Weibull Clutter Research Articles

Two-sided automatic censoring CFAR detector based on the interquartile range in a heterogeneous Weibull clutter

As it is well known, CFAR (Constant False Alarm Rate) detectors are intended to regulate the PFA (Probability of False Alarm) in the presence of a clutter background whose mean power is unknown and/or varying. In heterogeneous clutter backgrounds, CFAR detectors false alarm control and detection efficiency rely upon their ability of clutter edge resilience and/or interfering targets rejection. Aiming to improve radar signal detection in a heterogeneous Weibull clutter, the two-sided automatic censoring IQR-CFAR (InterQuartile Range-CFAR) detector is introduced in this paper. This new detector first resorts to a logarithmic amplifier to dynamically achieve a Weibull to Gumbel transformation of the reference samples. Then, working on a cell-by-cell basis, the CFCR (Constant False Censoring Rate) algorithm retains and rejects samples based on the IQR within the reference window. Upon removal of the unwanted samples, the remaining data set is utilized to estimate the unknown biparametric linear detection threshold through the BLU (Best Linear Unbiased) estimates of the Gumbel distribution’s location and scale parameters. Extensive MC (Monte Carlo) simulations with both simulated and real data show that the suggested detector outperforms its challenging automatic censoring CFAR detectors found in the literature.

Constant false alarm rate detection method in mixed Weibull distribution sea clutter

In maritime surveillance, sea clutter represents a major obstacle to target detection accuracy due to missed or false alarms. Several methods have been proposed to find the most efficient. However, most of these methods have only been tested with simulated data, and their applicability and success in a real environment cannot be guaranteed. This work proposes constant false alarm rate (CFAR) detection techniques tailored to mixed Weibull-distributed sea clutter. The mixed Weibull distribution was used to model a mixture of Gaussian and non-Gaussian data. For CFAR detection in mixed Weibull distribution and Weibull clutter, the log t CFAR (logt-CFAR), Weber Haykin CFAR (WHCFAR), Geometric Mean Order Statistic CFAR (GMOS-CFAR), Trimmed Mean Order Statistic CFAR (TMOS-CFAR), Inclusion/Exclusion CFAR (IE-CFAR), and Weber Haykin Order Statistic CFAR (WHOS-CFAR) algorithms were performed. Both synthetic and actual ice multi-parameter imaging X-band (IPIX) radar data were used for experimental verification of this distribution. Simulation studies demonstrated that the proposed detectors maintain the CFAR property in Weibull-distributed clutter, making them effective in controlled scenarios, and confirming how better is the detection performance compared to other detection methods. This research bridges a critical gap in radar signal processing by significantly improving the detection of targets in challenging clutter environments.

Multi-Target CFAR Detection Method Based on Neural Network for HF Hybrid Sky-Surface Wave Radar in Weibull Clutter Background

Multi-Target CFAR Detection Method Based on Neural Network for HF Hybrid Sky-Surface Wave Radar in Weibull Clutter Background

Multi-Target CFAR Detection Method for HF Over-The-Horizon Radar Based on Target Sparse Constraint in Weibull Clutter Background

High frequency radar has a wide monitoring range and low range resolution. It may contain multiple targets or outlier interference phenomena in different clutter regions of the range–Doppler (RD) spectrum in detected background. The key to the performance of target detection in multi target backgrounds is the ability to determine the attributes of targets or outliers. Our previous research shows that the number of targets belongs to an absolute minority compared to the number of background units. In this paper, we propose a new method for multi-target detection building on the ordered statistics constant false alarm detector (OS-CFAR). The new method fully utilizes the sparse characteristics of the target and uses the idea of introducing regularization processing to eliminate interfering targets, and obtain an estimate of shape parameters for target detection. To further improve the performance of the algorithm, a correction method is proposed for the inaccurate selection of the k value. Upon estimating the distribution parameters, the detection threshold is calculated, and the target’s constant false alarm detection is completed. Simulation and measured data show that our algorithm can effectively counter the interference of multiple targets and maintain a constant false alarm characteristic under different conditions, providing a reliable target detection method.

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.

