A new CFAR sidelobe canceler algorithm for radar

Signal or target detection is sometimes complicated by the presence of strong interference. When this interference occurs mainly in the sidelobes of the antenna pattern, a solution to this problem is realized through a sidelobe canceler (SLC) implementation. Since the false-alarm probability is a system parameter of special importance in radar, an interference-canceling technique for radar application should maintain the false-alarm probability constant over a wide range of incident interference power. With the requirements of sidelobe interference cancellation and constant false alarm rate (CFAR), a new algorithm for radar detection in the presence of sidelobe interference is developed from the generalized likelihood ratio test of Neyman-Pearson. In this development, the received interference is modeled as a nonstationary but slowly varying Gaussian random process. Cancellation of the sidelobe interference is based upon a `synchronous' estimate of the spatial covariance of the interference for the range gate being tested. This algorithm provides a fixed false-alarm rate and a fixed threshold which depend only upon the parameters of the algorithm     

一种变信噪比条件下的恒虚警野值检测方法

野值检测又称异常值检测,是模式识别、机器智能和知识发现等领域经常面临的一个问题。当出现环境失配,数据信噪比（SNR）发生变化时,测试样本和训练样本所含噪声会有不同方差,以往的野值检测方法在虚警控制方面将会失效。针对这一问题,提出一种基于归一化残差（NR）的野值检测方法。该方法首先根据所需虚警概率和噪声方差变化情况确定野值检测门限,其次基于训练样本计算待考查模式的NR值,再比较NR值与检测门限的相对大小,从而判断待考查模式是否为野值。这一方法所依赖的检测门限对所需虚警率和噪声方差变化具有适应能力,因此可以在变信噪比条件下实现恒虚警（CFAR）野值检测。仿真实验验证了所提方法在虚警控制和野值检测方面的优越性能。     

An algorithm for detection of moving optical targets

An algorithm is described for detecting moving optical targets against spatially nonstationary Poisson background and noise. The algorithm has applications in optical detection of objects such as meteors, asteroids, and satellites against a stellar background. A maximum-likelihood approach is used which results in reducing interference from stars. It is shown that by choosing a detection threshold to provide a constant false alarm rate, the resulting algorithm is independent of the signal strength of the target. An analysis of this algorithm is presented, showing the probability of detection for several false-alarm rates     

Detection Performance of a Mean-Level Threshold

The problem of detecting signals in nonstationary clutter is met by presenting a mean-level or adaptive threshold which adjusts to the changing background level. Such a threshold performs better than a fixed threshold that must be set for the highest amplitude clutter. However, the mean-level threshold does not perform as well for stationary noise as a fixed threshold set at the proper value. One measure of effectiveness of an adaptive threshold is its performance in stationary noise (compared to the optimum fixed threshold) for a specified speed of response. For the mean-level threshold, a simple mathematical solution is found for the detection probability when the noise is stationary and the signal scintillates rapidly. The performance is evaluated for a wide range of mean-level-threshold time constants and for several false-alarm probabilities. The results are presented graphically. As an example, the mean-level threshold suffers 3 dB in detectability (equivalent signal-to-noise ratio) in the presence of stationary noise as compared to the optimum fixed threshold for 50-percent probability of detection, false-alarm probability of 10-8, and an adjustment time of 15 times the signal duration.     

Optimum array detector for a weak signal in unknown noise

We study the design of constant false-alarm rate (CFAR) tests for detecting a rank-one signal in the presence of background Gaussian noise with unknown spatial covariance. We look at invariant tests, i.e., those tests whose performance is independent of the nuisance parameters, like the background noise covariance. Such tests are shown to have the desirable CFAR property. We characterize the class of all such tests by showing that any invariant decision statistic can be written as a function of two basic statistics which are in fact the adaptive matched filter (AMF) statistic and Kelly's generalized likelihood ratio statistic. Further, we establish an optimum test in the limit of low signal-to-noise ratio (SNR), the locally most powerful invariant (LMPI) test. We also derive the bound for the probability of detection of any invariant detector, at a fixed false-alarm rate, and compare the LMPI and the published detectors (Kelly and AMF) to it     

非线性非高斯模型的高斯和PHD滤波算法(英文)

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.     

