Constant False Alarm Rate Detector Research Articles

G-Wishart Distribution in Multilook Polarimetric Whitening Filter and its Application

The polarimetric whitening filter (PWF) is widely used in constant false alarm rate (CFAR) ship detection in polarimetric synthetic aperture radar (PolSAR) imagery. The detection threshold plays a key role in the CFAR detection, which is generally determined by the statistical model of clutter. Many product models with different distributed textures are considered to fit the PWF output for an accurate threshold. Unfortunately, the product model with the general inverse Gaussian (<i>G</i>) texture, which can be named <i>G</i>-Wishart model according to the polarimetric covariance matrix, has not been well studied for its effective calculation. In this letter, the probability density function (PDF), the probability of false alarm (PFA), and the threshold in the CFAR algorithm based on the PWF are all obtained corresponding to the <i>G</i> distribution. The closed forms for the PDF and PFA are obtained with the Fox H function and its multivariate version, respectively. The threshold is derived by the bisection method when the false alarm rate (FAR) is constant. Finally, experimental results using both simulated and real data demonstrate that the different statistical models with the same log-cumulants can achieve almost the same CFAR loss.

An IR-UWB Multi-Sensor Approach for Collision Avoidance in Indoor Environments

This article aims to propose new techniques to detect and distinguish humans from moving machines in indoor environments. Although many research efforts have been already dedicated to humans’ indoor detection, most of the work has been focused on counting people and crowd measurement for consumer business applications. Our objective is to develop a reliable approach for humans’ indoor detection and localization aiming at avoiding collisions inside a mixed Industry 4.0 manned and unmanned environment to enhance personal and equipment safety and to prevent unwanted intrusions. An original aspect of our research is that we have worked on the real-time estimation of humans’ and moving machines’ positions while addressing the problems of multipath components and noise clutter detection. A multipulse constant false alarm rate detection algorithm is also proposed for removing the misdetections due to heavy clutter components in the indoor environment. Four impulse radio ultrawideband transceivers are placed in a specific geometry and data fusion is performed to reduce the influence of multipath and noise on the detection process. A convolutional neural network (CNN) is then used to extract the patterns corresponding to a moving machine and humans and classify them accordingly. Experiments have been carried out in two different indoor environments to demonstrate the performance of the proposed algorithms.

Multi-Aircraft Formation Recognition Method of Over-the-Horizon Radar Based on Deep Transfer Learning

Over-the-horizon radar (OTHR) is an important equipment for the ultralong-range early warning in the military, but the use of constant false-alarm rate (CFAR), which is a traditional detection method, makes it difficult in multi-aircraft formation recognition. To solve this problem, a multi-aircraft formation recognition method based on deep transfer learning in OTHR is proposed. First, the range-Doppler images of aircraft formation in OTHR are simulated, which are composed of four categories of samples. Secondly, a recognition model based on Convolutional Neural Network (CNN) and CFAR detection technology is constructed, whose training method is designed as a two-step transfer. Finally, the trained model can well distinguish the spectral characteristics of aircraft formation, and then recognize the aircraft number of a formation. Experiments show that the proposed method is better than the traditional CFAR detection method, and can detect the number of aircraft more accurately in the formation with the same false alarm rate.

Cfar Detection in a Pareto Type Ii Clutter with Integration of Multiple Pulses

Cfar Detection in a Pareto Type Ii Clutter with Integration of Multiple Pulses

Outlier-Robust Superpixel-Level CFAR Detector With Truncated Clutter for Single Look Complex SAR Images

The constant false alarm rate (CFAR) detectors are well studied for ship detection in SAR images, which suffer performance degradation due to the capture effect from interfering outliers, such as nearby targets, sidelobes and ghosts in multi-target environments. To address this issue, the clutter truncation scheme is adopted to reduce the outlier contamination in clutter samples such that the accuracy of clutter modeling can be improved. However, the selection of clutter truncation depth is difficult, which often resorts to sensitivity study. In this paper, the complex signal kurtosis (CSK) is first utilized as a statistical indicator for the decision of truncation depth to guarantee that the true clutter samples are maintained. Besides, a coarse-to-fine detection process is designed, including global superpixel proposal with the CSK and local identification of target pixels with the superpixel-level CFAR detector based on truncated statistics. During the local CFAR detection stage, the segmented superpixels provide convenient sample indexing for the iterative clutter truncation processing. The elevated performance achieved by the proposed method mainly benefits from the schemes of two-stage detection and automatic clutter truncation, yielding the increased detection efficiency and accuracy at the same time. Besides, false alarms caused by radio frequency interference can be reduced. In the experiment, the comparative results with state-of-the-art methods based on the Sentinel-1 and Gaofen-3 SAR data validate the performance of the proposed method.

