Parametric Rao Test for Multichannel Adaptive Signal Detection

The parametric Rao test for a multichannel adaptive signal detection problem is derived by modeling the disturbance signal as a multichannel autoregressive (AR) process. Interestingly, the parametric Rao test takes a form identical to that of the recently introduced parametric adaptive matched filter (PAMF) detector for space-time adaptive processing (STAP) in airborne surveillance radar systems and other similar applications. The equivalence offers new insights into the performance and implementation of the PAMF detector. Specifically, the Rao/PAMF detector is asymptotically (for large samples) a parametric generalized likelihood ratio test (GLRT), due to an asymptotic equivalence between the Rao test and the GLRT. The asymptotic distribution of the Rao test statistic is obtained in closed form, which follows an exponential distribution under the null hypothesis H ₀ and, respectively, a noncentral Chi-squared distribution with two degrees of freedom under the alternative hypothesis H ₁. The noncentrality parameter of the noncentral Chi-squared distribution is determined by the output signal-to-interference-plus-noise ratio (SINR) of a temporal whitening filter. Since the asymptotic distribution under H ₀ is independent of the unknown parameters, the Rao/PAMF asymptotically achieves constant false alarm rate (CFAR). Numerical results show that these results are accurate in predicting the performance of the parametric Rao/PAMF detector even with moderate data support.     

Matched subspace CFAR detection of hovering helicopters

A constant false alarm rate (CFAR) strategy for detecting a Gaussian distributed random signal against correlated non-Gaussian clutter is developed. The proposed algorithm is based on Scharf's matched subspace detector (MSD) and has the CFAR property with respect to the clutter amplitude probability density function (apdf), provided that the clutter distribution belongs to the compound-Gaussian family and the clutter covariance matrix is known to within a scale factor. Analytical expressions of false alarm and detection probabilities are derived. An application to the problem of detecting hovering helicopters against vegetated ground clutter is reported     

False alarm analysis of the envelope detection GO-CFAR processor

The greatest of constant false alarm rate processor (GO CFAR) is a useful architecture for adaptively setting a radar detection threshold in the presence of clutter edges. The GO CFAR input is often the envelope detected in-phase (I) and quadrature (Q) channels of the baseband signal (x_e=√(I²+Q²)). This envelope detection can also be approximated using x=a max{|I|,|Q|}+b min{|I|,|Q|} which requires less complex hardware (a and b are simple multiplying coefficients). The envelope GO CFAR processor and several envelope approximation GO CFAR processors are compared in terms of the probability of false alarm (PFA) performance. Closed-form expressions which describe the PFA performance are given and their accuracy evaluated. It is shown that for all cases, the PFA is proportional to the number of reference cells n for small threshold multiplier T and inversely proportional to n for large T. A region of intersection occurs where the PFA is the same for two different values of n. For example, at T'=1.68 in the |I|+|Q| GO CFAR (a=1, b=1) the PFA for n=1 is equal to the optimal n=∞ fixed-threshold PFA (PFA=0.112)     

A persymmetric multiband GLR algorithm

By exploring the covariance structure information to reduce the uncertainty in adaptive processing, a persymmetric generalized likelihood ratio algorithm (PGLR) is developed together with the closed-form expressions of probabilities of detection and false alarm. This multiband algorithm, which requires less computation, can significantly outperform the corresponding unstructured multiband GLR algorithm, especially in a severely nonstationary and/or nonhomogeneous interference environment. Simulation shows that the constant false alarm rate (CFAR) performance of the new algorithm is as insensitive as that of the unstructured multiband GLR to the departure of interference distribution from Gaussian     

CFAR data fusion center with inhomogeneous receivers

Detection systems with distributed sensors and data fusion are increasingly used by surveillance systems. A system formed by N inhomogeneous constant false alarm rate (CFAR) detectors (cell-averaging (CA) and ordered statistic (OS) CFAR detectors) is studied. A recursive formulation of an algorithm that permits a fixed level of false alarms in the data fusion center is presented, to set the optimum individual threshold levels in the CFAR receivers and the optimum `K out of N' decision rule in order to maximize the total probability of detection. The algorithm also considers receivers of different quality or with different communication channel qualities connecting them with the fusion center. This procedure has been applied to several hypothetical networks with distributed CA-CFAR and OS-CFAR receivers and for Rayleigh targets and interference, and it was seen that in general the fusion decision OR rule is not always the best     

