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     

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.     

Analysis of CFAR performance in Weibull clutter

Recent interest has focused on order statistic-based (OS-based) algorithms for calculating radar detection thresholds. Previous analyses of these algorithms are extended, to determine closed-form approximations for the signal-to-clutter ratio required to achieve a particular probability of detection in clutter environments whose amplitude statistics are modeled by the Weibull distribution, and where the clutter dominates receiver noise. Performance is evaluated in both homogeneous and inhomogenous clutter. The analysis shows that the OS-based algorithm is quite robust against both interference and clutter edges. A method is suggested for improving performance at clutter inhomogeneities for short-range targets     

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     

False-Alarm Regulation in Log-Normal and Weibull Clutter

Automatic detection radars require some method of adapting to variations in the background clutter in order to control their false-alarm rate. Conventional cell-averaging techniques designed to maintain a constant false-alarm rate in Rayleigh clutter will fail to control the false-alarm rate in more severe clutter environments such as log-normal or Weibull clutter. A processor is described which is capable of maintaining false-alarm regulation in log-normal clutter and in Weibull clutter (and, under certain conditions, over the entire family of log-normal and Weibull distributions).     

Optimal radar threshold determination in Weibull clutter andGaussian noise

A technique is presented for determining the ideal detection threshold when Gaussian noise and Weibull distributed clutter returns are present on a radar receiver and neither is dominant. Quantitative data is presented for several clutter types and false alarm probabilities     

Biparametric linear estimation for CFAR against Weibull clutter

The authors deal with constant false alarm rate (CFAR) procedures against nonstationary clutter, modeled as a Weibull distributed process whose scale parameter α and shape parameter β are both variable. It is shown that conventional CFAR procedures, which compensate only for α, degrade intolerably as β deviates from β=2, namely, as the Rayleigh distributional assumption is violated. A biparametric CFAR procedure is shown to be suited to such situations. The authors introduce a logarithmic transformation to reduce the Weibull probability density function (pdf) to a Gumbel pdf, i.e., to the location-scale type, and then exploit the best linear unbiased estimation (BLUE) of location-scale parameters to adjust the detection threshold. True CFAR is thus achieved when the clutter is locally homogeneous. Resilience against local inhomogeneities can also be conferred since BLUE lends itself to censoring. Through a performance analysis, the influence of various system and distributional parameters is elicited     

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     

Multiframe detector/tracker: optimal performance

We develop the optimal Bayes multiframe detector/tracker for rigid extended targets that move randomly in clutter. The performance of this optimal algorithm provides a bound on the performance of any other suboptimal detector/tracker. We determine by Monte Carlo simulations the optimal performance under a variety of scenarios including spatially correlated Gaussian clutter and non-Gaussian (K and Weibull) clutter. We show that, for similar tracking performance, the optimal Bayes tracker can achieve peak signal-to-noise ratio gains possibly larger than 10 dB over the commonly used combination of a spatial matched filter (spatial correlator) and a linearized Kalman-Bucy tracker. Simulations using real clutter data with a simulated target suggest similar performance gains when the clutter model parameters are unknown and estimated from the measurements     

Correlated K-distributed clutter generation for radar detection andtrack

The generation of correlated vectors for non-Gaussian clutter is considered for log normal, Weibull, and K-probability distributions. Previous results for log normal and Weibull distributions are summarized. Expressions for the probability distributions and moments of K-distributed clutter of any correlation are derived. Procedures for forming samples of each type of clutter are shown to be equivalent to passing white Gaussian noise through a linear filter followed by a nonlinear operation. Curves of correlation coefficients necessary for the simulation of these vectors are presented for each distribution     

Generalized radar clutter model

A commonly used density model for radar clutter is chi-square for power, or, equivalently, Rayleigh for amplitude. However, for many modern high resolution radar systems, this density underestimates the tails of the measured clutter density. Log normal and Weibull distributions have proved to be better suited for the clutter in these high resolution radars. Generalizing the chi-square density by replacing it with the noncentral chi-square density and allowing the mean power level (the noncentrality parameter) to vary, we can both suitably shape the clutter density to produce larger tails and model the fluctuation of the average clutter power, commonly referred to as speckle. The resulting form, although appearing cumbersome, readily allows for efficient and accurate computations of the probability of detection in clutter     

Optimal polarimetric detection of radar target in a slowlyfluctuating environment of clutter

