accurate range-angle images by the methods based on sparse signal reconstruction (SSR) in Multiple-Input Multiple-Output (MIMO) radar imaging applications. The SSR based method discretizes the continuous target space into finite grid points and generates an observation model utilized in image reconstruction. However, inaccuracies in the observation model may cause various degradations and spurious peaks in the reconstructed images. In the process of the image formation, the off-grid problem frequently occurs that the true locations of targets that do not coincide with the computation grid. In this article, we consider the case that the true location of a target has both range and angle-varying two-dimensional (2D) off-grid errors with a noninformative prior. From a variational Bayesian perspective, an iterative algorithm is developed for joint MIMO radar imaging with orthogonal frequency division multiplexing (OFDM) linear frequency modulated (LFM) waveforms and 2D off-grid error estimation of off-grid targets. The targets during multiple probing pulses are modeled as Swerling II case and a unified generalized inverse Gaussian (GIG) prior is adopted for the target reflection coefficient variance at all snapshots. Furthermore, an approach to reducing the computational workload of the signal recovery process is proposed by using singular value decomposition. Experimental results show that the proposed algorithm is insensitive to noise and has improved accuracy in terms of mean squared estimation error under different computation grid interval.

Bi‐level JOMP for DOA estimation in coprime array with off‐grid targets

The direction of arrival (DOA) estimation for off-grid targets in the coprime array, which can extend degrees of freedom, is studied. Among existing research results, joint orthogonal matching pursuit (JOMP) has obvious advantages in complexity, but drawbacks in accuracy. Therefore, a bi-level iterative algorithm is proposed to improve estimation performance of JOMP in this study. First, JOMP is executed to obtain the initial estimations of DOAs and mismatch parameters. Then, an iterative proximity searching is implemented to update target vectors to decline the residual further. After that, on the strength of results of the secondary iteration, the signal spectrum and mismatch parameters can be obtained through exploiting LS algorithm. Simulation results verify effectiveness of the proposed algorithm.

Robust Mismatched Filter for Off-Grid Target

In this letter, we consider the robustness of the mismatched filter in presence of off-grid target. Since for an off-grid target, the received sampled signal differs from the on-grid signal, the mismatched filter as optimized in the literature is not optimal anymore, and in particular may present a deteriorated sidelobe level. We propose here a general optimization program enabling to get an optimal mismatched filter-with respect to the integrated sidelobe level (ISL)-within the resolution cell. We detail then the resulting solution in two particular radar cases, namely a Doppler steering vector and a linear chirp signal. In both cases, the proposed solution involves the discrete prolate spheroidal sequences. Simulation results show that this solution indeed provides the best ISL in the resolution cell.

Several Bits Are Enough: Off-Grid Target Localization in WSNs Using Variational Bayesian EM Algorithm

Several Bits Are Enough: Off-Grid Target Localization in WSNs Using Variational Bayesian EM Algorithm

Unambiguous Sparse Recovery of Migrating Targets With a Robustified Bayesian Model

The problem considered is that of estimating unambiguously migrating targets observed with a wideband radar. We extend a previously described sparse Bayesian algorithm to the presence of diffuse clutter and off-grid targets. A hybrid-Gibbs sampler is formulated to jointly estimate the sparse target amplitude vector, the grid mismatch, and the (assumed) autoregressive noise. Results on synthetic and fully experimental data show that targets can be actually unambiguously estimated even if located in blind speeds.

Grid Evolution: Joint Dictionary Learning and Sparse Bayesian Recovery for Multiple Off-Grid Targets Localization

In this letter, we propose an efficient grid evolution multiple targets localization framework for off-grid targets. First, we propose a more accurate localization model, enabling grid evolution by considering all the grids as random variables to be inferred. Then, the localization problem is formulated as a joint sparsifying dictionary learning and sparse signal recovery problem. Finally, the joint optimization problem is solved under the general framework of sparse Bayesian learning (SBL). Different to previous SBL based localization algorithms, we adopt the hierarchical Laplace distribution for sparse prior, rather than the Sudent’s t distribution. We compare the proposed framework with state-of-the-art off-grid targets localization algorithms as well as Cramer–Rao lower bound. Numerical simulations highlight the improved performance of the proposed framework in terms of localization error, noise robustness, and required number of measurements.