基于双边截断的双参数海上风电站 SAR图像 CFAR检测

文章提出了 1种基于双边截断的双参数海上风电站 SAR图像 CFAR检测器 DTCS-TPCFAR,目的是提高在具有多个目标海上区域和石油泄漏区域等环境下对海上风电站的检测性能。DTCS-TPCFAR所提出的双边截断杂波的方法,能够同时消除高强度和低强度异常值的干扰,同时保留真实的杂波样本。通过使用最大似然估计计算双边截断后样本的均值和标准差,然后通过这 2个参数估计值计算出截断阈值,最后再结合指定的虚警率(Probability of False Alarm,PFA)来对测试单元(Test Cell,TC)进行判断,完成最终的目标检测。这也是首次将 CFAR检测器用于检测海上风电站。文章通过 Sentinel-1数据集来验证该方法的有效性。实验结果表明,文章所提出的算法在相同指定虚警率下,具有更高的检测率(Detection Rate,DR)和更低的误报率(False Alarm Rate,FAR)。     

Performance analysis of linearly combined order statistic CFARdetectors

Linearly combined order statistic (LCOS) constant false-alarm rate (CFAR) detectors are examined for efficient and robust threshold estimation applied to exponentially distributed background observations for improved detection. Two optimization philosophies have been employed to determine the weighting coefficients of the order statistics. The first method optimizes the coefficients to obtain efficient estimates of clutter referred to the censored maximum likelihood (CML) and best linear unbiased (BLU) CFAR detectors. The second optimization involves maximizing the probability of detection under Swerling II targets and is referred to as the most powerful linear (MPL) CFAR detector. The BLU-CFAR detector assumes no knowledge of the target distribution in contrast to the MPL-CFAR detector which requires partial knowledge of the target distribution. The design of these CFAR detectors and the probability of detection performance are mathematically analyzed for background observations having homogeneous and heterogeneous distributions wherein the trade-offs between robustness and detection performance are illustrated     

Low-Loss Almost Constant False-Alarm Rate Processors

Conventional normalizing constant false-alarm rate (CFAR) circuits use the same configurations when detecting targets in interference regions and in clear regions. The CFAR penalty incurred in the clear region can be reduced by using CFAR processors that recognize the region is clear so that normalization is not necessary. An analysis of the target-detection performance for a particular modified CFAR processor, for an active-radar sensor, and for a passive infrared (IR), or sonar, sensor is given. It is shown that the decreased CFAR penalty in the clear is coupled with an increase of false-alarm rate in the clutter regions.     

A new and robust CFAR detection algorithm

A constant false alarm rate (CFAR) detection method which is based on a combination of median and morphological filters (MEMO) is proposed. The MEMO algorithm has robust performance with small CFAR loss, very good behavior at clutter edges and high detection performance in the case of closely spaced narrowband signals (targets). The proposed MEMO method is favourably compared with cell averaging (CA) and ordered statistics (OS) CFAR detectors. The Monte Carlo method is employed to analyze the MEMO-CFAR detector     

Data quantization effects in CFAR signal detection

In this paper, we investigate data quantization effects in constant false alarm rate (CFAR) signal detection. Exponential distribution for the input data and uniform quantization are assumed for the CFAR detector analysis. Such assumptions are valid in the case of radar for a Swerling I target in Gaussian clutter plus noise and a receiver with analog square-law detection followed by analog-to-digital (A/D) conversion. False alarm and detection probabilities of the cell averaging (CA) and order statistic (OS) CFAR detectors operating on quantized observations are analytically determined. In homogeneous backgrounds with 15 dB clutter power fluctuations, we show analytically that a 12-bit uniform quantizer is sufficient to achieve false alarm rate invariance. Detector performance characteristics in nonhomogeneous backgrounds, due to regions of clutter power transitions and multiple interfering targets, are also presented and detailed comparisons are given     

