non-Gaussian Clutter Research Articles

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.

Clutter Covariance Matrix Estimation for Radar Adaptive Detection Based on a Complex-Valued Convolutional Neural Network

In this paper, we address the problem of covariance matrix estimation for radar adaptive detection under non-Gaussian clutter. Traditional model-based estimators may suffer from performance loss due to the mismatch between real data and assumed models. Therefore, we resort to a data-driven deep-learning method and propose a covariance matrix estimation method based on a complex-valued convolutional neural network (CV-CNN). Moreover, a real-valued (RV) network with the same framework as the proposed CV network is also constructed to serve as a natural competitor. The obtained clutter covariance matrix estimation based on the network is applied to the adaptive normalized matched filter (ANMF) detector for performance assessment. The detection results via both simulated and real sea clutter illustrate that the estimator based on CV-CNN outperforms other traditional model-based estimators as well as its RV competitor in terms of probability of detection (PD).

Rao test of polarimetric detection for targets with energy spillover in non-Gaussian clutter

In this paper, we address the problem of polarimetric detection for targets with energy spillover in non-Gaussian clutter. The polarization diversity and spillover of target energy to consecutive range bins are jointly exploited to enhance the performance of target detection. Two adaptive detectors are designed according to the Rao test, as well as its two-step implementation, i.e., 2S-Rao test. It is shown that the 2S-Rao test detector coincides with the existing generalized likelihood ratio test (GLRT) detector, whereas the Rao test detector is new, and outperforms the existing detectors in probability of detection. Experiments based on both simulated and real data illustrate the superiority of the proposed detector.

Dual-Polarimetric Persymmetric Adaptive Subspace Detector for Range-Spread Targets in Heavy-Tailed Non-Gaussian Clutter

To solve the problem of range-spread targets detection in non-Gaussian clutter for dual-polarimetric radar systems, a novel dual-polarimetric persymmetric detector based on the two-step generalized likelihood ratio test (GLRT) is proposed. Firstly, the target signal is modeled as a multi-rank subspace signal, and the clutter is modeled as a compound Gaussian model with deterministic unknown texture. Then, by taking polarimetric and persymmetric characteristics of the clutter into account, the detection performance of the proposed detector is obviously improved. Finally, through the verification via both simulated data and measured data, it is shown that the proposed detector poses better detection performance in comparison with the existing non-polarimetric detectors. Due to the complexity of the detector form, the analytical expression of false alarm probability cannot be derived. Therefore, we verified the constant false alarm ratio (CFAR) characteristic of the proposed detector through simulation experiment.

Adaptive Range and Doppler Distributed Target Detection in Non-Gaussian Clutter

Adaptive Range and Doppler Distributed Target Detection in Non-Gaussian Clutter

Robust CFAR Detector Based on KLQ Estimator for Multiple-Target Scenario

The order statistic (OS) constant false alarm rate (CFAR) detector is designed from a perspective of quantile estimation and uses the sample quantile (SQ) estimator to estimate background level. Following this idea, we find a more efficient quantile estimator, i.e. Kaigh-Lachenbruch quantile (KLQ) estimator, to construct a robust CFAR detector, which is referred to as KLQ-CFAR. We prove that the KLQ estimator is an asymptotic unbiased estimator to the quantile function and derive the asymptotic variance of KLQ estimator in Exponential case. It is shown that the KLQ estimator has more efficient estimation efficiency than SQ estimator. Subsequently, we explore the performance of KLQ-CFAR in Exponential clutter. In homogeneous background, the KLQ-CFAR conquers the shortcoming of large detection loss of OS-CFAR, and exhibits comparable performance with trimmed mean (TM) CFAR. The superiority of KLQ-CFAR is also reflected in multiple-target scenario, especially in the case where the number of interferences exceeds the preset parameters of KLQ- and TM-CFAR. In this case, the detection performance and false alarm control ability of KLQ-CFAR have significant improvement compared with TM-CFAR. Then, we extend the KLQ-CFAR from Exponential background to non-Gaussian clutter via transformation approach, and obtain the transformed KLQ (TKLQ) CFAR. We take Weibull clutter as a specific example. It is found that the behavior of TKLQ-CFAR in Weibull background is very similar to that of the KLQ-CFAR in Exponential clutter, but the difference lies in that the performance of TKLQ-CFAR is related to Weibull shape parameter. The TKLQ-CFAR tends to have better detection performance with the increase of Weibull shape parameter. Finally, the validity of TKLQ-CFAR is verified in skywave over-the-horizon radar data.

