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     

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     

Nonparametric rank detectors under K-distributed clutter in radar applications

This correspondence deals with a comparative analysis of parametric detectors versus rank ones for radar applications, under K-distributed clutter and nonfluctuating and Swerling II target models. We show that the locally optimum detectors (LODs) (optimum for very low signal-to-clutter ratio (SCR)) under K-distributed clutter are not practical detectors; on the contrary, asymptotically optimum detectors (optimum for high SCR) are the practical ones. The performance analysis of the parametric log-detector and the nonparametric (linear rank) detector is carried out for independent and identically distributed (IID) clutter samples, correlated clutter samples, and nonhomogeneous clutter samples. Some results of Monte Carlo simulations for detection probability (P/sub d/) versus SCR are presented in curves for different detector parameter values.     

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.     

Adaptive detection schemes in compound-Gaussian clutter

Radar detection of coherent pulse trains embedded in compound-Gaussian disturbance with partially known statistics is discussed. We first give a thorough derivation of two recently proposed adaptive detection structures. Next, we derive a different detection scheme exploiting the assumption that the clutter is wide-sense stationary. Resorting to the theory of circulant matrices, in fact, we demonstrate that the estimation of the structure of the clutter covariance matrix can be reduced to the estimation of its eigenvalues, which in turn can be (efficiently) done via fast Fourier transform codes. After a thorough performance assessment, mostly carried on via computer simulations, the results show that the newly proposed detector achieves better performance than the two previously introduced adaptive detectors. Moreover, a sensitivity analysis shows that, even though this detector does not strictly guarantee the constant false alarm rate property with respect to the clutter covariance matrix, it is robust, in the sense that its performance is only slightly affected by variations in the clutter temporal correlation     

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     

Polarization diversity detection in compound-Gaussian clutter

We present the problem of polarization diversity detection in compound-Gaussian clutter with unknown covariance matrix. To this end we assume that a set of secondary data, free of signal components and with the same covariance structure of the cell under test, is available. Due to the lack of a uniformly most powerful (UMP) detector we resort to a design procedure based upon the Rao and the Wald tests. Specifically we first derive the Rao and the Wald tests assuming that the covariance matrix is known, and then we substitute into the derived decision rules a suitable estimate of the clutter covariance. Interestingly, the newly proposed detectors share the constant false alarm rate (CFAR) property with respect to the texture statistical characterization. Moreover simulation results have shown that the Wald test based detector ensures a performance level higher than the Rao test. We have also conducted a further performance analysis, in the presence of real clutter data and in comparison with the previously proposed generalized likelihood ratio test (GLRT) based receivers, which highlights that, in general, the Wald test receiver outperforms its counterparts. Finally, since the newly proposed decision rules as well as the previously designed GLRTs do not ensure the CFAR property with respect to the clutter covariance matrix, we have developed a sensitivity analysis on the probability of false alarm (P/sub fa/), based on simulated clutter with covariance matrix estimated from real radar data. The results have shown that (P/sub fa/) is only slightly affected by variations in the clutter correlation properties and hence the CFARness is substantially achieved.     

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     

Nonlinear clutter cancellation and detection using a memory-basedpredictor

In this paper, a nonlinear prediction (NLP) method is proposed as an alternative to the conventional linear prediction (LP) method for clutter cancellation. Because of the nonlinearity and non-Gaussianity of a clutter process, a nonlinear predictor is therefore needed to suppress clutter optimally. A memory-based predictor which uses a table look-up strategy to perform NLP is used in this work. The advantages of the memory-based approach are fast learning, algorithmic simplicity, robustness and suitability for parallel implementation. The memory-based predictor is then used as an adaptive detector for small surface target detection embedded in clutter. The effectiveness of the new method is demonstrated using real sea clutter data, and the results show improvement when compared with the conventional LP techniques     

Asymptotically optimum radar detection in compound-Gaussian clutter

An asymptotically optimum receiver designed for detecting coherent pulse trains in compound-Gaussian clutter is introduced and assessed. The proposed receiver assumes knowledge of the structure of the clutter covariance matrix, but does not require that of its amplitude probability density function (apdf). Performance is analytically evaluated, showing that the loss, as measured with respect to the corresponding optimum structure, is kept within a few dBs even for a relatively small number of integrated pulses and that it largely outperforms the matched-filter detector under all instances of practical interest. Interestingly, the proposed detector achieves constant false alarm rate (CFAR), regardless of the clutter envelope distribution and, consequently, its power     

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     

Structures for radar detection in compound Gaussian clutter

The problem of coherent radar target detection in a background of non-Gaussian clutter modeled by a compound Gaussian distribution is studied here. We show how the likelihood ratio may be recast into an estimator-correlator form that shows that an essential feature of the optimal detector is to compute an optimum estimate of the reciprocal of the unknown random local power level. We then proceed to show that the optimal detector may be recast into yet another form, namely a matched filter compared with a data-dependent threshold. With these reformulations of the optimal detector, the problem of obtaining suboptimal detectors may be systematically studied by either approximating the likelihood ratio directly, utilizing a suboptimal estimate in the estimator-correlator structure or utilizing a suboptimal function to model the data-dependent threshold in the matched filter interpretation. Each of these approaches is studied to obtain suboptimal detectors. The results indicate that for processing small numbers of pulses, a suboptimal detector that utilizes information about the nature of the non-Gaussian clutter can be implemented to obtain quasi-optimal performance. As the number of pulses to be processed increases, a suboptimal detector that does not require information about the specific nature of the non-Gaussian clutter may be implemented to obtain quasi-optimal performance     

