Discrimination Between Log-Normal and Weibull Clutter

Two simple tests are presented for classifying a set of clutter samples into either the log-normal or Weibull distribution. The results obtained by Monte Carlo simulation have shown that both of these tests are only slightly inferior to the test based on the ratio of maximized likelihoods. An application to constant false-alarm rate (CFAR) processing is also discussed.     

Radar Detection in Weibull Clutter

Radar detection in Weibull clutter is examined from a statistical detection viewpoint. Weibull clutter parameters are determined and related to measured values of land and sea clutter. Optimum performance in Weibull clutter is determined, and practical receivers that approach this performance are identified. Receiver performance in Rayleigh, log-normal, and Weibull clutter is evaluated and compared.     

Optimal CFAR detection in Weibull clutter

Optimal, in the maximum likelihood sense, constant false-alarm rate (CFAR) detection for Weibull clutter statistics, is investigated. The proposed OW (optimal Weibull) estimator is proved to be an asymptotically efficient estimator of the mean power of the Weibull clutter. Theoretical analysis of the OW-CFAR detector is provided, while detection performance analysis is carried out using the Monte Carlo simulation method. The operation of the median and morphological (MEMO)-CFAR detector in Weibull clutter statistics is also explained. It performs almost optimally in uniform clutter and, simultaneously, it is robust in multitarget situations. The performance of the proposed OW-CFAR detector in uniformal Weibull clutter is used as a yardstick in the analysis of the MEMO cell-averager (CA) and ordered statistic (OS) CFAR detectors. Nonfluctuating and fluctuating (Swerling II) targets are considered in detection analysis. The performance of the detectors is also examined at clutter edges     

Coverage area analysis for decentralized detection in Weibullclutter

The performance of a decentralized constant false-alarm rate (CFAR) detection system with data fusion in homogeneous non-Gaussian background is analyzed in terms of ground area covered. The advantages of using a distributed radar system and the differences between the system behavior in Rayleigh clutter and in Weibull clutter are stressed. Notably, the increasing benefit of cooperative decision making when clutter becomes spikier is pointed out     

UWB radar detection of targets in foliage using alpha-stableclutter models

We address the problem of detection of targets obscured by a forest canopy using an ultrawideband (UWB) radar. The forest clutter observed in the radar imagery is a highly impulsive random process that is more accurately modeled with the recently proposed class of alpha-stable processes as compared with Gaussian, Weibull, and K-distribution models. With this more accurate model, segmentation is performed on the imagery into forest and clear regions. Further, a region-adaptive symmetric alpha stable (SαS) constant false-alarm rate (CFAR) detector is introduced and its performance is compared with the Weibull and Gaussian CFAR detectors. The results on real data show that the SαS CFAR performs better than the Weibull and Gaussian CFAR detectors in detecting obscured targets     

Performance of max-mean level detector with and without censoring

The maximum-mean-level detector (MX-MLD) is a constant false-alarm rate (CFAR) detector designed to eliminate the excessively high false-alarm rate seen with the MLD at the edges of contiguous clutter regions. The concomitant high target suppression effect led M. Weiss (1982) to suggest a censored modification. The authors analyze the detection performance of the maximum-censored-mean-level detector (MX-CMLD). A homogeneous Swerling II target and clutter environment are assumed, and only single-pulse detection is considered. Analytic results apply equally to the MX-MLD and extend previous analysis. Simulation results are presented that demonstrate the qualitative effects of various CFAR detectors in nonhomogeneous clutter environments     

Detection Performance of Logarithmic Receivers Employing Video Integrators

The detection performance of logarithmic receivers in Rayleigh and non-Gaussian clutter is investigated. In Rayleigh clutter the performance is determined for steady, Swerling case 1, and Swerling case 2 targets. The detection loss of logarithmic receivers is generally less than the ? log n loss conjectured by Green, but consistent with the 1.08-dB asymptotic loss established by Hansen. The Swerling case 2 loss, important in frequency- agility applications, canbe severe for a small number of integrated pulses and high Pd, and apparently approaches the 1.08-dB asymptotic loss as a lower bound. Graphs of GramCharlier series cumulants are provided to allow determination of logarithmic-receiver performance. Curves are presented to allow the detection performance of logarithmic receivers in log-normal and Weibull clutter to be determineds.     