Ship Target Detection in SAR Imagery Based on Maximum Eigenvalue Detector

Ship target detection in synthetic aperture radar (SAR) imagery is of great significance in the field of ocean monitoring. Classical constant false alarm rate (CFAR) detectors and emerging information geometry methods are model-driven essentially, requiring precise modeling of the sea clutter distribution. In the complex and changeable ocean scenes, the performance of these two types of detectors is limited. To solve this problem, a ship target detection algorithm in SAR imagery based on the maximum eigenvalue of the sample covariance matrix is proposed in this letter. Without seeking the distribution model of clutter backgrounds, the difference between the target and the clutter background is fully captured by constructing the sample covariance matrix, and its maximum eigenvalue is utilized as the test statistic. Experimental results on measured SAR images show that the proposed method achieves better detection performance and faster calculation speed compared with the existing typical methods.

Performance Evaluation of SOCA-CFAR Detectors in Weibull-Distributed Clutter Environments

In this letter, we derive a novel exact expression for the probability of false alarm (PFA) and an approximate closed-form solution for the probability of detection (PD) of a smallest of cell-averaging constant false alarm rate (SOCA-CFAR) detector operating over Weibull-distributed clutter. For the analysis, we consider an exponentially distributed target and allow arbitrary values for the shape parameter of clutter interference. To the best of our knowledge, there are no exact or approximate performance evaluations for an SOCA-CFAR detector considering arbitrary values for the shape parameter of the Weibull interference samples (i.e., different from 1) contained within the CFAR window. Therefore, our analytical derivations generalize previous performance evaluation studies and take a small step toward a better understanding of more realistic SOCA-CFAR detectors. Moreover, we obtain exact formulations for the probability density function (PDF) and the cumulative distribution function (CDF) for a minimum of two sums of independent and identically distributed (i.i.d.) Weibull random variables. Numerical results indicate that the system performance improves as the shape parameter of the Weibull interference increases. The validity of all our expressions is confirmed via Monte Carlo simulations.

Deep Learning-Based UAV Detection in Pulse-Doppler Radar

With the popularity of unmanned aerial vehicles (UAVs), how to conduct automatic and effective detection to prevent unauthorized flying has become an important issue. The conventional constant false alarm rate (CFAR) detector based on radar signal has shown advantages in moving target detection. However, the CFAR-based detectors are strongly dependent on some manual experience, such as the ambient noise distribution estimation and the detection windows’ size selection, and usually suffered poor performance on small UAV detection due to the weak signal. Inspired by the success of deep learning (DL) on natural scene object detection, this article tries to explore a DL-based method for UAV detection in pulse-Doppler radar. Concretely, we propose a convolutional neural network (CNN) with two heads: one for the classification of the input range-Doppler map patch into target present or target absent and the other for the regression of offset between the target and the patch center. Then, based on the output of the network, a nonmaximum suppression (NMS) mechanism composed of probability-based initial recognition, distribution density-based recognition, and voting-based regression is developed to reduce false alarms as well as control the false alarms. Finally, experiments on both simulated data and real data are carried out, and it is shown that the proposed method can locate the target more accurately and achieve a much lower false alarm rate at a comparable detection rate than CFAR.

Robust Sliding Window CFAR Detection Based on Quantile Truncated Statistics

In this paper, the concept of quantile is introduced and elaborately related to the truncation depth, based on which quantile truncated statistics (QTS) is put forward. The QTS gives a reasonable explanation of truncation depth and makes the selection of truncation depth well-founded and controllable. In addition, maximum likelihood estimation based on QTS (QTS-MLE) for the probability density function (PDF) parameters is derived. We start the analysis from Weibull background assuming that the shape parameter is known, and then extend it to the case where the shape parameter is unknown. By analyzing the variance and mean square error (MSE) of the estimated parameters in Weibull background, it is found that QTS-MLE has better estimation performance than the MLE based on truncated statistics (TS-MLE). On this basis, the constant false alarm rate (CFAR) detector based on QTS-MLE, i.e. QTS-CFAR, is proposed. The analytic expressions of the false alarm rate and detection probability of QTS-CFAR are derived under the Weibull background with known shape parameter. The full CFAR characteristics of TS- and QTS-CFAR detectors in Weibull background with unknown shape parameter are proved by invariant theory. Monte Carlo simulations show that QTS-CFAR detector has better anti-interference performance and false alarm control ability in multiple-target environment. Furthermore, the superiority of QTS-CFAR detector is verified by the real data collected by skywave over-the-horizon radar. Finally, we present the expression of QTS-MLE for the scale parameter in the Gamma background.