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     

Growler detection in sea clutter with coherent radars

Ship navigation through ice-infested waters is a problem of deep concern to the Canadian shipping and exploration industry. Conventional marine radars have difficulty detecting small pieces of glacial ice called growlers which are very hazardous to vessels if struck. In an effort to improve detection performance, X-band radar measurements were collected and analyzed to determine the characteristics of clutter and growler returns that could lead to their separability. These analyses suggested that coherent medium dwell-time processing (i.e., integration times of a fraction of a second) could provide improvement In growler detectability over conventional methods; and long dwell-time processing (i.e., integration times on the order of seconds) could provide even further improvement. We report on the performance of two new coherent, medium dwell-time detectors. A third detector which is representative of conventional marine radar serves as a basis for comparison Although significant improvement in growler detectability is achieved, the two coherent detectors still fall short of operational requirements. This leads to the development of a long dwell-time detector which provides considerably better performance. Empirical results indicate that this new detector could well satisfy stringent operational requirements     

Adaptive detection threshold optimization for tracking in clutter

The adaptive optimization of detection thresholds for tracking in clutter is investigated for the probabilistic data association (PDA) filter. Earlier work on this problem by T.E. Fortmann et al. (1985) involved an approximate steady-state analysis of the state error covariance and is only suitable for time-invariant systems. Furthermore, the method requires numerous assumptions and approximations about the error covariance update equation, and uses a cumbersome graphical optimization algorithm. In this work we propose two adaptive schemes for threshold optimization, namely prior and posterior optimization algorithms which minimize the mean-square state estimation error over detection thresholds which depend on data up to the previous and current time-step, respectively. These algorithm are suitable for real-time implementation in time-varying systems. Some simulation results are presented     

CFAR detection in clutter with unknown correlation properties

We develop a constant false-alarm rate (CFAR) approach for detecting a random N-dimensional complex vector in the presence of clutter or interference modeled as a zero mean complex Gaussian vector whose correlation properties are not known to the receiver. It is assumed that estimates of the correlation properties of the clutter/interference may be obtained independently by processing the received vectors from a set of reference cells. We characterize the detection performance of this algorithm when the signal to be detected is modeled as a zero-mean complex Gaussian random vector with unknown correlation matrix. Results show that for a prescribed false alarm probability and a given signal-to-clutter ratio (to be defined in the text), the detectability of Gaussian random signals depends on the eigenvalues of the matrix R_c^-1R_s. The nonsingular matrix R_c and the matrix R_s are the correlation matrices of clutter-plus-noise and signal vectors respectively. It is shown that the “effective” fluctuation statistics of the signal to be detected is determined completely by the eigenvalues of the matrix R_c^-1R_s. For example the signal to be detected has an effective Swerling II fluctuation statistics when all eigenvalues of the above matrix are equal. Swerling I fluctuation statistics results effectively when all eigenvalues except one are equal to zero. Eigenvalue distributions between these two limiting cases correspond to fluctuation statistics that lie between Swerling I and II models     

Covariance matrix estimation for adaptive CFAR detection incompound-Gaussian clutter

We address the estimation of the structure of the covariance matrix and its application to adaptive radar detection of coherent pulse trains in clutter-dominated disturbance modeled as a compound-Gaussian process. For estimation purposes we resort to range cells in spatial proximity with that under test and assume that these cells, free of signal components, can be clustered into groups of data with one and the same value of the texture. We prove that, plugging the proposed estimator of the structure of the covariance matrix into a previously derived detector, based upon the generalized likelihood ratio test (GLRT), leads to an adaptive detector which ensures the constant false alarm rate (CFAR) property with respect to the clutter covariance matrix as well as the statistics of the texture. Finally, we show that this adaptive receiver has an acceptable loss with respect to its nonadaptive counterpart in cases of relevant interest for radar applications     

Optimum time delay detection and tracking

An optimum solution to the time delay tracking problems has been previously achieved by recursively computing the time-delay posterior probability density function (PDF), or time-delay PDF conditioned on knowing all observed data, by numerical means. Any optimum estimate is determined from the posterior PDF. The same approach is extended to an optimum solution for the time delay detection problem with a randomly appearing and disappearing signal. The detector-tracker is suitable for a stand-alone detection and tracking system     

海杂波背景下小目标检测及其运动信息的提取

介绍了在基于Hough变换的检测前跟踪算法检测海杂波背景下的低可观测目标的基础上,将动态规划方法引入其中,从每一条“特征直线”所包含的数据点迹中提取最可能构成目标点迹的数据点的方法。仿真结果表明,将Hough变换与基于动态规划的航迹搜索相结合,能够提高低信噪比条件下的目标检测概率,并能比较准确地提取出目标点迹。然后对提取出来的目标点迹进行Kalman滤波,以估计目标的速度,从而为后续的检测与跟踪提供比较准确的目标信息。     

扫描模式航管监视雷达风电场杂波检测与抑制

近年来,全球风力发电装机容量呈指数增长。研究表明,风轮机对其附近的航管(ATC)监视雷达会产生严重影响。风轮机杂波的有效检测及抑制,对于保证空中交通安全具有重要意义。首先提出了基于回波谱宽特征的航管监视雷达的风轮机杂波检测方法。针对扫描模式下航管监视雷达频谱分辨率较低的问题,将基于自回归(AR)模型的超分辨率方法和质量中心的概念应用于雷达回波的快速谱宽和谱中心估计算法中,提高谱宽估计的精度。其次针对扫描模式下的风轮机回波数据不是一个完整周期数据的问题,基于缺省数据幅度和相位估计(GAPES)算法实现了扫描模式下风轮机雷达回波缺省数据的估计,而后利用风轮机杂波的周期性抑制风轮机杂波。该算法实现了风轮机杂波的有效检测和抑制,并且其不受限于风轮机与飞机目标在同一个距离单元的情况。仿真结果验证了所提方法的有效性。