TenDSuR: Tensor-Based 4D Sub-Nyquist Radar

We propose tensor-based four-dimensional sub-Nyquist radar that samples in spectral, spatial, Doppler, and temporal domains at sub-Nyquist rates while simultaneously recovering the target's direction, Doppler velocity, and range without loss of native resolutions. We formulate the radar signal model wherein the received echo samples are represented by a partial third-order tensor. We then apply compressed sensing in the tensor domain and use our tensor-orthogonal matching pursuit (OMP) and tensor completion algorithms for signal recovery. Our numerical experiments demonstrate joint estimation of all three target parameters at the same native resolutions as a conventional radar but with reduced measurements. Furthermore, tensor completion methods show enhanced performance in off-grid target recovery with respect to tensor-OMP.

Variational Bayesian Inference-Based Counting and Localization for Off-Grid Targets With Faulty Prior Information in Wireless Sensor Networks

The benefits of compressive sensing (CS) on counting and localization in wireless sensor networks have already been demonstrated in previous works. However, most existing solutions usually become infeasible in the presence of off-grid targets, which is inevitable for the traditional CS-based localization methods. To mitigate the error caused by off-grid targets, in this paper, a more accurate sparse approximation model is applied where the true and unknown sparsifying dictionary is approximated with its first-order Taylor expansion around a known dictionary. Based on the model, the counting and localization problem is formulated as a sparse reconstruction problem that recovers two sparse signals with related supports. To solve the problem, we develop an iterative algorithm under a variational Bayesian inference framework. Moreover, in practice, some faulty prior information (e.g., coarse positions) is usually available. To incorporate the information, a three-level hierarchical prior model is introduced and imposed on the sparse signals to be recovered, where the supports of sparse signals are learned in the third level. Additionally, a grid pruning mechanism and matrix inversion lemma are leveraged to accelerate the inference process. Extensive simulation results demonstrate that, compared with state-of-the-art algorithms, the proposed algorithm can achieve counting and localization with higher accuracy as well as lower cost.

Sparse Bayesian Learning Based Three-Dimensional Imaging Algorithm for Off-Grid Air Targets in MIMO Radar Array

In recent years, the development of compressed sensing (CS) and array signal processing provides us with a broader perspective of 3D imaging. The CS-based imaging algorithms have a better performance than traditional methods. In addition, the sparse array can overcome the limitation of aperture size and number of antennas. Since the signal to be reconstructed is sparse for air targets, many CS-based imaging algorithms using a sparse array are proposed. However, most of those algorithms assume that the scatterers are exactly located at the pre-discretized grids, which will not hold in real scene. Aiming at finding an accurate solution to off-grid target imaging, we propose an off-grid 3D imaging method based on improved sparse Bayesian learning (SBL). Besides, the Bayesian Cramér-Rao Bound (BCRB) for off-grid bias estimator is provided. Different from previous algorithms, the proposed algorithm adopts a three-stage hierarchical sparse prior to introduce more degrees of freedom. Then variational expectation maximization method is applied to solve the sparse recovery problem through iteration, during each iteration joint sparsity is used to improve efficiency. Experimental results not only validate that the proposed method outperforms the existing off-grid imaging methods in terms of accuracy and resolution, but have compared the root mean square error with corresponding BCRB, proving effectiveness of the proposed method.

Fast super-resolution estimation of DOA and DOD in bistatic MIMO Radar with off-grid targets

ABSTRACTIn this paper, we focus on the problem of joint DOA and DOD estimation in Bistatic MIMO Radar using sparse reconstruction method. In traditional ways, we usually convert the 2D parameter estimation problem into 1D parameter estimation problem by Kronecker product which will enlarge the scale of the parameter estimation problem and bring more computational burden. Furthermore, it requires that the targets must fall on the predefined grids. In this paper, a 2D-off-grid model is built which can solve the grid mismatch problem of 2D parameters estimation. Then in order to solve the joint 2D sparse reconstruction problem directly and efficiently, three kinds of fast joint sparse matrix reconstruction methods are proposed which are Joint-2D-OMP algorithm, Joint-2D-SL0 algorithm and Joint-2D-SOONE algorithm. Simulation results demonstrate that our methods not only can improve the 2D parameter estimation accuracy but also reduce the computational complexity compared with the traditional Kronecker Compressed Sensing method.