Energy Detection of a Random Process in Colored Gaussian Noise

A likelihood receiver for a Gaussian random signal process in colored Gaussian noise is realized with a quadratic form of a finite-duration sample of the input process. Such a receiver may be called a "filtered energy detector." The output statistic is compared with a threshold and if the threshold is exceeded, a signal is said to be present. False alarm and detection probabilities may be estimated if tabulated distributions can be fitted to the actual distributions of the test statistic which are unknown. Gamma distributions were fitted to the conditional probability densities of the output statistic by equating means and variances, formulas for which are derived assuming a large observation interval. A numerical example is given for the case in which the noise and signal processes have spectral densities of the same shape or are flat. The optimum filter turns out to be a band-limited noise whitener. The factors governing false alarm and detection probabilities are the filter bandwidth, the sample duration, and the signal level compared to the noise. Two sets of receiver operating characteristic curves are presented to complete the example.     

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     

Coherent detection in Laplace noise

The discrete-time detection of a time-varying, additive signal in independent Laplace noise is considered. Previous efforts in this area have been restricted to the constant signal, and identically distributed noise case. Theoretical (closed form) expressions for the false alarm and detection probabilities are developed for both the Neyman-Pearson optimal detector and the classical matched filter detector. Comparisons between the two detectors are made which illustrate the effects of signal-to-noise power ratio and sample size for certain false alarm and detection probability constraints. In view of the fact that the optimal Laplace detector is not UMP, we also investigate the effect of signal amplitude mismatch     

The Detection Performance of the Siebert and Dicke-Fix CFAR Radar Detectors

The Siebert and the Dicke-fix CFAR radar detectors, used to maintain a constant false alarm rate (CFAR) in radar receivers under very similar circumstances, are considered. The Siebert detector represents the maximum-likelihood detection procedure for a signal in Gaussian noise of unknown power level, whereas the Dicke-fix makes use of a bandpass limiter to normalize the input and thus ensure a constant false alarm rate. The detection performance of the two detectors is determined and a comparison shows that over a wide range of parameters, the Dicke-fix introduces a loss which is approximately 1 B larger than for the Siebert detector.     

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     

基于杂波对消-自聚焦的多通道SAR-GMTI

对超高频(UHF)波段多通道合成孔径雷达(SAR)动目标检测技术进行研究,解决了长相干积累时间导致动目标在方位向散焦严重的问题。采用分块自聚焦技术对多通道SAR地面移动目标指示(GMTI)系统自适应杂波抑制后的SAR图像进行处理,改善杂波抑制后的SAR图像中动目标的聚焦情况,增强动目标与周围剩余杂波的对比度,进而提高恒虚警率(CFAR)检测的性能。与传统杂波抑制后直接进行CFAR检测方法相比较,该方法降低了检测虚警概率。实测数据处理结果显示动目标的信杂比明显提高,动目标方位向聚焦成功,证明了该方法的有效性。     

Importance sampling for characterizing STAP detectors

This paper describes the development of adaptive importance sampling (IS) techniques for estimating false alarm probabilities of detectors that use space-time adaptive processing (STAP) algorithms. Fast simulation using IS methods has been notably successful in the study of conventional constant false alarm rate (CFAR) radar detectors, and in several other applications. The principal objectives here are to examine the viability of using these methods for STAP detectors, develop them into powerful analysis and design algorithms and, in the long term, use them for synthesizing novel detection structures. The adaptive matched filter (AMF) detector has been analyzed successfully using fast simulation. Of two biasing methods considered, one is implemented and shown to yield good results. The important problem of detector threshold determination is also addressed, with matching outcome. As an illustration of the power of these methods, two variants of the square-law AMF detector that are thought to be robust under heterogeneous clutter conditions have also been successfully investigated. These are the envelope-law and geometric-mean STAP detectors. Their CFAR property is established and performance evaluated. It turns out the variants have detection performances better than those of the AMF detector for training data contaminated by interferers. In summary, the work reported here paves the way for development of advanced estimation techniques that can facilitate design of powerful and robust detection algorithms     