On Maximum Likelihood Quantile Matching CFAR Detection in Weibull Clutter and Multiple Rayleigh Target Situations: A Comparison

On Maximum Likelihood Quantile Matching CFAR Detection in Weibull Clutter and Multiple Rayleigh Target Situations: A Comparison

A Robust Variability Index CFAR Detector for Weibull Background

The Weibull distribution is commonly used for clutter modeling as it can provide a good fit to the experimental data over a wide range of conditions, and as such there is considerable attention to the development of constant false alarm rate (CFAR) detectors under such a clutter model assumption. The detection backgrounds of some radar systems are nonhomogeneous, which is a challenging task for CFAR detection. The variability index CFAR (VI-CFAR) detector is proposed for the nonhomogeneous Gaussian clutter in the literature. However, it might increase the false alarm rate significantly in the Weibull clutter due to the target-like clutter samples, and its performance degrades in the nonhomogeneous clutter with the presence of interfering targets at both sides of the cell under test. To address these problems, we propose a robust variability index CFAR detector for the Weibull background (RWVI-CFAR) with known shape parameters in this paper. In the RWVI-CFAR, we extend the VI-CFAR to the Weibull clutter and design an automatic outlier censoring maximum likelihood CFAR (AOCML-CFAR) strategy to improve the detection performance in multiple target situations. The proposed AOCML-CFAR strategy exploits the sparsity of interfering targets to censor the outliers adaptively. By selecting the AOCML-CFAR strategy, the anti-interference capability of the RWVI-CFAR is significantly improved. Simulated and experimental results show the favorable and robust performance of the RWVI-CFAR in the Weibull background.

Square-Law Detection of Exponential Targets in Weibull-Distributed Ground Clutter

Modern radar systems use square-law detectors to search and track fluctuating targets embedded in Weibull-distributed ground clutter. However, the theoretical performance analysis of square-law detectors in the presence of Weibull clutter leads to cumbersome mathematical formulations. Some studies have circumvented this problem by using approximations or mathematical artifacts to simplify calculations. In this work, we derive a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closed-form</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">exact</i> expression for the probability of detection (PD) of a square-law detector in the presence of exponential targets and Weibull-distributed ground clutter, given in terms of the Fox H-function. Unlike previous studies, no approximations nor simplifying assumptions are made throughout our analysis. Furthermore, we derive a fast convergent series for the referred PD by exploiting the orthogonal selection of poles in Cauchy’s residue theorem. In passing, we also obtain closed-form solutions and series representations for the probability density function and the cumulative distribution function of the sum statistics that govern the output of a square-law detector. Numerical results and Monte Carlo simulations corroborate the validity of our expressions.

Radar CFAR detection for multiple-targets situations for Weibull and log-normal distributed clutter

In the presence of Weibull clutter, the development of sliding window detection processes, based on scale and power invariant distributions, has been extensively examined. This involves the selection of two functions labeled as scale-invariant and secondary CRP (clutter range profile) functions. However, due to the presence of outliers, existing CFAR (constant false alarm rate) algorithms show remarkable CFAR losses. We resort in this work to the practice of a suitable choice of these two functions in order to have a new decision rule with immunity against interfering targets. To do this, a quadruple-order statistics-based CFAR detection algorithm with different four-order statistics are proposed in the presence of log-normal and Weibull clutter disturbances. Via Monte Carlo simulations, the analysis of the false alarm regulation of the proposed detector is studied showing its robustness with respect to clutter parameters. Moreover, for comparison purposes with existing CFAR algorithms, simulated results indicate that lowest CFAR losses can be obtained by the proposed quadruple-order statistics named WHWH-CFAR (Weber–Haykin-Weber–Haykin) in the presence of strong interfering targets. IPIX real data are also performed to test the validity of the proposed detector.

A robust constant false alarm rate detector based on the Bayesian estimator for the non-homogeneous Weibull Clutter in HFSWR

Target detection is a challenging problem in the complex detection environment of high-frequency surface wave radar (HFSWR). Due to the existence of various clutter and interferences, the detection environment in HFSWR is highly non-homogeneous with sharp/smooth clutter edges and multiple interfering targets. In this paper, we propose an effective detector for the non-homogeneous Weibull clutter in HFSWR with the use of prior information on the environmental context. Considering the spatial information of distribution parameters among neighboring cells and sparse information of interfering targets, the proposed method uses the Bayesian method to estimate distribution parameters and designs an objective function, which is composed of the data fidelity term, block matching 3-D frames and a sparsity regularization term. With the estimates of distribution parameters, the detection threshold is calculated accordingly and the presence of the target cell is decided. By minimizing the proposed model, the proposed method provides robust and accurate estimates of distribution parameters and can achieve the root-mean-squared error less than 0.12 in the simulated detection scenarios. Simulation and experimental results from a real HFSWR system are given to demonstrate the effectiveness of the proposed detector.

Detection of Range-Spread Target in Spatially Correlated Weibull Clutter Based on AR Spectral Estimation

Detection of Range-Spread Target in Spatially Correlated Weibull Clutter Based on AR Spectral Estimation

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.