Modeling and Parameter Estimation of Radar Sea-Clutter with Trimodal Gamma Population

Real radar data often consist of a mixture of Gaussian and non-Gaussian clutter. Such a situation creates one or more inflexion points in the curve of the empirical cumulative distributed function (CDF). In order to obtain an accurate fit with sea reverberation data, we propose, in this paper, a trimodal gamma disturbance model and two parameter estimators. The non-linear least-squares (NLS) fit approach is used to avoid computational issues associated with the maximum likelihood estimator (MLE) and moments-based estimator for parameters of the mixture model. For this purpose, a combination of moment fit and complementary CDF (CCDF) NLS fit methods is proposed. The simplex minimization algorithm is used to simultaneously obtain all parameters of the model. In the case of a single gamma probability density function, a zlog(z) method is derived. Firstly, simulated life tests based on a gamma population with different shape parameter values are worked out. Then, numerical illustrations show that both MLE and zlog(z) methods produce closer results. The proposed trimodal gamma distribution with moments NLS fit and CCDF NLS fit estimators is validated to be in qualitative agreement with different cell resolutions of the available IPIX database.

CRLBs for Location and Velocity Estimation for MIMO Radars in CES-Distributed Clutter

In this article, we investigate the problem of jointly estimating target location and velocity for widely separated multiple-input multiple-output (MIMO) radar operating in correlated non-Gaussian clutter, modeled by a complex elliptically symmetric (CES) distribution. More specifically, we derive the Cramér–Rao lower bounds (CRLBs) when the target is modeled by the Swerling 0 model and the clutter is complex t-distributed. We thoroughly analyze the impact of the clutter correlation and spikiness to provide accurate performance estimation. Index terms—Cramér–Rao lower bounds (CRLBs), MIMO radar, location and velocity estimation, performance analysis, complex elliptically symmetric (CES) distributed, and complex t-distribution.

GLRT-Based Polarimetric Detection in Compound-Gaussian Sea Clutter With Inverse-Gaussian Texture

This letter presents the derivation of the generalized likelihood ratio test (GLRT)-based polarimetric detector in the non-Gaussian clutter. We model the non-Gaussian sea clutter as compound-Gaussian distribution with inverse-Gaussian texture (IG-CG), which has better goodness-of-fit for the high-resolution sea clutter. Based on the two-step GLRT criterion, we develop the test statistic of the proposed detector by assuming the texture component is known in the first step. In the second step, with the texture of the secondary data estimated as the power of the clutter, we insert the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> estimate (MAPE) of the texture of the primary data into the test statistic to achieve the fully adaptive detection. Furthermore, the model-based polarimetric detector, which exploits the independence between the co-polarized and the cross-polarized component, is derived. Finally, we conduct experiments with simulated clutter and real sea clutter to evaluate the performance of the proposed detector. The simulation results verify that the proposed detectors have better detection performance and the MAPE under different hypotheses leads to different levels of robustness to the mismatched signal.

Radar system simulation and non-Gaussian mathematical model under virtual reality technology

Abstract The characteristics of non-Gaussian clutter in radar systems are different from standard waveforms. To fully filter to achieve the accuracy of radar detection, the paper developed a radar simulation system based on virtual reality technology. The article uses a non-Gaussian mathematical model to simulate and collect the clutter generated by the system and realise the generation of data sequence according to the power spectrum. The research results show that the radar cross-section modelling, target recognition, anti-recognition and data fusion technology of visible targets can all be well applied in this system.

Simulation and comparison of distributed target detectors in compound Gaussian background

In the non Gaussian background modelled by compound Gaussian distribution, a variety of distributed target detectors are addressed. Firstly, the detection statistics of different detectors are given. Then, the detection performance of five detectors is compared when the non Gaussian clutter covariance matrix is known. Secondly, when the non Gaussian clutter covariance matrix is unknown, a two-step architecture is adopted. Based on the same estimation method for non-Gaussian clutter covariance matrix structure, seven adaptive distributed target detectors are introduced and compared. Finally, through comparative analyses, the applicable conditions and application range of different detectors are summarized, which provide a theoretical reference for the practical application of radar target detection.

