A branch-and-bound algorithm applied to optimal radar search pattern

In the article, the radar acquisition problem, e.g. the determination of a directional energy allocation sequence, is studied. The radar search pattern goal is the detection of a moving target whose initial location is approximately known. We have turned towards the general search theory where the observer allocates indivisible search efforts while the target presence probability spreads due to its dynamics. A few years ago, a Branch and Bound algorithm was proposed to determine the optimal sequence for a conditionally deterministic target. This operational research algorithm supposes a negative exponential detection function and a one over N detection logic, meaning that the target is declared detected if it has been detected once over a horizon of N looks. We have applied it to a narrow-beam tracking radar attempting to acquire a ballistic target. Non-trivial search patterns, such as expanding-contracting spirals, are obtained.     

The optimal distribution of search effort: existence, uniquenessand the minimax solution

The detection search problem, one of distributing limited resources so as to maximize the detection probability in the single-try search for a concealed target with known probability density, is analyzed. Under fairly general assumptions, the optimal search density uniquely exists when the detection index is governed by the law of diminishing returns and another simple regularity condition. Numerical procedure based on the bisection method, which is guaranteed to converge if the solution uniquely exists, may be used to solve for the optimal search density and the associated Lagrange multiplier. When it is not possible to confidently estimate the target a priori probability density, the minimax solution guarantees a positive detection probability at the expense of degradation in performance     

Range gate straddling loss and joint probability with partial correlation

Straddling loss arises because a target is not always precisely centered in a gate. This loss cannot be estimated by simply averaging the signal voltage or power over target location. The probability of detection must be averaged. We show how to do this and present results for rectangular gates. We also present an equation for estimating joint probability of partially correlated events.     

Detection Performance in Clutter with Variable Resolution

Experiments were conducted to determine the influence of background clutter on target detection criteria. The experiment consisted of placing observers in front of displayed images on a TV monitor. Observer ability to detect military targets embedded in simulated natural and manmade background clutter was measured when there was unlimited viewing time. Results were described in terms of detection probability versus target resolution for various signal to clutter ratios (SCR). The experiments were preceded by a search for a meaningful clutter definition. The selected definition was a statistical measure computed by averaging the standard deviation of contiguous scene cells over the whole scene. The cell size was comparable to the target size. Observer test results confirmed the expectation that the resolution required for a given detection probability was a continuum function of the clutter level. At the lower SCRs the resolution required for a high probability of detection was near 6 line pairs per target (LP/TGT), while at the higher SCRs it was found that a resolution of less than 0.25 LP/TGT would yield a high probability of detection. These results are expected to aid in target acquisition performance modeling and to lead to improved specifications for imaging automatic target screeners.     

Optimization of multiframe target detection schemes

We optimize the performance of multiframe target detection (MFTD) schemes under extended Neyman-Pearson (NP) criteria. Beyond the per-track detection performance for a specific target path in conventional MFTD studies, we optimize the overall detection performance which is averaged over all the potential target paths. It is shown that the overall MFTD performance is limited by the mobility of a target and also that optimality of MFTD performance depends on how fully one ran exploit the information about the target dynamics. We assume a single target situation and then present systematic optimization by formulating the MFTD problems as binary composite hypotheses testing problems. The resulting optimal solutions suggest computationally efficient implementation algorithms which are similar to the Viterbi algorithm for trellis search. The optimal performances for some typical types of target dynamics are evaluated via Monte-Carlo simulation     

对随机运动目标的一种最优搜索算法

针对一维随机恒速运动目标施加离散搜索,基于目标初始位置分布和速度分布,建立运动目标在离散空间中的分布模型,在一定探测宽度条件下,以每次探测最大发现概率为准则,计算离散时间点上的最优探测位置。     