Statistical analyses of measured radar ground clutter data

The performance of ground-based surveillance radars strongly depends on the distribution and spectral characteristics of ground clutter. To design signal processing algorithms that exploit the knowledge of clutter characteristics, a preliminary statistical analysis of ground-clutter data is necessary. We report the results of a statistical analysis of X-band ground-clutter data from the MIT Lincoln Laboratory Phase One program. Data non-Gaussianity of the in-phase and quadrature components was revealed, first by means of histogram and moments analysis, and then by means of a Gaussianity test based on cumulants of order higher than the second; to this purpose parametric autoregressive (AR) modeling of the clutter process was developed. The test is computationally attractive and has constant false alarm rate (CFAR). Incoherent analysis has also been carried out by checking the fitting to Rayleigh, Weibull, log-normal, and K-distribution models. Finally, a new modified Kolmogorov-Smirnoff (KS) goodness-of-fit test is proposed; this modified test guarantees good fitting in the distribution tails, which is of fundamental importance for a correct design of CFAR processors     

Constant-False-Alarm-Rate Processors for Locally Nonstationary Clutter

A technique for designing normalizing processors for locally non-stationary clutter is discussed. The design procedure assumes the logarithm of the clutter power varies as a polynomial with range. When the actual environment matches the design environment, the false-alarm rate is a constant that is independent of the polynomial coefficients. A measure of the relative target detection capability as a function of the number of normalization cells and the degree of the design-environment polynomial is given. The applicability of the processors to non-Rayleigh clutter is discussed.     

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.     

Radar detection in clutter

Clutter is defined as any unwanted radar return. The presence of clutter in a range/Doppler cell complicates the detection of a target return signal in that cell. In order to quantify the effect of clutter on the probability of detection, we must first specify sets of models suitable for representing the clutter and target. The simplest and most common model for clutter is based on the gamma density. We include two additional models, the NCG and NCGG clutter models for low grazing angles. They are motivated by physical arguments, the latter of which can accommodate the well-known phenomenon of speckle. Using one of these models for clutter together with one of several models for targets, we determine, in a range/Doppler cell, expressions for probabilities of detection of a target in the presence of clutter. It is important to control the probability of false alarms. The presence of clutter in a cell necessitates an increase in the detection threshold setting in order to control false alarms, thus lowering the probability of detection. If the clutter level is unknown, then we need to take measurements of the clutter and use it to adjust the threshold. The more clutter samples we take, the better the estimate of the clutter level and the less is the resulting detection loss. Using the expressions for the probability of detection in clutter, we can quantify the detection loss for a pair of commonly used constant false-alarm rate (CFAR) techniques and investigate how the loss varies with different parameter values, especially with regard to the number of clutter samples taken to estimate the clutter level.     

Analysis of multiplicative speckle models for template-based SARATR

It has been noted that signal aperture radar (SAR) imagery of clutter exhibits Rayleigh multiplicative noise due to speckle. We use a database of MSTAR target chips to verify that the noise is multiplicative rather than additive for all regions in the chip. Then, by examining histograms corresponding to the noise residuals, we show that a Weibull distribution that is almost Rayleigh best fits the data. However, when we restrict the analysis over the target region, the log-normal and Rayleigh models fit the noise equally as well. This can be attributed to scattering mechanisms that are unstable over five degrees of aspect angle     

OS-CFAR theory for multiple targets and nonuniform clutter

The performance of a cell averaging constant false-alarm rate (CA-CFAR) detector degrades rapidly in nonideal conditions caused by multiple targets and nonuniform clutter. The ordered-statistic CFAR (OS-CFAR) is an alternative to the CA-CFAR. The OS-CFAR trades a small loss in detection performance relative to the CA-CFAR in ideal conditions for much less performance degradation in nonideal conditions. A formula is given for the detection probability of the OS-CFAR when there are multiple Swerling I targets in the CFAR window, and a formula is given for the probability of false alarm in nonuniform Raleigh clutter     

Radar CFAR Thresholding in Clutter and Multiple Target Situations

Radar detection procedures involve the comparison of the received signal amplitude to a threshold. In order to obtain a constant false-alarm rate (CFAR), an adaptive threshold must be applied reflecting the local clutter situation. The cell averaging approach, for example, is an adaptive procedure. A CFAR method is discussed using as the CFAR threshold one single value selected from the so-called ordered statistic (this method is fundamentally different from a rank statistic). This procedure has some advantages over cell averaging CFAR, especially in cases where more than one target is present within the reference window on which estimation of the local clutter situation is based, or where this reference window is crossing clutter edges.     