Knowledge-aided covariance estimation and radar adaptive detection

We address the covariance matrix estimation problem for radar adaptive detection in a non-Gaussian clutter environment. We first propose an estimation method based on α log-determinant divergence, which estimates the true covariance accurately by solving the geometric mean of the sample covariance matrix (SCM). Since the estimation performance would be seriously degraded when the number of secondary data is insufficient, a knowledge-aided method is then proposed. Under the similarity constraint between the a priori covariance and the true one, a closed form expression is derived by minimizing the α log-determinant divergence between the real covariance and the SCM. Simulation results verify the accuracy of the proposed algorithms in covariance estimation and superiority in target adaptive detection.

Kernel Minimum Error Entropy Based Estimator for MIMO Radar in Non-Gaussian Clutter

In this paper, a kernel minimum error entropy (KMEE) based estimator is proposed for the estimation of multiple targets’ direction of departure (DOD), the direction of arrival (DOA), and the Doppler shift with multiple input multiple output radar in the presence of non-Gaussian clutter. Most existing estimation approaches are based on optimization of a complex cost function which often leads to a sub-optimum solution. Therefore, for the accurate estimation of DOD, DOA and Doppler shift, an efficient, kernel adaptive filter (KAF) based estimation approach is proposed. The proposed estimator utilizes the minimum error entropy (MEE) criterion and minimizes the error entropy function. The MEE, being an information-theoretic criterion, optimizes the higher-order statistics of error and thus makes the proposed estimator robust against the effects of outliers like clutter. The KMEE based estimator without any sparsification suffers from a linear increase in computational complexity. Thus, subsequently, the computational complexity of the proposed KMEE based estimator is reduced by incorporation of novelty criterion (NC) based sparsification technique, and the resulting estimator is called KMEE-NC. The performance of the proposed KMEE-NC based estimator is compared with the recently introduced sparse estimators based on kernel maximum correntropy criterion, and kernel minimum mean square error criterion. Additionally, KMEE-NC based estimator is also compared with other existing conventional estimators. Further, for assessing the accuracy of the proposed estimator, the modified Cramer-Rao lower bound is derived using the modified Fisher information matrix.

Invariance Theory for Adaptive Detection in Non-Gaussian Clutter

This paper studies the problem of detecting range-spread targets in (possibly non-Gaussian) clutter whose joint distribution belongs to a very general family of complex matrix-variate elliptically contoured distributions. Within the family, we explore invariance with respect to both the distributional type and relevant parameters. Several groups are used to describe these invariance mechanisms, and a relationship is revealed between the group invariance and the constant false alarm rate (CFAR) properties in terms of model parameters, the generator function, or both. We then build a maximal invariant framework for the detection problem. This involves deriving the corresponding maximal invariants as well as their statistical characterizations. Using these results, we put forward several maximal invariant detectors, all of which are fully CFAR in that their false alarm rates are completely independent of the underlying clutter distribution. Numerical results show that all the proposed fully CFAR detectors are effective, and for the considered simulation setup, one of them outperforms the others and several existing ones.

Range and Velocity Estimation Using Kernel Maximum Correntropy Based Nonlinear Estimators in Non-Gaussian Clutter

In this article, we propose kernel maximum correntropy based nonlinear estimators for range and velocity estimation in non-Gaussian clutter and system nonlinearity. The proposed estimators are analyzed for linear frequency modulated and stepped frequency radar systems. Additionally, an adaptive update equation is derived for optimization of the kernel width, which further lowers the dictionary size and the variance of the proposed estimators. For performance evaluation of the proposed estimators, an expression is derived for the Cramer-Rao lower bound using a modified Fisher information matrix.

Knowledge-Aided Structured Covariance Matrix Estimator Applied for Radar Sensor Signal Detection.