It is shown that in a situation where a radar target is distant enough from the radar and is included in a natural or artificial clutter environment in such a manner that the conventional detection methods fail, it is possible to improve the radar detection performance by using appropriate signal processing on two orthogonal polarization states. A CFAR (constant false alarm rate) polarimetric detection system based on the study of the polarization difference between clutter and target is proposed. Since the polarization state of the clutter echoes fluctuates slowly from cell to cell, an autoregressive model can be applied to the components of the polarization vector to predict the detection thresholds needed to follow the polarization state variation. The detection thresholds are determined to maintain a false alarm probability equal to 10^-6. The presence of a target registers as a significant variation of the estimation error of the polarization vector. Results obtained from measurements of simple and canonical targets with artificial clutter are presented, and these results validate the principle of polarimetric detection     

A method for estimating parameters of K-distributed clutter

A method for estimating the parameters of K-distributed clutter when the available sample size of the data is limited is proposed. In this method, the arithmetic mean and geometric mean of the given data are used to estimate the model parameters. Expressions characterizing the performance of the proposed estimator are presented, along with some simulation results. For spiky clutter, simulations show that parameter estimates obtained from the arithmetic and geometric mean are approximately equal to the numerically evaluated maximum-likelihood (ML) estimates. The method is also used to estimate the parameter of the Weibull density     

Spatially distributed target detection in non-Gaussian clutter

Two detection schemes for the detection of a spatially distributed, Doppler-shifted target in non-Gaussian clutter are developed. The non-Gaussian clutter is modeled as a spherically invariant random vector (SIRV) distribution. For the first detector, called the non-scatterer density dependent generalized likelihood ratio test (NSDD-GLRT), the detector takes the form of a sum of logarithms of identical functions of data from each individual range cell. It is shown under the clutter only hypothesis, that the detection statistic has the chi-square distribution so that the detector threshold is easily calculated for a given probability of false alarm P_F. The detection probability P_D is shown to be only a function of the signal-to-clutter power ratio (S/C)_opt of the matched filter, the number of pulses N, the number of target range resolution cells J, the spikiness of the clutter determined by a parameter of an assumed underlying mixing distribution, and P_F. For representative examples, it is shown that as N, J, or the clutter spikiness increases, detection performance improves. A second detector is developed which incorporates a priori knowledge of the spatial scatterer density. This detector is called the scatterer density dependent GLRT (SDD-GLRT) and is shown for a representative case to improve significantly the detection performance of a sparsely distributed target relative to the performance of the NSDD-GLRT and to be robust for a moderate mismatch of the expected number of scatterers. For both the NSDD-GLRT and SDD-GLRT, the detectors have the constant false-alarm rate (CFAR) property that P_F is independent of the underlying mixing distribution of the clutter, the clutter covariance matrix, and the steering vector of the desired signal     

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     

Low-altitude target detection by coastline operated marine radar

Relevant to a Richian family of fluctuating targets with a composite background of sea-plus-land clutter, the performance prediction of a radar operating in near-coastal regions is elucidated by assuming noncoherent integration of the pulses. Considering the dominance of land clutter, a modified K-distributed statistic is indicated for the overall clutter envelope; and the corresponding probability of false alarm and probability of detection are deduced for fixed threshold detection (s) based on N pulses integrated in the presence of the sea-plus-land clutter and the noise. Even when the target offers a dominant scattered echo, the worst situations of the land clutter affecting the detection performance are indicated     

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     

Detection performance in K-distributed and correlatedRayleigh clutters

Performance prediction for a detection system employing noncoherent integration is carried out for a chi-square family of fluctuating targets in K-distributed clutter plus noise. The detection performance for Swerling 11 targets in the K-distributed clutter plus noise is compared with that in exponentially correlated Rayleigh clutter. The results show that the performance prediction based on N pulses integrated in clutter plus noise using the K-distributed clutter model may be approximately equivalent to that using the exponentially correlated Rayleigh-distributed clutter model     

On Weibull-Distributed Weather Clutter

Weather clutter was observed using an L band range (200nmi) air-route surveillance radar (ARSR). It is shown that the measured clutter amplitudes obey a Weibull distribution.     

Fractal interpolation of radar signatures for detecting stationarytargets in ground clutter

The fundamentals of fractal geometry are reviewed, and its application to the millimeter-wave radar detection of stationary targets in a clutter background is described. First, high-range-resolution (HRR) profiles are used to determine the fractal interpolation functions needed to create fractal signatures. The fractal dimension is then determined for these signatures. On the basis of the value of the fractal dimension, the signature is declared to represent either a target of interest or clutter. The results of a CFAR (constant false alarm rate) simulation are presented to illustrate the performance of the method. They indicate that the fractal dimension feature used seems to be independent of amplitude. Thus, the fractal dimension information combined with traditional amplitude processing techniques will improve probabilities of detection