Radar CFAR detection in Weibull clutter based on zlog(z) estimator

ABSTRACTIn this paper, the zlog(z) based estimator for constant false alarm rate (CFAR) detection in Weibull clutter is proposed. This estimation method is obtained in terms of the digamma function where the estimates of the shape parameter are determined by the interpolation tool. The non-integer order moments estimator (NIOME) is also given and coincides the zlog(z) estimation results for low values of the moment’s fractional order. Via simulated data, it is shown that the CFAR detection performances based on the zlog(z) estimator have almost similar results as well as the existing maximum likelihood (ML) CFAR detector, but with low time-consuming which is very important in real-time applications.

Optimization of Clutter Simulation Based on GPU

Weibull clutter is used as an example in this paper. Based on the serial parallel analysis of Zero-memory non-linear transformation's Weibull distributed clutter algorithm, fine-grained optimization is performed. The fine-grained part uses the cuBLAS library to optimize the performance of convolution calculations. Compared with CUDA shared memory convolution method and GPU parallel matrix multiplication convolution method, its computational performance can be significantly improved under a large amount of data. Simulation results show that the Zero-memory non-linear transformation's Weibull distributed clutter simulation method is optimized and accelerated. The real-time performance of clutter data is significantly improved and its acceleration effect will be better as the amount of clutter data increases. It turns out that through fine-grained optimization, the performance of convolution calculations with large amounts of data is improved.

Binary Integration Performance Analysis of CA Family of CFAR Strategies in Homogeneous Weibull Clutter

Binary Integration Performance Analysis of CA Family of CFAR Strategies in Homogeneous Weibull Clutter

Constant false alarm rate detection based on estimating statistical distribution of non‐homogeneous sea clutter in sky‐wave over‐the‐horizon radar

In sky-wave over-the-horizon radar (OTHR), there are some difficulties to efficiently detect targets in the non-homogeneous sea clutter by using conventional constant false alarm rate detectors. The amplitude of the clutter is supposed to follow the Weibull distribution in OTHR. Moreover, the characteristic of the clutter with a continuous region distribution in the range-Doppler (RD) map suggests that there exist the spatial relationship between neighbouring cells. The authors propose a rigorous algorithm to incorporate these relationships and the regularisation of interferences into the estimation of the shape parameter and scale parameter for every cell under test. This algorithm is mainly based on the consideration that the improvement of detection performance could be carried out by properly utilising the spatial information between neighbouring cells in the non-homogeneous Weibull clutter. Then, the adaptive detection threshold is calculated by the estimated parameters. The validity and effectiveness of the proposed algorithm are verified by simulations and the experiments in the real RD maps collected from an experimental sky-wave OTHR system.

Performance comparison of mean-level CFAR detectors in homogeneous and non-homogeneous Weibull clutter for MIMO radars

In this paper, we analyze and compare the performance of the CA-CFAR, GO-CFAR and the SO-CFAR detectors in homogeneous and non-homogeneous Weibull background with known shape parameter for Multi-Input Multi-Output radars with widely separated antennas. The non-homogeneity is represented by the presence of interfering targets and a clutter edge in the reference window. We derive closed-form expressions of the probability of false alarm of the three detectors in homogeneous environment. Detector performance in non-homogeneous environment is investigated by means of Monte Carlo simulations. The numerical results show that the best performance is obtained by the SO-CFAR in the case of a high number of interferences, whereas the GO-CFAR has the best false-alarm regulation when the number of cells contaminated by clutter exceeds half the number of reference cells.

CA-CFAR Detection Performance in Homogeneous Weibull Clutter

This letter presents a novel and exact formulation for the probability of detection of a cell-averaging, constant false-alarm rate (CFAR) radar system operating in a homogeneous Weibull clutter environment. We consider a realistic scenario with both target returns and clutter residues within the cell under test by the radar processing. In passing, we derive novel closed-form expressions for the probability density function and the cumulative distribution function of the sum of an exponentially fluctuating target embedded in Weibull clutter. The derived exact expressions are given in terms of both: 1) bivariate Fox H-function, for which we provide a portable and efficient MATHEMATICA code and 2) easily computable series representations. The validity of all expressions is confirmed via Monte Carlo simulation. The derived results are compared with the idealized Neyman–Pearson detector so as to quantify the CFAR losses, and they indicate that even a small change in the shape parameter of the clutter distribution can significantly affect the radar detection performance.

Constant false alarm rate detector based on sparsity regularisation in multi‐target interfering Weibull clutter

In this study, the authors propose a new constant false alarm rate detection algorithm in the non-homogeneous Weibull clutter caused by point-like targets interference. In their algorithm, sparsity regularisation is imposed on the target, which makes use of the target minority in detection background. On the basis of the regularised estimate of outliers, the indicator function is introduced to select the clean samples out of the background to estimate the distribution parameters, which further improves the robustness of the proposed detector. Simulation and experimental results verify the performance of the proposed detector which illustrates its superiority by making a comparison with the conventional detectors.

威布尔杂波下扩展目标检测

威布尔杂波下扩展目标检测