This study deals with the problem of covariance matrix estimation for radar sensor signal detection applications with insufficient secondary data in non-Gaussian clutter. According to the Euclidean mean, the authors combined an available prior covariance matrix with the persymmetric structure covariance estimator, symmetric structure covariance estimator, and Toeplitz structure covariance estimator, respectively, to derive three knowledge-aided structured covariance estimators. At the analysis stage, the authors assess the performance of the proposed estimators in estimation accuracy and detection probability. The analysis is conducted both on the simulated data and real sea clutter data collected by the IPIX radar sensor system. The results show that the knowledge-aided Toeplitz structure covariance estimator (KA-T) has the best performance both in estimation and detection, and the knowledge-aided persymmetric structure covariance estimator (KA-P) has similar performance with the knowledge-aided symmetric structure covariance estimator (KA-S). Moreover, compared with existing knowledge-aided estimator, the proposed estimators can obtain better performance when secondary data are insufficient.

Метод адаптивного нелинейного подавления негауссовских помех в когерентном полосовом тракте приемника

This article suggests a method of amplitude adaptive nonlinear suppression of non-Gaussian cluter in the coherent band pass of the receiver, which retains its effectiveness in any distribution of the clutter envelope and in any signal-to-noise ratio. At the same time, for “low level” signals, as compared to clutter, the algorithms that implement this method are not inferior to known asymptotically optimal algorithms, and the proposed algorithms do not introduce losses for “high level” signals. The proposed method also ensures a stable probability of false alarm. A description of this method is given, as well as a study of its effectiveness by modeling in the MathCAD environment in the task of detecting a deterministic signal against a background of non-Gaussian clutter in the form of reflections from the sea surface. When modeling such clutter, the K-distribution is used and the internal noise of the receiver is taken into account. Research shows that the proposed method really has these advantages.

GLRT detector based on knowledge aided covariance estimation in compound Gaussian environment

Abstract In order to alleviate the effect of the limited secondary data in the non-Gaussian clutter, a knowledge aided adaptive detector is proposed. The covariance matrix estimation is modeled as a general linear combination of prior covariance matrix and sample covariance matrix. Within this consideration, we obtain an adaptive detector based on the generalized likelihood ratio test. Experimental results on simulation and real data demonstrate that the proposed detector achieves better performance than the existing one-step GLRT (1S-GLRT) detectors when the secondary data are insufficient.

Radar Detection of Fluctuating Targets under Heavy-Tailed Clutter Using Track-Before-Detect.

This paper considers the detection of fluctuating targets in heavy-tailed clutter through the use of dynamic programming based on track-before-detect (DP–TBD) in radar systems. The clutter is modeled in terms of K-distribution, which can be widely used to describe non-Gaussian clutter received from high-resolution radars and radars working at small grazing angles. Swerling type 1 is considered to describe the target fluctuation between scans. Conventional TBD techniques suffer from significant performance loss in heavy-tailed environments due to the more frequent occurrences of target-like outliers. In this paper, we resort to a DP–TBD algorithm based on prior information, which can enhance the detection performance by using the environment and target fluctuating information during the integration process of TBD. Under non-Gaussian background, the expressions of the likelihood ratio merit function for Swerling type 1 targets are derived first. However, the closed-form of the merit function is difficult to obtain. In order to reduce the complexity of evaluating the merit function and the computational load, an efficient approximation method as well as a two-stage detection approach is proposed and used in the integration process. Finally, several numerical simulations of the new strategy and the comparisons are presented to verify that the proposed algorithm can improve the detection performance, especially for fluctuating targets in heavy-tailed clutter.

Polarimetric detection and range estimation for a point‐like target in non‐Gaussian clutter

In this study, a method is presented to deal with the problem of polarimetric detection of a point-like target with energy spillover in non-Gaussian clutter. Consecutive range samples are employed to enhance the detection and range estimation performances. Within the framework of the generalised likelihood ratio test, the decision statistic of the proposed polarimetric detector involves the textures and the covariance structure of the clutter, the target return, and the residual delay. Suitable estimates of these parameters are plugged into the decision statistic. Simulations show that, the proposed detector achieves a considerable performance improvement over the polarimetric adaptive detectors that ignore either the non-Gaussian clutter or the spillover, in terms of both the probability of detection and the root mean squared error of range estimation.