Performance of a Two-Sample Mann-Whitney Nonparametric Detector in a Radar Application

The detection of signals in an unknown, typically non-Gaussian noise environment, while attempting to maintain a constant false-alarm rate, is a common problem in radar and sonar. The raw receiver data is commonly processed initially by a bank of frequency filters. The further processing of the outputs from the filter bank by a two-sample Mann-Whitney detector is considered. When the noise statistics in all filters are identical, the Mann-Whitney detector is distribution free, i. e., the false-alarm probability may be prescribed in advance regardless of the precise form of the noise statistics. The primary purpose of this paper is to demonstrate the potential advantage of nonparametric detectors over conventional detectors. The signal detection performance of the Mann-Whitney detector is compared to that of an ordinary linear envelope detector plus integrator in the presence of Gaussian and several hypothetical forms of non-Gaussian noise. This comparison is made for both uniform and nonuniform distributions of noise power across the filter bank. Besides providing a much more constant false-alarm rate than the conventional detector, the Mann-Whitney detector's signal detection performance is found also to be much less sensitive to the form of the noise statistics. In one case, its detection sensitivity is found to be 11 dB better than that of the conventional detector. Even when the noise power density is made moderately nonuniform across the filter bank, the detection performance of the Mann-Whitney detector is found not to be significantly affected.     

Weak Signal Detection in Non-Gaussian Noise of Unknown Level

An adaptive threshold detector to test for the presence of a weak signal in additive non-Gaussian noise of unknown level is discussed. The detector consists of a locally optimum detector, a noise level estimator, and a decision device. The detection threshold is made adaptive according to the information provided by the noise level estimator in order to keep a fixed false-alarm probability. Asymptotic performance characteristics are obtained indicating relationships among the basic system parameters such as the reference noise sample size and the underlying noise statistics. It is shown that, as the reference noise sample size is made sufficiently large, the adaptive threshold detector attains the performance of a corresponding locally optimum detector for detecting the weak signal were the noise level known.     

Polygonal Detection Thresholds for In-Phase and Quadrature Channels

A joint detection threshold corresponding to a circle around the origin of the in-phase and quadrature components of a radar IF process is equivalent to envelope thresholding. Square and octagonal approximations to the circle are evaluated for prescribed false-alarm probabilities and the variation of detection probability with signal phase.     

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.     

Simple Expressions for Determining Radar Detection Thresholds

The threshold value required to obtain a specified false-alarm probability, when postdetection integration follows a square-law or an envelope detector, is frequently needed in theoretical and practical studies of radar signal processor performance. The determination of such threshold values requires a substantial numerical computational effort. In this correspondence, simple expressions are presented with which these thresholds can be determined with excellent accuracy using only a scientific calculator.     

Decentralized CFAR signal detection

The authors develop the theory of CA-CFAR (cell-averaging constant false-alarm rate) detection using multiple sensors and data fusion, where detection decisions are transmitted from each CA-CFAR detector to the data fusion center. The overall decision is obtained at the data fusion center based on some k out of n fusion rule. For a Swerling target model I embedded in white Gaussian noise of unknown level, the authors obtain the optimum threshold multipliers of the individual detectors. At the data fusion center, they derive an expression for the overall probability of detection while the overall probability of false alarm is maintained at the desired value for the given fusion rules. An example is presented showing numerical results     