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     

基于正交小波变换的目标检测方法

理论分析表明,独立高斯噪声经过正交小波变换后保持方差和独立性不变。基于Mallat的小波多分辨分析,通过对小波系数进行平方律处理,建立了基于正交小波变换的恒虚警率检测器模型,推导了相应的虚警和检测概率公式,分析了噪声未知情况下小波系数序列长度对检测性能的影响,并给出了合适的长度值。实验结果表明,所提出的检测器能满足不同虚警概率和杂波背景的要求,具有较好自适应性。     

基于子空间投影的未知背景航拍高光谱图像恒虚警目标检测

针对航拍高光谱图像中未知背景地物特征条件下小目标的检测问题,给出一种检测算法。利用目标的低概率特性,通过模糊聚类获取高光谱图像中背景的光谱特性;然后将高光谱数据向背景光谱信号的正交子空间及目标信号子空间投影以抑制背景和噪声信号;最后在特征层利用广义似然比检验构造出具有恒虚警特性的检测器,完成融合检测过程。理论分析和实验结果表明了算法的有效性。     

Multistatic-Radar Binomial Detection

The performance of multistatic-radar binomial detectors is investigated. Although conceptually similar to the well-knwn "M-out-of-N" detector frequently considered for monostatic systems, the multistatic detector must cope with false alarms generated by target et ghosting as well as by noise threshold crossings. A procedure for deriving the detection statistics of multistatic binomial detectors ors is presented. The procedure is applied to derive the detection probabilities for a spectrum of false alarm probabilities, target densities, and numbers of radar receivers.     

Radar detection and preclassification based on multiple hypothesis

This work presents a single-scan-processing approach to the problem of detecting and preclassifying a radar target that may belong to different target classes. The proposed method is based on a hybrid of the maximum a posteriori (MAP) and Neyman-Pearson (NP) criteria and guarantees the desired constant false alarm rate (CFAR) behavior. The targets are modeled as subspace random signals having zero mean and given covariance matrix. Different target classes are discriminated based on their different signal subspaces, which are specified by their corresponding projection matrices. Performance is investigated by means of numerical analysis and Monte Carlo simulation in terms of probability of false alarm, detection and classification; the extra signal-to-noise power ratio (SNR) necessary to classify once target detection has occurred is also derived.     

Detection of stochastic signals in the frequency domain

The optimum detector for a random signal, the estimator-correlator, is difficult to implement. If the power spectral density (PSD) of a continuous time signal is known, a locally optimum detector is available. It maximizes the deflection ratio (DR), a measure of the detector output signal-to-noise ratio (SNR). A discrete version of this detector is developed here, called the discrete-MDRD, which takes a weighted sum of the spectral components of the signal data as the detection statistic. Its derivation is applicable to nonwhite noise samples as well. A comparison of this new detector against three other common types, through their DR values and simulation results, reveals that the discrete-MDRD is near optimal at low SNRs. When the PSD of a signal is not known, a common test statistic is the peak of the PSD of the data. To reduce spectral variations, the PSD estimator first divides the data sequence into several segments and then forms the averaged PSD estimate. The segment length affects the DR values; the length that maximizes the DR is approximately the reciprocal of the signal bandwidth. Thus for unknown signal PSD, a detector that approaches the maximum DR is realizable from just the knowledge of the signal bandwidth, which is normally available. Examples and simulation results are provided to illustrate the properties and performance of the new detector     