Persymmetric Range-Spread Targets Detection in Compound Gaussian Sea Clutter With Inverse Gaussian Texture

This letter addresses the persymmetric adaptive detection problem of range-spread targets in compound Gaussian sea clutter. Based on the generalized likelihood ratio test (GLRT), Rao test, and Wald test, three novel compound Gaussian detectors are developed. Specifically, the sea clutter is modeled as compound Gaussian with inverse Gaussian distribution, and the detectors are derived by the two-step maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posterior</i> (MAP) procedures. In the first step, we assume the clutter covariance matrix (CCM) and the inverse Gaussian texture are known and derive the proposed detectors’ test statistics. In the second step, we use the persymmetric property and MAP criterion to estimate the CCM and inverse Gaussian texture parameters. Then the proposed detectors are proved to be constant false alarm rate (CFAR) detectors with respect to the real CCM. The simulation experiments are conducted by comparing the proposed detectors with their counterparts on both synthetic data and real sea clutter data. The numerical results indicate that the novel detectors exhibit better detection performance than their competitors.

Single-Channel Circular SAR Ground Moving Target Detection Based on LRSD and Adaptive Threshold Detector

Due to the advantages of long-time and multi-angle observation, ground moving target detection with circular synthetic aperture radar (SAR) has recently attracted lots of interest from researchers. Our team has previously proposed the logarithm background subtraction algorithm for moving target detection in single-channel circular SAR. Its principle is that the background image (static clutter) is obtained by median filtering of the image sequence, and the foreground image (moving target) is obtained by subtraction. To further improve the performance of background and foreground separation, we introduce the low-rank sparse decomposition (LRSD) method into the previous framework. A new algorithm based on LRSD and adaptive threshold detector (ATD) is proposed in this letter. First, this letter introduces entropy metric to optimize parameters in LRSD to obtain better background and foreground separation. Second, since the statistical distribution of the foreground image is unknown, the constant false alarm rate (CFAR) detector cannot be applied to the foreground image. Therefore, an adaptive threshold detector (ATD) built on Otsu is presented in this letter, which is independent of image statistical properties. The final detection result is obtained via clustering using the modified density-based spatial clustering of applications with noise (DBSCAN) method. The effectiveness of the proposed algorithm is verified by the experimental results on the airborne X-band Gotcha Volumetric SAR Data.

Design of Customized Adaptive Radar Detectors in the CFAR Feature Plane

The paper addresses the design of adaptive radar detectors having desired behavior, in Gaussian disturbance with unknown statistics. Specifically, given detection probability specifications for chosen signal-to-noise ratios and steering vector mismatch levels, a methodology for the optimal design of customized CFAR detectors is devised in a suitable feature plane based on maximal invariant statistics. To overcome the analytical and numerical intractability of the resulting optimization problem, a novel general reduced-complexity algorithm is developed, which is shown to be effective in providing a close approximation of the desired detector. The proposed approach solves the open problem of ensuring a prefixed false alarm probability while controlling the behavior under both matched and mismatched conditions, so enabling the design of fully customized adaptive CFAR detectors.

Nonstationary Moving Target Detection in Spiky Sea Clutter via Time-Frequency Manifold

Nonstationary moving target detection in spiky sea clutter is a challenging task due to the high-power, time-varying, and target-like properties of sea spikes. In this letter, we propose a time-frequency correlation (TFC)-based constant false alarm rate (TFC-CFAR) detection method on the time-frequency manifold, and apply it to the nonstationary moving target detection in spiky sea clutter. The data samples in each range cell are modeled as a TFC matrix that captures the correlation between two frequency components of the time-frequency distribution. The clutter covariance matrix is estimated by the geometric mean of a set of TFC matrices in reference cells. Three geometric metrics are employed to measure the dissimilarity between the clutter and target signals. Based on these geometric measures, three TFC-CFAR detectors are compared. Experiments performed on a real IPIX radar dataset confirm that the TFC can be used for identifying and eliminating sea spikes, while the TFC-CFAR detector achieves better detection performance than the conventional detectors.