基于改进型CFAR的SAR图像目标检测算法

针对传统的双参数恒虚警率(Constant False Alarm Rate,CFAR)算法存在的虚警率高、实现过程繁琐、算法执行效率低等问题,提出了一种改进型的CFAR检测算法。该算法根据SAR图像的统计直方图,对可疑的目标像素进行预筛选,再用2个滑动窗口对像素进行判别。改进型的CFAR检测算法简化了原检测算法的结构,降低了检测结果的虚警率,提高了算法的计算效率,并在国际公开的雷达数据集上进行软件与DSP硬件的应用验证,测试表明该算法的有效性。     

CFAR for homogeneous part of high-resolution imagery

In high-resolution imaging, weak target pixel amplifiers may not be detected in the presence of clutter containing strong nonhomogeneities, when conventional approaches are used. The authors describe a constant false alarm rate (CFAR) approach that avoids the elimination of these significant target returns. The nonhomogeneous clutter as well as the weak target components are detected with this approach. The targets could then be discriminated from the homogeneities by discrimination techniques. It is shown how the lower amplitude components of the background noise and homogeneous clutter (which have Rayleigh statistics) can be detected in the presence of strong homogeneous clutter and targets. The average level of the homogeneous component is then determined using these lower-amplitude components. This CFAR approach avoids having a CFAR on the strong nonhomogeneities as well as the homogeneous component. The avoidance is what yields the ability to detect weak target pixel amplitudes     

Analysis of some modified ordered statistic CFAR: OSGO and OSSOCFAR

It is necessary for automatic detection radars to be adaptive to variations in background clutter in order to maintain a constant false alarm rate (CFAR). A CFAR based on an ordered statistic technique (OS CFAR) has some advantages over the cell-averaging technique (CA CFAR), especially in clutter edges or multiple target environments; unfortunately the large processing time required by this technique limits its use. The authors present two new OS CFARs that require only ahlf the processing time. One is an ordered statistic greatest of CFAR (OSGO), while the other is an ordered statistic smallest of CFAR (OSSO). The OSGO CFAR has the advantages of the OS CFAR with only a negligible increment to the CFAR loss     

CFAR integration processors in randomly arriving impulseinterference

Time diversity transmission is often used to circumvent the high probability of a deep fade on a single transmission which may result in loss of the signal. One way to combat deep fades is to postdetection integrate the received observations from each range resolution cell. The false alarm rate of the postdetection integrator (PI) is extremely sensitive to randomly arriving impulse interference. Such interfering pulses may be unintentionally generated by nearby radars or intentionally generated by pulse jammers seeking to destroy the visibility of the radar. The binary integrator (PI) which uses an M-out-of-L decision rule is insensitive to at most M-1 interfering pulses. We consider the adaptive implementation of the PI and BI detectors for constant false alarm rate (CFAR) operation. We show that the CFAR BI detector when the “AND” (L-out-of-L) decision rule is used exhibits more robust false alarm control properties in the presence of impulse interference at the expense of severe detection loss when no interference is present. The CFAR adaptive PI (API) detector is proposed to alleviate this problem. The CFAR API detector implements an adaptive censoring algorithm which determines and censors with high probability the interference samples thereby achieving robust false alarm control in the presence of interference and optimum detection performance in the absence of interference     

GLRT subspace detection for range and Doppler distributed targets

A generalized likelihood ratio test (GLRT) is derived for adaptive detection of range and Doppler-distributed targets. The clutter is modeled as a spherically invariant random process (SIRP) and its texture component is range dependent (heterogeneous clutter). We suppose here that the speckle component covariance matrix is known or estimated thanks to a secondary data set. Thus, unknown parameters to be estimated are local texture values, the complex amplitudes and Doppler frequencies of all scattering centers. To do so, we use superresolution methods. The proposed detector assumes a priori knowledge on the spatial distribution of the target and has the precious property of having a constant false alarm rate (CFAR) with the assumption of a known speckle covariance matrix or by the use of frequency agility.     