Sum-difference Reduced-dimensional Processing in SAR Image Domain and Statistical Analysis for Ground Moving Target Indication

In this article, a new reduced-dimensional adaptive processing algorithm based on joint pixels sum-difference data for clutter rejection is proposed. The sum-difference data are obtained by orthogonal projection of the joint pixels data of different synthetic aperture radar (SAR) images generated by a multi-satellite radar system. In the sense of statistical expectation, the sum-differ- ence data contain the common and different information of the SAR images. Therefore, the objective of clutter cancellation can be achieved by adaptive processing. Moreover, based on the residual image after clutter rejection, statistical analysis of constant false-alarm rate (CFAR) detection of moving targets is also presented. Simulation results demonstrate the effectiveness and robustness of the proposed algorithm even with heterogeneous clutter and image co-registration error.     

Vector subspace detection in compound-Gaussian clutter. Part I: survey and new results

Deals with the problem of detecting subspace random signals against correlated non-Gaussian clutter exploiting different degrees of knowledge on target and clutter statistical characteristics. The clutter process is modeled by the compound-Gaussian distribution. In the first part of the paper, the optimum Neyman-Pearson (NP) detector, the generalized likelihood ratio test (GLRT), and a constant false-alarm rate (CFAR) detector are sequentially derived both for the Gaussian and the compound-Gaussian scenarios. Different interpretations of the various detectors are provided to highlight the relationships and the differences among them. In particular, we show how the GLRT detector may be recast into an estimator-correlator form and into another form, namely a generalized whitening-matched filter (GWMF), which is the GLRT detector against Gaussian disturbance, compared with a data-dependent threshold. In the second part of this paper, the proposed detectors are tested against both simulated data and measured high resolution sea clutter data to investigate the dependence of their performance on the various clutter and signal parameters.     

Correlated Clutter and Resultant Properties of Binary Signals

A simple Markov process model of binary, digitized radar clutter returns is assumed. Probability distributions for the number of hits in n observations are developed for small n with a binary parameter describing the process derived for Rayleigh distributed clutter. Tables of distributions are included, along with an example to show the effects of correlation on the false-alarm probabilities of a sliding-window detector.     

Vector subspace detection in compound-Gaussian clutter. Part II: performance analysis

For pt. I see ibid., vol. 38, no. 4, p. 1295 (2002). In this second part we deal with the problem of detecting subspace random signals against correlated non-Gaussian clutter modeled by the compound-Gaussian distribution. In the first part of the paper, we derived the optimum Neyman-Pearson (NP) detector, the generalized likelihood ratio test (GLRT), and a constant false-alarm rate (CFAR) detector; we also provided some interesting interpretations of them. In this second part, these detectors are tested against both simulated data and measured high resolution sea clutter data to investigate the dependence of their performance on the various clutter and signal parameters. Numerical examples concern a space-time adaptive processing (STAP) scenario and a ground-based surveillance radar system scenario.     

Modified Generalized Sign Test Processor for 2-D Radar

The modified generalized sign test processor is a nonparametric, adaptive detector for 2-D search radars. The detector ranks a sample under test with its neighboring samples and integrates (on a pulse-to-pulse basis) the ranks with a two-pole filter. A target is declared when the integrated output exceeds two thresholds. The first threshold is fixed and yields a 10-6 probability of false alarm when the neighboring samples are independent and identically distributed. The second threshold is adaptive and maintains a low false-alarm rate when the integrated neighboring samples are correlated and when there are nonhomogeneities, such as extraneous targets, in the neighboring cells. Using Monte Carlo techniques, probability of false-alarm results, probability of detection curves, and angular accuracy curves have been generated for this detector. The detector was built and PPI photographs are used to indicate the detector's performance when the radar is operated over land clutter.     

Incoherent radar detection in compound-Gaussian clutter

The detection of incoherent pulse trains in compound-Gaussian disturbance with known spectral density is dealt with here. Two alternative approaches are investigated, The first, assuming perfect knowledge of the signal fluctuation law and implementing the Neyman-Pearson test on the observed waveform, turns out to be not applicable to the radar problem. The second, instead, relying on the generalized likelihood ratio optimization strategy, leads to a canonical detector, whose structure is independent of the clutter amplitude probability density function. Interestingly, this detector turns out to be constant false-alarm rate in the sense that threshold setting does not require any knowledge as to the clutter distribution, Moreover, since such a processor is not implementable in real situations, we also present an FFT-based (fast Fourier transform) suboptimum structure. Finally, we give closed-form formulas for the detection performance of both receivers, showing that both of them largely outperform the square-law detector, especially in the presence of very spiky clutter