Deep Learning-Aided Signal Enumeration for Lens Antenna Array

This work investigates a data-driven approach to detect the number of incoming signals for a lens antenna array (LAA). First, the energy-focusing property of an electromagnetic (EM) lens is utilized to generate an input spectrum, which can be used to enumerate both the multipath and independent signals. Next, we present the deep learning (DL)-assisted sharp peak recognition method referred to as the power spectrum-based convolutional neural network (PSCNet). Unlike classical techniques, such as constant false alarm rate (CFAR) detection, this data-driven detector can count received signals adaptively based on the LAA power spectrum without requiring any initial configurations. In addition, the PSCNet outperforms other state-of-the-art subspace-based detectors, even under challenging conditions, such as a low signal-to-noise ratio (SNR), a small observation size, and angular ambiguity. For the training phase, we propose a pretrained-model reusing strategy and an input pre-processing approach referred to as the power spectrum shortening (PSS) to alleviate the training burden and achieve lower complexity compared to fully retraining all isolated networks. The simulation results demonstrate that our proposed sharp peak-recognition algorithm not only accomplishes the improved signal enumeration performance but also requires lower computational resources than other subspace-based approaches.

Adaptive Registration for Optical and SAR Images With a Scale-Constrained Matching Method

Images registration for optical and synthetic aperture radar (SAR) is a key of multi-sensor images analysis. And parameters selection affects the final result of the registration algorithms for optical and SAR images. For images obtained by different sensors, how to choose an appropriate parameter for accurate registration is a key problem. In this letter, a parameter adaptive registration algorithm between optical and SAR images based on SIFT is proposed. Because of the different imaging mechanisms of these two kinds of images, the algorithm uses the multiscale Sobel operator to calculate the gradient for the optical image, while for the SAR image, a new adaptive operator based on the neighborhood pixel value is proposed to calculate the gradient. In the feature extraction, the adaptive value estimated by constant false alarm rate (CFAR) detection is used instead of the fixed threshold. Finally, a matching method constrained by image size scaling (Scale-Constrained Fast Sample Consensus) is proposed. The evaluation was designed in two aspects: feature extraction and image registration. The algorithm we proposed shows excellent performances in the aspects of repeatability, correct matching rate and root mean square error. The experimental results show that our method maintains the performance of the original algorithm and has some optimization and breakthrough.

A Statistical Model Based on Modified Generalized-K Distribution for Sea Clutter

Sea clutter magnitude distribution exhibits important guiding significance for the design of marine target detection algorithms and the selection of the constant false alarm rate (CFAR) detection threshold. In this letter, to deal with the limitation of the traditional generalized-K (GK) distribution in highly heterogeneous clutter scene, a modified GK (MGK) distribution is proposed for sea clutter magnitude. By combining the traditional GK and generalized Pareto distributions, the value range of power parameter and the applicable range of the distribution model are extended. The applicability of the proposed distribution model is verified by real-measured sea clutter data.

A SAR-GMTI Approach Aided by Online Knowledge With an Airborne Multichannel Quad-Pol Radar System

In the complicated geographical environment, there will be a seriously deleterious effect to the performance of synthetic aperture radar (SAR)-ground moving target indication (SAR-GMTI) system, because it is difficult to obtain the homogeneous training samples to accurately estimate the clutter covariance matrix (CCM) without prior information of the observed scene. To this end, this paper proposes a SAR-GMTI approach aided by online knowledge with an airborne multichannel quadrature-polarimetric (quad-pol) radar system. Generally, this paper can be divided into two parts: online knowledge acquisition and polarization knowledge-aided (Pol-KA) SAR-GMTI processing. Firstly, based on the similarity of pixels from the multichannel and multi-polarization information, a weighed estimation method of polarimetric coherency matrix is proposed, which can overcome the over-smoothing problem and increase the estimation accuracy of coherency matrix. Further, a hybrid weighted local K-means based on geodesic distance (GD-HWLKM) clustering algorithm is proposed to achieve the aim of unsupervised classification. Here, geodesic distance (GD) is exploited to measure the distance between multi-feature region covariance matrixes (MFRCMs) and a hybrid weight from different scales (including local cover class distribution, region and pixel) is calculated to automatically update the cluster centroid, which can make full use of the local spatial information by taking the interclass samples' similarity and the diversity of different classes into consideration. Secondly, with the assistance of the previous polarization SAR (PolSAR) image classification result, a Pol-KA SAR-GMTI method is developed. For each ground cover category, an accurate CCM can be estimated with the independent and identically distributed (IID) training samples. Then, the multichannel clutter suppression and preliminary constant false alarm rate (CFAR) detection are performed. Finally, with an airborne multichannel quad-pol radar system, the experimental results on real measured data demonstrate that the proposed method can efficiently improve the clutter suppression preformation and moving-target detection preformation.

