Cell Under Test Research Articles

Knowledge-aided multi-dictionary block sparsity-aware STAP for airborne polarimetric conformal array radar

Airborne polarimetric conformal array radar has gained increased attention recently. However, the conformal array configuration and polarization factors may lead to non-stationary clutter, which significantly degrades the performance of space–time adaptive processing (STAP), particularly in short-range clutter environments. In this paper, we introduce a knowledge-aided multi-dictionary block sparse Bayesian learning (KA-MDBSBL) algorithm to improve the clutter suppression performance. Using prior knowledge, the proposed algorithm designs multi-dictionary matrices for each training sample, rather than a single dictionary matrix for the cell under test (CUT). We take advantage of the identical clutter profile under each dictionary matrix. In the multi-dictionary case, we enforce shared sparsity in the clutter profiles. Additionally, we utilize the inherent block structure of the dictionary matrix to jointly recover clutter and noise power through a fast convergence learning framework. Subsequently, the clutter plus noise covariance matrix is reconstructed using precisely estimated clutter and noise power, along with the dictionary matrix corresponding to the CUT. Numerical simulations are included to demonstrate the effectiveness and superiority of the proposed algorithm.

Target detection based on generalized Bures–Wasserstein distance

Radar target detection with fewer echo pulses in non-Gaussian clutter background is a challenging problem. In this instance, the conventional detectors using coherent accumulation are not very satisfactory. In contrast, the matrix detector based on Riemannian manifolds has shown potential on this issue since the covariance matrix of radar echo data during one coherent processing interval(CPI) has a smooth manifold structure. The Affine Invariant (AI) Riemannian distance between the cell under test (CUT) and the reference cells has been used as a statistic to achieve improved detection performance. This paper uses the Bures–Wasserstein (BW) distance and Generalized Bures–Wasserstein (GBW) distance on Riemannian manifolds as test statistics of matrix detectors, and propose relevant target detection method. Maximizing the GBW distance is formulated as an optimization problem and is solved by the Riemannian trust-region (RTR) method to achieve enhanced discrimination for target detection. Our evaluation of simulated data and measured data show that the matrix detector based on GBW distance leads to a significant performance gain over existing methods.

Fast Heterogeneous Clutter Suppression Method Based on Improved Sparse Bayesian Learning

In order to deal with the problem space-time adaptive processing (STAP) performance degradation of an airborne phased array system caused by the serious shortage of independent and identical distributed (IID) training samples in the nonhomogeneous clutter environment, an improved direct data domain method based on sparse Bayesian learning is proposed in this paper, which only uses a single snapshot data of a cell under test (CUT) to suppress the clutter and has fast computational speed. Firstly, three hyper-parameters required to obtain the sparse solution are derived. Secondly, the comparative analysis of their iterative formulas is made, and the piecewise iteration of hyper-parameter that has an obvious influence on the computational complexity of obtaining sparse solution is presented. Lastly, with the approximate prior information of the target, the clutter sparse solution is given and its covariance matrix is effectively estimated to calculate the adaptive filter weight and realize the clutter suppression. Simulation results verify that the proposal can dramatically decrease the computational burden while keeping the superior heterogeneous clutter suppression performance.

Beam Scheduling for Early Warning With Distributed MIMO Radars

Distributed multiple-input multiple-output (MIMO) radars achieve long-range detection by steering and focusing the narrow beams of all transmit and receive antennas on a single point. This paper proposes a beam scheduling scheme based on the joint optimization of three components: arrangement of focal points, beam dwell time allocation of each focal point, and scanning order of focal points. The purpose is to enable distributed MIMO radars to provide early warning of incursions entering a broad surveillance region. To this end, a mathematical model is first developed to evaluate radar detection capability in a cell under test (CUT) over a scheduling period. By integrating all the CUTs within the region, the detection time required to reach a specified performance in terms of cumulative detection probability is then derived. On this basis, a beam scheduling strategy is devised, considering the maximum speed and minimum average radar cross-section constraints of targets to be detected. The main mechanism of the strategy is to minimize the detection time without sacrificing performance. To address the optimization problem of beam scheduling, we propose a two-stage method using a detection capability threshold as an extra optimization variable. In our method, the first stage is used to obtain optimal schemes for different given thresholds, and in the next stage, the optimal threshold is determined from these schemes. The simulation results show that the proposed algorithm is effective.

