Distributed decision fusion using empirical estimation

The problem of optimal data fusion in multiple detection systems is studied in the case where training examples are available, but no a priori information is available about the probability distributions of errors committed by the individual detectors. Earlier solutions to this problem require some knowledge of the error distributions of the detectors, for example, either in a parametric form or in a closed analytical form. Here we show that, given a sufficiently large training sample, an optimal fusion rule can be implemented with an arbitrary level of confidence. We first consider the classical cases of Bayesian rule and Neyman-Pearson test for a system of independent detectors. Then we show a general result that any test function with a suitable Lipschitz property can be implemented with arbitrary precision, based on a training sample whose size is a function of the Lipschitz constant, number of parameters, and empirical measures. The general case subsumes the cases of nonindependent and correlated detectors.     

Detection of Target Maneuver Onset

A classical maneuvering target tracking (MTT) problem (detection of the onset of a target maneuver) is presented in two parts. The first part reviews most traditional maneuver onset detectors and presents results from a comprehensive simulation study and comparison of their performance. Six algorithms for maneuver onset detection are examined: measurement residual chi-square, input estimate chi-square, input estimate significance test, generalized likelihood ratio (GLR), cumulative sum, and marginalized likelihood ratio (MLR) detectors. The second part proposes two novel maneuver onset detectors based on sequential statistical tests. Cumulative sums (CUSUM) type and Shiryayev sequential probability ratio (SSPRT) maneuver onset detectors are developed by using a likelihood marginalization technique to cope with the difficulty that the target maneuver accelerations are unknown. The proposed technique gives explicit solutions for Gaussian-mixture prior distributions, and can be applied to arbitrary prior distributions through Gaussian-mixture approximations. The approach essentially utilizes a~priori information about the maneuver accelerations in typical tracking engagements and thus allows to improve detection performance as compared with traditional maneuver detectors. Simulation results demonstrating the improved capabilities of the proposed onset maneuver detectors are presented.     

Distributed CFAR detection in homogeneous and nonhomogeneousbackgrounds

The performance of distributed constant false alarm rate (CFAR) detection with data fusion both in homogeneous and nonhomogeneous Gaussian backgrounds is analyzed. The ordered statistics (OS) CFAR detectors are employed as local detectors. With a Swerling type I target model, in the homogeneous background, the global probability of detection for a given fixed global probability of false alarm is maximized by optimizing both the threshold multipliers and the order numbers of the local OS-CFAR detectors. In the nonhomogeneous background with multiple targets or clutter edges, the performance of the detection system is analyzed and its performance is compared with the performance of the distributed cell-averaging (CA) CFAR detection system     

Difference beam aided target detection in monopulse radar

The classical detection step in a monopulse radar system is based on the sum beam only,the performance of which is not optimal when target is not at the beam center. Target detection aided by the difference beam can improve the performance at this case. However, the existing difference beam aided target detectors have the problem of performance deterioration at the beam center, which has limited their application in real systems. To solve this problem, two detectors are proposed in this paper. Assuming the monopulse ratio is known, a generalized likelihood ratio test(GLRT) detector is derived, which can be used when targeting information on target direction is available. A practical dual-stage detector is proposed for the case that the monopulse ratio is unknown. Simulation results show that performances of the proposed detectors are superior to that of the classical detector.     

M-correlated sweeps performance analysis of mean-level CFARprocessors in multiple target environments

This paper is devoted to the detection performance evaluation of the mean-level (ML) constant false-alarm rate (CFAR) detectors processing M-correlated sweeps in the presence of interfering targets. The consecutive pulses are assumed to be fluctuating according to the Swerling I model. Exact expressions are derived for the detection probability of the conventional mean-level detector (MLD) and its modified versions under Rayleigh fluctuating target model. Performance for independent sweeps can be easily obtained by setting the sweep-to-sweep correlation coefficient equal to zero. Results are obtained for both homogeneous and nonhomogeneous background environments. It is shown that for fixed M, the relative improvement over the single sweep case increases as the correlation between sweeps decreases. For the same parameter values, the minimum MLD has the best performance in the presence of extraneous target returns among the reference noise samples     