Further results on adaptive filtering with embedded CFAR

Among the few known adaptive filtering algorithms which have an embedded (integrated) constant false alarm rate (CFAR) performance feature, the generalized likelihood ratio (GLR) test algorithm has been found to be robust in non-Gaussian clutter. This paper examines the detection performance of the GLR algorithm in nonhomogeneous/nonstationary clutter environments which lead to nonidentical distribution of secondary (training) data. For two common types of nonhomogeneity, i.e., the so-called “signal contamination” and “clutter edge”, the asymptotic detection performance is derived and compared with simulations. These asymptotic results are relatively simple to use and they predict the GLR performance in nonhomogeneous environments quite well. The GLR performance loss due to the nonhomogeneity is also evaluated. It is found that the “generalized angle” between the desired and contaminating signal plays an important role in the study of the effects of signal contamination. It is also found that the performance degradation due to the clutter edge depends largely on the width of the clutter spectrum and target-clutter Doppler separation     

Clutter Map CFAR Analysis

An analysis of the probability of target detection for a clutter map CFAR using digital exponential filtering has been performed. General performance equations are derived. The probability of detection versus signal-to-noise ratio is plotted for a false alarm probability of 1.E-06 for several weight values. The CFAR loss is plotted for a detection probability of 0.9 and false alarm probabilities of 1.E-06 and 1.E-08.     

Detection Performance of the Cell Averaging LOG/CFAR Receiver

The cell averaging LOG/CFAR receiver is a special implementation of a constant-false-alarm-rate (CFAR) receiver in which the noise level estimate is derived from a set of contiguous time samples of the output of a logarithmic (LOG) detector as obtained from a tapped delay line. This CFAR receiver is capable of operating over a larger dynamic range of noise levels than a conventional cell averaging CFAR receiver, but with somewhat poorer detectability. The performance in stationary Gaussian noise of the cell averaging LOG/CFAR receiver with no post-detection integration is determined in this paper. For a small number of reference noise samples, results were obtained by a Monte Carlo simulation using the technique of importance sampling. For a large number of reference noise samples, a second moment analysis gave the desired results. Both these results can be summarized in the following simple formula, NLOG = 1.65NLIN - 0.65, which relates the number of reference samples required by each of the two receivers for equivalent performance. Thus, for the cell averaging LOG/CFAR receiver to give the same detection performance as the conventional cell averaging CFAR receiver, the number of reference noise samples has to be increased by up to 65 percent.     

CFAR detection and estimation for STAP radar

The algorithm presented here provides both a constant false-alarm rate (CFAR) detection and a maximum likelihood (ML) Doppler-bearing estimator of a target in a background of unknown Gaussian noise. A target is detected, and its parameters estimated within each range gate by evaluating a statistical test for each Doppler-angle cell and by selecting the cell with maximum output and finally comparing it with a threshold. Its CFAR performance is analyzed by the use of the sample matrix inversion (SMI) method and is evaluated in the cases of a fully adaptive space-time adaptive processing (STAP) and two partially adaptive STAPs. The performances of these criteria show that the probability of detection is a function only of the sample size K used to estimate the covariance matrix and a generalized signal-to-noise ratio. The choice of the number K is a tradeoff between performance and computational complexity. The performance curves demonstrate that the finer the resolution is, the poorer the detection capability. That means that one can trade off the accuracy of ML estimation with the performance of the CFAR detection criterion     

Analysis of an adaptive CFAR detector in non-Gaussian interference

Coherent signal detection in non-Gaussian interference is presently of interest in adaptive array applications. Conventional array detection algorithms inherently model the interference with a multivariate Gaussian random vector. However, non-Gaussian interference models are also under investigation for applications where the Gaussian assumption may not be appropriate. We analyze the performance of an adaptive array receiver for signal detection in interference modeled with a non-Gaussian distribution referred to as a spherically invariant random vector (SIRV). We first motivate this interference model with results from radar clutter measurements collected in the Mountain Top Program. Then we develop analytical expressions for the probability of false alarm and the probability of detection for the adaptive array receiver. Our analysis shows that the receiver has constant false alarm rate (CFAR) performance with respect to all the interference parameters. Some illustrative examples are included that compare the detection performance of this CFAR receiver with a receiver that has prior knowledge of the interference parameters