Space-Time Adaptive Processing Based on Modified Sparse Learning via Iterative Minimization for Conformal Array Radar.

Space-time adaptive processing (STAP) is a well-known technique for slow-moving target detection in the clutter spreading environment. For an airborne conformal array radar, conventional STAP methods are unable to provide good performance in suppressing clutter because of the geometry-induced range-dependent clutter, non-uniform spatial steering vector, and polarization sensitivity. In this paper, a knowledge aided STAP method based on sparse learning via iterative minimization (SLIM) combined with Laplace distribution is proposed to improve the STAP performance for a conformal array. The proposed method can avoid selecting the user parameter. the proposed method constructs a dictionary matrix that is composed of the space-time steering vector by using the prior knowledge of the range cell under test (CUT) distributed in clutter ridge. Then, the estimated sparse parameters and noise power can be used to calculate a relatively accurate clutter plus noise covariance matrix (CNCM). This method could achieve superior performance of clutter suppression for a conformal array. Simulation results demonstrate the effectiveness of this method.

Floating small target detection based on the dual-polarization cross-time-frequency distribution in sea clutter

In this paper, a polarization fusion detection method based on dual-polarization cross-time-frequency distribution is proposed to improve the detection performance compared with the original TF-feature-based detector in floating target detection in sea clutter background. Utilizing the received echoes information from the dual-polarization channels, time-frequency distributions (TFD) of radar returns from each polarization channel and the cross-time-frequency distribution (CTFD) of the two channels are computed. Weighted geometric average based on the signal-to-clutter ratio (SCR) is used to calculate a weighted fusion TFD based on the TFDs and CTFD from dual-polarization channels. To observe differences between sea clutter and target precisely, normalized time-frequency distributions (NTFD) of the cell under test (CUT) are calculated by the mean and variance of the fusion TFD computed from the reference range cells adjacent to the CUT. And the three existing features, the ridge integration (RI), the number of connected regions (NR) and the maximal size of connected regions (MS) are extracted from the NTFD and the convexhull learning algorithm is used to construct a polarization fusion detector in the feature space. Analyses of experimental results on the recognized IPIX database show that the proposed polarization fusion detector obtains superior detection performance compared to the original TF-feature-based detector and has competitive detection performance compared to other existing excellent feature-based detectors.

Robust Space–Time Joint Sparse Processing Method with Airborne Active Array for Severely Inhomogeneous Clutter Suppression

Due to clutter inhomogeneity, the clutter suppression ability of space–time adaptive processing (STAP) is usually constrained by the insufficient number of independent and identically distributed (IID) clutter training samples and, as a result, is sacrificed to achieve the demanded sample reduction. Moreover, since clutter heterogeneity is exacerbated in the real environment, the IID training sample size can be heavily reduced, leading to the deterioration in clutter suppression. To solve this problem, a novel robust space–time joint sparse processing method with airborne active array is proposed. This method has several outstanding advantages: (1) only the single snapshot cell under test (CUT) data is used for the superior clutter suppression performance; and (2) the proposed method completely removes the dependence of the system processing ability on IID training samples. In this paper, the signal model of uniform transmitting subarray diversity is first established to obtain the single snapshot echo observed CUT data. Then, with the matched reconstruction, the single snapshot data are equivalently converted into multi-frame echo data. Finally, a fast multi-frame echo data joint sparse Bayesian algorithm is used to achieve heterogeneous clutter suppression. Numerous experiments were performed to verify the advantages of the proposed method.

Modelling and Analysis of Constant False Alarm Rate Performance in Presence of Jamming Environments

A novel “Bernoulli experiment model” of constant false alarm rate (CFAR) is presented in order to analyze CFAR performance in jamming condition. In this model, target detection can be treated as a sequence of independent subevents, and the detection process equals to pick up target energy from an energy pool diluted with noise, interference, and jamming pulses. In a multiple-jammer case, each jammer contributes independently, and the content of the energy pool only relates to the corresponding jammer. Impacts of jammer factors, such as signal-to-interference ratio (SIR), jamming-to-interference ratio (JIR), the number of false targets in reference cells, and the number of false targets in a cell under test (CUT), are analyzed and compared in detail, and two jamming operation principles are deduced as an application. The deduction procedure and conclusions drawn from the model can also be utilized on similar occasions.