随机恒速运动目标的搜索方程及持续探测概率

根据目标位置的初始分布和速度分布,给出了随机恒速运动目标在任意时刻位置和速度分布密度函数。定义了探测函数、目标存在和探测不成功的联合概率密度函数和目标存活概率函数,建立了基于目标速度分布的搜索方程并给出了其特征迹线解。在目标初始分布和速度分布均为圆正态分布条件下,分析了搜索方程特征迹线的基本特征和持续探测发现概率积分域的形态。给出了一个以直升机吊放声纳探测潜艇为背景的持续探测发现概率的算例,算例表明,对随机恒速运动目标持续探测的发现概率,与对静止目标进行持续探测的发现概率相似,服从时间的指数规律。     

随机运动目标区域持续探测概率的近似模型

研究了随机运动目标区域持续探测的探测概率描述和计算问题。定义了探测函数及目标存在和探测不成功的联合概率密度函数,推导了基于速度分布密度的搜索方程和基于特征迹线的方程的解。鉴于在搜索理论应用中难以获得时变的速度分布,以及搜索方程精确解的复杂性,提出了基于初始速度分布密度的对随机恒速运动目标的一个近似的搜索方程,给出了探测概率的解,并以直升机吊放声纳的一次探测过程,进行了算例仿真。     

Performance of Search via Track-Before-Detect for Distributed Sensor Networks

We consider the search for moving targets over large areas using a network of fixed sensor nodes. The concept of track-before-detect is defined and used to both manage the information between sensors and reduce the likelihood of false searches. We develop expressions for the probability of search success and the probability of reporting false search in this system concept. Using these as performance measures, we examine how the track-before-detect search strategy impacts design choices in these networks, by showing which parameter changes in the sensor design have the greatest impact on improving the desired performance goals.     

Effects of two-way decorrelation on radar detection inscintillation

A 3 dB gain in average signal-to-noise ratio of a monostatic radar operating in scintillation has recently been established both theoretically and observationally. The statistics of two-way scintillation are derived here for the case where the uplink and downlink both experience Rayleigh fading and where there is arbitrary correlation between the scintillation on the two paths. These statistics are then used to compute radar detection curves. A surprising result is obtained. The probability of detection is only weakly dependent (for P _D in the range 0.1 to 0.9) on the degree of uplink-downlink correlation in the scintillation when the average (nonfading) signal-to-noise ratio is constant and when proper account is taken of the change in mean power between the monostatic and bistatic cases. Much larger differences are seen in the detection curves with scintillation compared with nonfading curves (for P_D equal to 0.7 this scintillation loss is about 7 dB). Thus the difference in detection performance of monostatic and bistatic radars is determined primarily by the difference in the radar cross section (RCS) of the target for the two cases     

An intelligent target detection method of UAV swarms based on improved KM algorithm

Complete and efficient detection of unknown targets is the most popular application of UAV swarms. Under most situations, targets have directional characteristics so that they can only be successfully detected within specific angles. In such cases, how to coordinate UAVs and allocate optimal paths for them to efficiently detect all the targets is the primary issue to be solved. In this paper, an intelligent target detection method is proposed for UAV swarms to achieve real-time detection requirements. First, a target-feature-information-based disintegration method is built up to divide the search space into a set of cubes. Theoretically, when the cubes are traversed, all the targets can be detected. Then, a Kuhn-Munkres (KM)-algorithm-based path planning method is proposed for UAVs to traverse the cubes. Finally, to further improve search efficiency, a 3D real-time probability map is established over the search space which estimates the possibility of detecting new targets at each point. This map is adopted to modify the weights in KM algorithm, thereby optimizing the UAVs’ paths during the search process. Simulation results show that with the proposed method, all targets, with detection angle limitations, can be found by UAVs. Moreover, by implementing the 3D probability map, the search efficiency is improved by 23.4%–78.1%.     

Searching tracks

Search theory is the discipline that studies the problem of how best to search for an object when the amount of searching efforts is limited and only probabilities of the possible position of the object are given. Then, the problem is to find the optimal distribution of this total effort that maximizes the probability of detection. Although the general formalism of search theory will be used subsequently, we consider now a radically different problem. The problem is to detect target tracks. In the "classical" search theory, the target is said detected if a detection occurs during any time of the time frame. Here, on the contrary, the target track will be said to be detected if elementary detections occur at various times. That means that there is a test for acceptance (or detection) of a target track and that the problem is to optimize the allocation of the search effort for track detection. So, specific optimization problems are solved by means of the primal-dual formalism, in an original setup. Other aspects concern Markovian targets and two-sided search for which simple and efficient algorithms are derived.     