Adaptive cell-averaging CFAR detection in distributed sensornetworks

The problem of adaptive cell-averaging constant false-alarm rate (CFAR) detection is considered for two distributed sensor network topologies, namely the parallel and the tandem topologies. The compressed data transmitted amongst the detectors is assumed to be in the form of decisions. The overall systems are optimized to yield the maximum probability of detection for a fixed probability of false alarm. The performance of the systems is also analyzed     

Performance analysis of linearly combined order statistic CFARdetectors

Linearly combined order statistic (LCOS) constant false-alarm rate (CFAR) detectors are examined for efficient and robust threshold estimation applied to exponentially distributed background observations for improved detection. Two optimization philosophies have been employed to determine the weighting coefficients of the order statistics. The first method optimizes the coefficients to obtain efficient estimates of clutter referred to the censored maximum likelihood (CML) and best linear unbiased (BLU) CFAR detectors. The second optimization involves maximizing the probability of detection under Swerling II targets and is referred to as the most powerful linear (MPL) CFAR detector. The BLU-CFAR detector assumes no knowledge of the target distribution in contrast to the MPL-CFAR detector which requires partial knowledge of the target distribution. The design of these CFAR detectors and the probability of detection performance are mathematically analyzed for background observations having homogeneous and heterogeneous distributions wherein the trade-offs between robustness and detection performance are illustrated     

Performance Analysis of the Censored Mean-Level Detector

The censored mean-level detector (CMLD) is an alternative to the mean-level detector that achieves robust detection performance in a multiple-target environment by censoring several of the largest samples of the maximum likelihood estimate of the background noise level. Here we derive exact expressions for the probability of detection of the CMLD in a multiple-target environment when a fixed number of Swerling II targets are present. The primary target is modeled by Swerling case II, and only single-pulse processing is analyzed. Optimization of the CMLD parameters is considered, and a comparison to other detectors is presented.     

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     

A Suboptimum Rank Test for Nonparametric Radar Detection

The optimum rank detector structure, in the Neyman-Pearson sense and under Gaussian noise conditions, is approximated by a suboptimum structure that depends on an adjustable parameter. This new rank detector, which operates on radar video signal, includes other well-known detectors as particular cases. The asymptotic relative efficiency (ARE) of the proposed rank detector is computed, with its maximum value the ARE of the locally optimum rank detector (LORD). The detection probability versus signal-to-noise ratio, and the effects of interfering targets are also calculated by Monte-Carlo simulations for different parameter values.     

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     

Quickest detection for sequential decentralized decision systems

Quickest detection procedures are techniques used to detect sudden or abrupt changes (also called disorders) in the statistics of a random process. The goal is to determine as soon as possible that the change occurred, while at the same time minimizing the chance of falsely signaling the occurrence of a disorder before the change. In this work the distributed quickest detection problem when the disorder occurs at an unknown time is considered. The distributed local detectors utilize a simple summing device and threshold comparator, with a binary decision at the output. At the fusion center, the optimal maximum likelihood (ML) procedure is analyzed and compared with the more practical Page procedure for quickest detection. It is shown that the two procedures have practically equivalent performance. For the important case of unknown disorder magnitudes, a version of the Hinkley procedure is also examined. Next, a simple method for choosing the thresholds of the local detectors based on an asymptotic performance measure is presented. The problem of selecting the local thresholds usually requires optimizing a constrained set of nonlinear equations; our method admits a separable problem, leading to straightforward calculations. A sensitivity analysis reveals that the resulting threshold settings are optimal for practical purposes. The issue of which sample size to use for the local detectors is investigated, and the tradeoff between decision delay and communication cost is evaluated. For strong signals, it is shown that the relative performance deteriorates as the sample size increases, that is, as the system cost decreases. Surprisingly, for the weak signal case, lowering the system cost (increasing the sample size) does not necessarily result in a degradation of performance     

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.     

Envelope Threshold Detection in a Class of Non-Gaussian Interference

This paper considers the detection of a sinusoidal or chirp signal imbedded in wideband FM interference (as might be generated by some types of active jamming), such that after pulse compression or other integration, the interference can be approximated by a sum of sinusoids of independent phase. The detection probability in such non-Gaussian noise is compared to that for Gaussian noise, with the Gaussian result approached, as required, in the limit that the number of sinusoids in the sum increases without bound. For detection using a comparison of the envelope with a threshold which yields a given false-alarm probability (CFAR detection), the detection probability is improved over the case of Gaussian noise, so that the usual approach basing the design on Gaussian noise would be conservative. Using a threshold determined from the envelope mean, the FM interference yields a lower false-alarm probability than for Gaussian noise, with detection probability only slightly degraded.     