Detection of sea‐surface target of coastal defense radar based on Stacked Autoencoder (SAE) algorithm

In recent years, machine learning theory has set off a wave of research in the field of radar signal processing. In this study, a novel algorithm for sea-surface target detection based on a stacked autoencoder (SAE) is proposed, which has already been applied in the authors’ coastal defense radar system. In the proposed algorithm, the sea surface echo data are cut into a large number of two-dimensional (2-D) images through a sliding window, mapping the cell under test (CUT) and the 2-D images one by one and performing classification or detection from the perspective of 2-D signal processing. Experimental results of simulated data and real radar data show that the proposed algorithm based on the SAE has better target detection performance compared with the traditional cell averaging constant false alarm rate (CA-CFAR) algorithm. Besides, the proposed algorithm shows certain interference suppression ability in real data processing. As far as it is known, there is no public report on the detection of 2-D sea surface targets based on the SAE algorithm in coastal defense radar.

A generalised eigenvalue reweighting covariance matrix estimation algorithm for airborne STAP radar in complex environment

To improve the space-time adaptive processing (STAP) performance of airborne radar in complex environment, a generalised eigenvalue reweighting covariance matrix estimation algorithm called GERCM is proposed here. First, the interference plus noise (IPN) covariance matrix of cell under test (CUT) data is estimated by the selected target-free training samples around the CUT with the sample covariance matrix method. Then, with the component decompositions of the selected training samples and the assumption of approximately equal subspace, the IPN covariance matrix of CUT data is reformulated by the eigenvector matrix, eigenvalue matrix, and the eigenvalue reweighting vector. Subsequently, based on the modified covariance matching estimation criterion, the eigenvalue reweighting vector is estimated by solving the redesigned convex optimisation problem with the Lagrange dual method. Finally, the STAP weight vector is calculated to process the CUT data. The proposed algorithm can obtain a relatively accurate IPN covariance matrix of CUT data by sufficiently utilising the non-homogeneous training samples and can effectively protect the moving targets in CUT data, which can be applied to airborne radar with arbitrary array structure and antenna configuration. Simulation results and performance analyses based on the multi-channel airborne radar measurement data demonstrate the effectiveness of the proposed GERCM algorithm.

Sea Clutter Covariance Matrix Estimation and Its Application to Whitening Filter

The accurate estimation of clutter covariance matrix (CCM) is essential in designing a radar detector/filter to suppress sea clutter. This estimation might not be easily accomplished because of the scarcity of valid training vectors adjacent to the range cell under test (CUT). We propose a new CCM estimation algorithm that is derived by modeling time-series clutter returns into a clutter Doppler spectrum in the frequency domain and exploiting mutual independence among spectral components. To justify its excellence over the conventional sample covariance matrix (SCM) algorithm, we design two filters—a maximum signal-to-interference-plus-noise ratio (SINR)-based filter and a whitening filter—that use the estimated CCMs and compare their performance in a numerically simulated sea clutter scenario. Comparisons are made by showing the eigenvector spectra of the estimated CCMs and the frequency responses and outputs of the filters. Moreover, SINRs at the target Doppler bin are examined and compared with a theoretical, analytically derived SINR.

Covariance Matrix Whitening-Based Training Sample Selection Method for Airborne Radar

As training samples are not always target-free in space-time processing for airborne radar, the traditional methods usually use the sample covariance matrix (SCM) as the test covariance matrix (TCM) to censor contaminated training samples. However, the SCM cannot represent the property of the cell under test (CUT) accurately, resulting in low selection efficiency. To deal with this problem, this letter proposes a novel training sample selection method based on covariance matrix whitening. Specifically, we utilize the reconstructed subaperture's clutter covariance matrix (RSCCM) of the CUT as the TCM. The RSCCM is only determined by the CUT and can characterize the CUT directly. Then, we use the RSCCM to whiten the subaperture's covariance matrix of the training sample. A criterion for selecting the training samples is derived based on the maximum eigenvalue of the whitened subaperture's covariance matrix, which is related to the energy of the outliers and more stable than the statistic of the generalized inner product method. Simulations are conducted to evaluate the performance of the proposed method.