Second time around radar return suppression using PRI modulation

A technique for suppressing second-time-around radar returns using pulse-repetition interval (PRI) modulation is presented and analyzed. It is shown that a staggered PRI radar system can offer considerable improvement over a nonstaggered radar system in rejecting second-time-around returns which cause false alarms. This improvement is a function of detector implementation (noncoherent integrator or binary integrator), the number of staggered PRIs, the quiescent false alarm number, the Swerling number of the false return, the transmitted signal power, the second-time-around noise power, and the quiescent noise power of the radar. Small changes in transmitted signal power can be traded off with the quiescent false alarm number to suppress the bogus return significantly. In addition, for a noncoherent integrator, all other parameters being equal, if the second-time-around return is a Swerling case II or IV target, then there is an optimum number of staggered PRIs that can be chosen to minimize the likelihood of its detection. It is also shown that the binary integrator significantly reduces the number of second-time-around return detections when compared with the noncoherent integrator. However, there is an accompanying loss of detection     

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     

A variably trimmed mean CFAR radar detector

A variably trimmed mean (VTM) constant false alarm rate (CFAR) detector in which the threshold is determined by processing a linear combination of a group of ordered samples in each window is introduced. Unlike the trimmed mean detector, the number of ordered samples that require further processing is allowed to vary according to a data-dependent rule. It is demonstrated that the VTM detector exhibits performance characteristics that are independent of the total (stationary) noise power. Simulated performance results are presented for regions of clutter power transitions and for multiple target environments to illustrate the possible improvement over the order-statistic detector that can be obtained by using a VTM detector     

A new distributed constant false alarm rate detector

A new constant false alarm rate (CFAR) test termed signal-plus-order statistic CFAR (S+OS) using distributed sensors is developed. The sensor modeling assumes that the returns of the test cells of different sensors are all independent and identically distributed In the S+OS scheme, each sensor transmits its test sample and a designated order statistic of its surrounding observations to the fusion center. At the fusion center, the sum of the samples of the test cells is compared with a constant multiplied by a function of the order statistics. For a two-sensor network, the functions considered are the minimum of the order statistics (mOS) and the maximum of the order statistics (MOS). For detecting a Rayleigh fluctuating target in Gaussian noise, closed-form expressions for the false alarm and detection probabilities are obtained. The numerical results indicate that the performance of the MOS detector is very close to that of a centralized OS-CFAR and it performs considerably better than the OS-CFAR detector with the AND or the OR fusion rule. Extension to an N-sensor network is also considered, and general equations for the false alarm probabilities under homogeneous and nonhomogeneous background noise are presented.     

Two Methods of Spectral Estimation for SARSAT Signals

Search and rescue satellite aided tracking (SARSAT) depends on the processing of emergency locator transmitter (ELT) signals which are received by a satellite in low polar orbit. Since the signal from a distressed vehicle is normally immersed in a background of other ELT signals (false alarms), interference, and noise, different methods of spectral estimation can provide advantages in estimating carrier frequency. A comparison between average spectrum and minimum spectrum for several real signals is provided here.     

Adaptive array CFAR detection

Presented here is a large class of adaptive array detection algorithms with constant false alarm rate (CFAR), so that the false alarm rate can be set to any preassigned number without knowledge of the noise covariance matrix. This class map incorporate any usual method of cell averaging and any method for array weight vector synthesis. A sufficient condition for CFAR is derived, which is easy to satisfy in practice. Basic system parameters are discussed. An example of detection performance for a simple cell-averaging detector, in which the array weight vector is synthesized by the method of diagonal loading, is provided using Monte Carlo simulations     

A comparison of two adaptive detection schemes

Two schemes for adaptive detection are compared: Kelly's generalized likelihood ratio test (GLRT) and the mean level adaptive detector (MLAD). Detection performance, P_D, is predicted for the two schemes under the assumptions that the input noises are zero-mean complex Gaussian random variables that are temporally independent but spatially correlated; and the amplitude of the desired signal is Rayleigh distributed. P_D is computed as a function of the false alarm probability, the number of input channels, the number of independent samples per channel, and the matched filtered output signal-to-noise (S/N) power ratio. In this analysis the GLRT is shown to have better detection performance than the MLAD. The difference in detection performance increases as one uses fewer input samples. However, the required number of samples necessary to have only a 3 dB detection loss for both detection schemes is approximately the same. This is significant since for the present, the MLAD is considerably less complex to implement than the GLRT