Interference Effects of Pseudo-Random Frequency-Hopping Signals

When a pseudo-random frequency-hopping signal is intercepted by a conventional receiver operating within the same frequency band, the interfering signal has the form of a pulse-amplitude modulated signal. Each pulse amplitude is dependent upon the hopping frequency and the selectivity characteristic of the victim receiver. The probability density function for the interfering pulse amplitude prior to demodulation is determined when the probability density function for the hopping frequency is uniform and the victim-receiver characteristic is 1) ideal flat bandpass, 2) single tuned, and 3) Gaussian shaped. It is shown that the average interfering pulse amplitude and interference power decrease as the frequency-hopping bandwidth increases with respect to the victim-receiver bandwidth. Fast Fourier transform computer techniques are used to obtain the probability density function of the interference amplitude in a Gaussian receiver when several (from 2 to 10) pseudo-random frequency-hopping systems are simultaneously using the same frequency band. The probability that the interference exceeds a prescribed threshold value is computed from the derived probability density functions. This probability may be used in signal-to-interference ratio calculations, to describe the capture effect, or to compute the expected number of clicks produced in an FM discriminator.     

Performance of Sidelobe Blanking Systems

Sidelobe blanking systems are useful in preventing acquisition of strong targets in the antenna sidelobes and also in rejecting pulsed interference originating in the sidelobes. The analysis of a common two-channel system is presented in which the relationship between the probability of main-lobe detection and the probability of sidelobe detection are given in terms of false-alarm probability, signal-to-noise ratio, and the ratio of sidelobe levels of the two channels. The numerical results given provide a basis for the selection of the sidelobe blanking channel antenna gain and threshold levels.     

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     

Sonar Array Detection of Gaussian Signals in Gaussian Noise of Unknown Power

A statistical test is postulated for detecting, with an M-element hydrophone array, a Gaussian signal in spatially independent Gaussian noise of unknown power. The test is an extension of the uniformly-most-powerful (UMP) unbiased test for a two-element array. The output signal-to-noise ratio of the test is calculated and, for a large number of independent space-time samples, is shown to be no better than a mean-level detector (MLD). Receiver operating characteristic curves (ROC) for the MLD are computed and compared to the ROC curves for the optimum (Bayes) parametric detector. The input signal-to-noise power ratios required to provide a detection probability of 0.5 differ by less than 0.2 dB for a fifty-element array with wide variation in false-alarm probability and time-bandwidth product. This result suggests that both the extended bivariate UMP unbiased test and the MLD perform close to the unknown UMP unbiased test for independence of a multivariate Gaussian distribution.     

Improved multilevel quantization for detection of narrowbandsignals

Nearly optimum quantization levels for multileveled quantizers in radar receivers and distributed-detection are calculated for preassigned false-alarm probability Q₀ by maximizing the detection probability Q_d after replacing both Q ₀ and (1-Q_d) by the saddlepoint approximations. Narrowband signals of random phase and with both fixed and Rayleigh-fading amplitudes in Gaussian noise are treated, and the loss in signal detectability incurred by quantization is estimated     

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     

Calculating Detection Probabilities for Adaptive Thresholds

In calculating detection probabiities for radar and sonar systems it is usually assumed that the threshold required to yield a certain probability of false alarm is known. This is often not the case for real systems and therefore the threshold must be estimated using some measure related to the test statistic. This paper presents a calculation technique that handles estimated (adaptive) thresholds in a general framework that can be applied easily to many detection problems. False alarm and detection probabilities are calculated from the characteristic function of the noise or signal plus noise variate and the characteristic function of the threshold estimate. To illustrate the method the detection performance of overlapped discrete Fourier transforms (DFTs) is calculated for a narrowband Gaussian target signal.     

Data-Adaptive Detection of a Weak Signal

Motivated by a form of the likelihood-ratio-tesf statistic for detection of a rank-one Gaussian signal in colored Gaussian noise, we apply our earlier technique for estimation of a low-rank signal to the problem of estimating and subtracting the waveform of a strong sinusoidal interference prior to detection of a weak sinusoidal signal. We consider the difficult case in which samples of data are taken over a short interval of time or space and the frequencies of the sinusoidal signal and sinusoidal interference are more closely spaced than the reciprocal of the extent of the aperture. The method can be applied to cases of nonsinusoidal and/or random signals and interference. The most important assumption is that when the samples of the interference are arranged in matrix form the matrix is approximately of low rank in the sense that, with high probability, the interference-only matrix can be well approximated by a matrix of low rank.