A Knowledge-Based Auxiliary Channel STAP for Target Detection in Shipborne HFSWR

The broadened first-order sea clutter in shipborne high frequency surface wave radar (HFSWR), which will mask the targets with low radial velocity, is a kind of classical space–time coupled clutter. Space–time adaptive processing (STAP) has been proven to be an effective clutter suppression algorithm for space-time coupled clutter. To further improve the efficiency of clutter suppression, a STAP method based on a generalized sidelobe canceller (GSC) structure, named as the auxiliary channel STAP, was introduced into shipborne HFSWR. To obtain precise clutter information for the clutter covariance matrix (CCM) estimation, an approach based on the prior knowledge to auxiliary channel selection is proposed. Auxiliary channels are selected along the clutter ridge of the first-order sea clutter, whose distribution can be determined by the system parameters and regarded as pre-knowledge. To deal with the heterogeneity of the spreading first-order sea clutter, an innovative training samples selection approach according to the Riemannian distance is presented. The range cells that had shorter Riemannian distances to the cell under test (CUT) were chosen as training samples. Experimental results with measured data verified the effectiveness of the proposed algorithm, and the comparison with the existing clutter suppression algorithms showed the superiority of the algorithm.

Short-range clutter suppression method combining oblique projection and interpolation in airborne CFA radar

The airborne conformai array (CFA) radar's clutter ridges are range-modulated, which result in a bias in the estimation of the clutter covariance matrix (CCM) of the cell under test (CUT), further, reducing the clutter suppression performance of the airborne CFA radar. The clutter ridges can be effectively compensated by the space-time separation interpolation (STS-INT) method, which costs less computation than the space-time interpolation (STINT) method, but the performance of interpolation algorithms is seriously affected by the short-range clutter, especially near the platform height. Location distributions of CFA are free, which yields serious impact that range spaces of steering vector matrices are non-orthogonal complement and even no longer disjoint. Further, a new method is proposed that the short-range clutter is pre-processed by oblique projection with the intersected range spaces (OPIRS), and then clutter data after being pre-processed are compensated to the desired range bin through the STSINT method. The OPIRS also has good compatibility and can be used in combination with many existing methods. At the same time, oblique projectors of OPIRS can be obtained in advance, so the proposed method has almost the same computational load as the traditional compensation method. In addition, the proposed method can perform well when the channel error exists. Computer simulation results verify the effectiveness of the proposed method.

Polarimetric detection of maritime floating small target based on the Complex-valued Entropy Rate Bound Minimization

Detection of sea-surface small floating targets in maritime high-resolution surveillance radar has been an active area of research in recent years. In this paper, we propose a new detector based on a complex-valued independent component analysis (cICA) algorithm proposed by Geng-Shen Fu et al. called complex entropy rate bound minimization (CERBM), to look for targets in polarimetric radars. It uses received time series at cell under test (CUT) with different polarizations as distinct mixtures. The proposed detector can exploit all information of polarimetric radar for an accurate detection. It does separation on the mixtures using CERBM which results in two output sources, i.e. clutter and target. Finally, the target is detected using estimation of the parameters of K-distribution for outputted sources. Our experiments on the recognized IPIX radar database show that the proposed detector obtains better detection performance in comparison to the newly proposed detectors. The robustness of the detector is also investigated by experiment in either low and high sea state which shows its appropriate results.

CFAR Detection Based on Adaptive Tight Frame and Weighted Group-Sparsity Regularization for OTHR

In high-frequency over-the-horizon radar (OTHR), it is a challenging work to detect targets in the nonhomogeneous range-Doppler (RD) map with multitarget interference and sharp/smooth clutter edges. The intensity transition of the clutter edge may be sharp or smooth due to the coexistence of atmospheric noise, sea clutter, and ionospheric clutter in OTHR. The analysis of the RD map shows the spatial correlation among neighboring cell-under-test (CUT) that varies from clutter to clutter. This article proposes an algorithm that uses the spatial relationship to estimate the statistical distribution parameters of every CUT by the adaptive tight frame and the weighted group-sparsity regularization. In the proposed algorithm, the spatial relationship is formulated mathematically by regularization terms and combined with the log-likelihood function of CUTs to construct the objective function. The proposed algorithm is verified by the simulated data and real RD maps collected from both trial sky-wave and surface-wave OTHRs in which it shows robust and improved detection.