Protection of PSK Communication Systems with Adaptive Arrays

The performance of binary phase-shift-keyed (BPSK), binarydifferential phase-shift-keyed (DPSK), and quadrature phase-shift-keyed(QPSK) communication systems that use adaptive arrayantennas for interference rejection is examined. The case where thedesired signal is corrupted by continuous wave (CW) interference isspecifically addressed. The performance of the adaptive array andthe ideal BPSK, DPSK, and QPSK detectors are evaluated first andthe results of these calculations are combined to determine theoverall system performance. The bit-error probability at the systemoutput is used as the performance measure. Several examples arepresented which illustrate the effects of signal powers, arrivalangles, frequencies, and the array input bandwidth.     

Performance of receivers with linear detectors

The false-alarm and detection probabilities of a receiver summing M independent outputs of a linear detector are calculated by numerical saddlepoint integration. The saddlepoint approximation is also considered. Both constant-amplitude and Rayleigh-fading signals are treated, and the relative efficiency of the quadratic and the linear detectors for these is calculated for a broad range of values of M . The numerical integration method is the more efficient, the smaller the false-alarm probability or the false-dismissal probability, that is, under just those conditions for which the terms in the Gram-Charlier series oscillate most violently and the series becomes least reliable. The simpler saddlepoint approximation yields values that in those same regions have been found close enough to the exact probabilities to be adequate for most engineering purposes. The larger the number M of samples, the more efficient methods are     

Algorithms for Spatial Laser Beacon Acquisition

The pointing system for optical data transmission over unguided channels uses a return beacon from the receiver back to the transmitter to aid the reciprocal alignment of the two stations. We concentrate on CW or pulsed-beacon acquisition with array detectors in the presence of extended clutter in addition to background and receiver noises. Acquisition in the presence of a single interferer (jammer) is also considered. A maximum likelihood (ML) approach is used when preliminary scene information is available. In the case of unknown scenario, a picture-picture subtraction algorithm is considered for the pulsed laser. Performance is evaluated in terms of probability of an acquisition error for Poisson statistics of the photodetector output.     

Detectability of signals in Laplace noise

Closed-form expressions for the false-alarm and detection probabilities attained by the optimum and the linear detectors of a positive signal in n independent samples of noise having a bilateral exponential or Laplace distribution require lengthy computation when n is large, and those for the optimum detector suffer from round-off error because their terms alternate in sign. It is shown how the method of saddlepoint integration can be conveniently applied to compute these probabilities, and numerical comparisons of the accuracies of the methods are presented. The relative efficiency of the two detectors is calculated as a function of n and found to approach the asymptotic value of 2 very slowly     

基于双边截断的双参数海上风电站 SAR图像 CFAR检测

文章提出了 1种基于双边截断的双参数海上风电站 SAR图像 CFAR检测器 DTCS-TPCFAR,目的是提高在具有多个目标海上区域和石油泄漏区域等环境下对海上风电站的检测性能。DTCS-TPCFAR所提出的双边截断杂波的方法,能够同时消除高强度和低强度异常值的干扰,同时保留真实的杂波样本。通过使用最大似然估计计算双边截断后样本的均值和标准差,然后通过这 2个参数估计值计算出截断阈值,最后再结合指定的虚警率(Probability of False Alarm,PFA)来对测试单元(Test Cell,TC)进行判断,完成最终的目标检测。这也是首次将 CFAR检测器用于检测海上风电站。文章通过 Sentinel-1数据集来验证该方法的有效性。实验结果表明,文章所提出的算法在相同指定虚警率下,具有更高的检测率(Detection Rate,DR)和更低的误报率(False Alarm Rate,FAR)。     

Detectors for Multiomial Input

The binary detection problem is considered. Under an arbitrary noise environment, the input sample space can be transformed into a multinomial vector. Based on observations of this vector, the Neyman-Pearson optimal detector is developed for a known signal. When the signal strength is unknown, the likelihood ratio principle is followed to obtain consistent tests which use the Pearson's chisquare statistic. The resulting detectors are compared to others in terms of asymptotic relative efficiency under some actual noise distributions.