Robust Variability Index CFAR Detector Based on Bayesian Interference Control

The methods of Bayesian predictive inference and variation index are vital in the constant false alarm rate (CFAR) detection, which adaptively predicts and evaluates the background level to achieve target detection. However, in complex scenarios, the interference effect can lead to imprecise prediction and complex calculations of the background level, which results in severely degraded CFAR performance. To solve the above situation, a robust variation index CFAR detector based on Bayesian interference control (BVI-CFAR) is proposed. The clutter range profile (CRP) is equally divided and the decision-making selection is optimized to dynamically evaluate the background clutter level in this algorithm; meanwhile, the clutter level will feedback control the former. Then, based on the Bayesian interference control theory, the Bayesian classification interference control idea is proposed to simultaneously predict inference multiple targets in the background. Therefore, the anti-interference ability of the detector is improved while reducing the computational complexity. The false alarm rate and decision expression are given, and the detection is extended when the segmentation and interference are arbitrary. Both the simulation results and the field test results verify the favorable performance of the algorithm in complex scenarios.

DNN-Based Peak Sequence Classification CFAR Detection Algorithm for High-Resolution FMCW Radar

Multitarget detection is very challenging, especially when targets are densely distributed. In conventional constant false alarm rate (CFAR) detection algorithms, the detection threshold is determined based on a pre-estimated background level (BL). However, interfering targets inevitably lead to inaccurate BL estimation, resulting in degraded detection performance. In our previous work, a new solution was developed and verified to be effective; in that solution, compressed sensing (CS)-based detector performs target detection without relying on BL estimation, and a subsequent CFAR regulation processor achieves the desired false alarm rate based on the statistical information of the reduced samples obtained by removing the detected targets and adjacent guard cells from the original samples. However, for scenes with a high target density, the CS-based detector suffers from performance degradation while acquiring the correlation between linear measurements of the signal and the sensing matrix due to the high local signal sparsity. To address this shortcoming, this article proposes a deep neural network (DNN)-based detector that further improves the detection performance by converting the target detection into a problem of peak sequence classification of frequency intensity (FI) measurements from radar. A DNN detector trained on augmented simulated data shows excellent generalization ability for deployment in real scenes. In addition, to achieve better computational efficiency, a Taylor-series-based approximate maximum likelihood estimator with an explicit expression is applied in the CFAR regulation process for the first time. Both simulation and field tests are performed to verify the superiority of the proposed algorithm over conventional algorithms.

Coherent Radar Target Detection With In-Band Cyclostationary Wireless Interference

Spectral congestion necessitates the in-band operation or the spectrum-sharing of legacy radar and communication systems. Since these systems operate in the same band in spectrum-sharing mode, they interfere with one another. To address this problem from the radar&#x2019;s perspective, this paper considers the coherent detection of target-reflected radar signals in the presence of interference from an in-band cyclostationary digital modulated wireless communication signal. Three different cases of target-reflected radar signals, namely, deterministic signals, signals with random phase, and completely random signals, are considered in this paper. The optimum detection rules are derived for these three cases and the corresponding receiver structures for the equalization of the interfering signal are presented. Sub-optimum detection structures are also derived with the assumption that the in-band interference is a white stationary time-invariant Gaussian process. Further, considering the equalization, modified CFAR receiver structures are also presented. By considering the mathematical models for cyclostationary or periodic in-band interference, the performances of the optimum, sub-optimum detectors, and modified CFAR detectors are quantified analytically in terms of detection probability and false alarm probability, and the resulting receiver operating characteristic (ROC) curves are analyzed as a function of the signal-to-interference ratio. It is demonstrated that improper equalization of the interfering signal significantly affects the performance of the optimum detector and this impact is analyzed in detail. As spectrum-sharing becomes more prevalent due to spectrum congestion, the proposed optimal, sub-optimal, and modified CFAR detection rules and receiver structures can be incorporated into existing systems with substantial savings.