A Bayesian CFAR detector for interference control in Weibull clutter

In modern radar system, constant false alarm rate (CFAR) detection is a key technique for automatic target detection in unknown and nonstationary environment. Recently, a novel Bayesian methodology has been introduced for the design of CFAR detector. This method uses Bayesian predictive inference approach to produce a predictive density of the cell under test (CUT) conditioned on the reference samples. The probability of false alarm (Pfa) can then be calculated by integrating this density. As a result, a Bayesian CFAR detector is produced. In this paper, we propose a Bayesian CFAR detector for Weibull clutter under the assumption that the shape parameter is known and extend the Weibull CFAR detector for interference control where the number of interfering targets is determined or not. The simulation results verify the immunity of the proposed detector to the presence of interference.

Performance Evaluation of a Real-Time Seismic Detection System Based on CFAR Detectors

In this research work, we present a novel application specific Ordered cell averaging-CFAR (OCA-CFAR) detector for anthropogenic seismic events. We investigate the use of geophones and real-time hardware for the detection of moving targets such as vehicle, human footsteps and activities such as hammering on the ground. We present here energy assisted variants of Constant False Alarm Rate (CFAR) detector implemented on a real-time embedded platform to obtain detection cues of the ground seismic source. The OCA-CFAR algorithm has been modified in terms of window length and position of Cell Under Test (CUT), suitably adapted to the nature of seismic events engendered from moving vehicles and humans. The proposed detector has been compared with the popularly known variants such as Cell Averaging-CFAR, Least Of-CFAR, Greatest Of-CFAR and Ordered Statistics-CFAR for probabilities of false alarm ranging from 1e-1 to 1e-5. The proposed method shows an increased detection rate with minimized false alarms on the field trials and a dataset containing the seismic signature of human activities and some of civilian vehicles.

Robust CFAR Detection for Multiple Targets in K-Distributed Sea Clutter Based on Machine Learning

For K-distributed sea clutter, a constant false alarm rate (CFAR) is crucial as a desired property for automatic target detection in an unknown and non-stationary background. In multiple-target scenarios, the target masking effect reduces the detection performance of CFAR detectors evidently. A machine learning based processor, associating the artificial neural network (ANN) and a clustering algorithm of density-based spatial clustering of applications with noise (DBSCAN), namely, DBSCAN-CFAR, is proposed herein to address this issue. ANN is trained with a symmetrical structure to estimate the shape parameter of background clutter, whereas DBSCAN is devoted to excluding interference targets and sea spikes as outliers in the leading and lagging windows that are symmetrical about the cell under test (CUT). Simulation results verified that the ANN-based method provides the optimal parameter estimation results in the range of 0.1 to 30, which facilitates the control of actual false alarm probability. The effectiveness and robustness of DBSCAN-CFAR are also confirmed by the comparisons of conventional CFAR processors in different clutter conditions, comprised of varying target numbers, shape parameters, and false alarm probabilities. Although the proposed ANN-based DBSCAN-CFAR processor incurs more elapsed time, it achieves superior CFAR performance without a prior knowledge on the number and distribution of interference targets.

A novel KA-STAP method based on Mahalanobis distance metric learning

The estimation accuracy of the clutter covariance matrix will be degraded when using the heterogeneous and contaminated training samples. To improve the performance of clutter suppression in heterogeneous environments, a novel knowledge aided space-time adaptive processing method is proposed in this paper, which is based on Mahalanobis distance metric learning (MML-KA STAP). Exploiting the difference of the Mahalanobis distances between the actual echo data and the synthesized data, the data is divided into the pure part and non-pure part. Taking the pure data as training samples, the interference covariance matrix of the cell under test (CUT) is reconstructed. Finally, by learning the Mahalanobis distance function between the CUT and training samples, the proper training samples can be chosen and reweighted to construct the interference covariance matrix. When the termination condition of iteration is satisfied, a relatively accurate interference covariance matrix can be estimated. The MML-KA method avoids the effect of target self-nulling and has superior performance in heterogeneous environments. Using the measured data, numerical simulations validate the effectiveness of the proposed method.