Beam overlap impact on phased-array target detection

The impact of beam overlap on the probability of detection during a single scan of a phased-array volumetric scan radar is examined. Rectangular and triangular beam packing arrangements are considered. Beam positions near the beam most centered on the target are allowed to contribute to the detection process. The treatment of the impact of beam overlap on target detection for a phased array is consistent with the results that would be achieved by proper use of the search radar range equation     

Automatic target recognition for hyperspectral imagery using high-order statistics

Due to recent advances in hyperspectral imaging sensors many subtle unknown signal sources that cannot be resolved by multispectral sensors can be now uncovered for target detection, discrimination, and identification. Because the information about such sources is generally not available, automatic target recognition (ATR) presents a great challenge to hyperspectral image analysts. Many approaches developed for ATR are based on second-order statistics in the past years. This paper investigates ATR techniques using high order statistics. For ATR in hyperspectral imagery, most interesting targets usually occur with low probabilities and small population and they generally cannot be described by second-order statistics. Under such circumstances, using high-order statistics to perform target detection have been shown by experiments in this paper to be more effective than using second order statistics. In order to further address a challenging issue in determining the number of signal sources needed to be detected, a recently developed concept of virtual dimensionality (VD) is used to estimate this number. The experiments demonstrate that using high-order statistics-based techniques in conjunction with the VD to perform ATR are indeed very effective     

OS-CFAR thresholding in decentralized radar systems

In a decentralized detection scheme, several sensors perform a binary (hard) decision and send the resulting data to a fusion center for the final decision. If each local decision has a constant false alarm rate (CFAR), the final decision is ensured to be CFAR. We consider the case that each local decision is a threshold decision, and the threshold is proportional, through a suitable multiplier, to a linear combination of order statistics (OS) from a reference set (a generalization of the concept of OS thresholding). We address the following problem: given the fusion rule and the relevant system parameters, select each threshold multiplier and the coefficients of each linear combination so as to maximize the overall probability of detection for constrained probability of false alarm. By a Lagrangian maximization approach, we obtain a general solution to this problem and closed-form solutions for the AND and OR fusion logics. A performance assessment is carried on, showing a global superiority of the OR fusion rule in terms of detection probability (for operating conditions matching the design assumptions) and of robustness (when these do not match). We also investigate the effect of the hard quantization performed at the local sensors, by comparing the said performance to those achievable by the same fusion rule in the limiting case of no quantization     

Probability of Detecting a Fluctuating Target Immersed in Both Noise and Clutter

The probability of detecting either a Swerling 1 or Swerling 2 target immersed in both Rayleigh-distributed noise and log-normally distributed clutter is calculated. Results are presented which demonstrate the effect of noise-to-clutter ratio, signal-to-noise ratio, and number of pulses integrated on the detection statistics.     

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.     

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     

A Practical PRSD System for Multiple Target Detection

A block diagram of a practical system using the sequential detection technique for radar detection of multiple targets is given. The system is designed to obtain better detection probability with a lower value of signal-to-noise ratio for a given false-alarm probability and average transmitted power. The total pulse duration is divided into a number of range elements which are tested for the presence or absence of a target before switching the antenna beam to the next position.     

吊放声纳应召搜潜效能的建模与仿真

基于反潜直升机吊放声纳的探测原理及战术使用特点,在目标初始位置概略已知,速度和航向未知的条件下,分析了目标散布规律,建立了搜潜效能分析计算模型,给出了吊放声纳在扩展方形搜索方式下的应召搜潜概率；并采用蒙特卡洛法的基本思想对该计算模型进行了仿真验证,证明了该方法的有效性；最后,基于扩展方形搜索方式,研究了在单机和双机搜潜条件下搜索概率的不同结果,分析了潜艇速度、应召延迟时间、吊放次数等参数 对搜索概率的影响。