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。     

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。     

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.     

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.     

探测点序列的最优化与简化计算方法

在搜索状态建模和求解一阶搜索状态方程的特征迹线解的基础上,建立了对随机运动进行离散时间探测的发现概率最优控制模型,结合动态规划原理给出一种最优探测点序列的逼近算法,并给出了短时计算的算法简化形式。在满足一阶搜索状态方程的随机恒速目标条件以及有限指数探测函数条件下,将给出的算法及其简化形式应用到算例。算例表明,当随机恒速运动目标初始位置和速度均服从圆正态分布时,该算法及其简化形式均能够由任意给定的初始探测点序列优化收敛到满足精度要求的最优探测点序列。     

Overall Detection Probability for Fluctuating and Nonfluctuating Target Models

The power selection of a search radar is best obtained in the framework of the overall detection probability concept. This concept is here applied to fluctuating target models for single- and multiple-scan detection. The approach combines the pulse train statistics over the detection interval to the mean target statistics over the search region and directly relates the overall detection probability POD to a single system parameter ?0, proportional to the transmitted power.     

Optimal Target t Designation Techniques

Studies of signal processing techniques are presented for achieving optimal autonomous acquisition of stationary targets located in a moderately intense nonhomogeneous radar ground clutter background. The process of target acquisition comprises three basic functions: 1) target detection, 2) target selection or designation, and 3) reacquiring the target for tracking. It is the second of these functions, i.e., autonomous designation of a target, that is the subject of this discussion. Theoretical analyses and predictions of the probability of correct target designation for two acquisition search methods are presented and compared with results achieved using real radar imagery.     

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%.     

An Upper Bound on Detection Probability for Fluctuating Signals

In the theory of signal detectability, the signal-to-noise ratio (SNR), defined as the quotient of the average received signal energy and the spectral density of the white Gaussian noise, is a fundamental parameter. For a signal which is exactly known, or known except for a random phase, this ratio uniquely defines the detection performance which can be achieved with a matched filter receiver. However, when the signal amplitude is a random parameter, the detection performance is changed and must be determined from the probability density function (pdf) of the amplitude. Relative to the case of a constant signal amplitude, such signal amplitude fluctuation usually degrades performance when a high probability of detection (Pd) is required, but improves performance at low values of Pd; the corresponding change in the required SNR is the so-called signal fluctuation loss Lf. Thus, since Lf in some cases represents an improvement in performance for low values of Pd, a question of at least theoretical interest is: how large might this improvement be, when the class of all signal amplitude pdf's is considered. The solution, presented here, results in a lower bound on the signal fluctuation loss Lf as a function of Pd, or equivalently an upper bound on Pd as a function of SNR. The corresponding most favorable pdf was determined using the Lagrange multiplier technique and results of a numerical maximization are included to provide insight into the general properties of the solution.     

联合截获威胁下的雷达射频隐身目标搜索算法

针对基于射频(RF)隐身需求的机载雷达目标搜索问题进行了研究。通过分析实际作战中射频辐射面临的截获威胁,提出了一种基于联合截获威胁的射频隐身性能表征方法,并给出了具体的值估算方法;对机载雷达搜索任务中辐射参数的优化问题进行了建模,并采用优化算法对目标函数进行求解。通过分析典型情景下解集的分布特点,给出了从最优解集中选取最终解的方法。结果表明,提出的射频隐身性能表征方法能更好地反映截获实现过程的多域需求,提出的雷达搜索方法能够在保证探测性能的同时,提高射频隐身性能和搜索速度,能够为相控阵雷达搜索任务中参数的优化控制提供方法和依据。     

Sequential track extraction

Sensors like radar or sonar usually produce data on the basis of a single frame of observation: target detections. The detection performance is described by quantities like detection probability Pd and false alarm density f. A different task of detection is formation of tracks of targets unknown in number from data of multiple consecutive frames of observation. This leads to quantities which are of a higher level of abstraction: extracted tracks. This again is a detection process. Under benign conditions (high Pd, low f and well separated targets) conventional methods of track initiation are recommended to solve a simple task. However, under hard conditions the process of track extraction is known to be difficult. We here concentrate on the case of well separated targets and derive an optimal combinatorial method which can be used under hard operating conditions. The method relates to MHT (multiple hypothesis tracking), uses a sequential likelihood ratio test and derives benefit from processing signal strength information. The performance of the track extraction method is described by parameters such as detection probability and false detection rate on track level, while Pd and f are input parameters which relate to the signal-to-noise interference ratio (SNIR), the clutter density, and the threshold set for target detection. In particular the average test lengths are analyzed parametrically as they are relevant for a user to estimate the time delay for track formation under hard conditions     

PHD filters of higher order in target number

The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this is indeed possible. We derive a closed-form cardinalized PHD (CPHD) filter, which propagates not only the PHD but also the entire probability distribution on target number.     

基于先验目标航向的主/被动联合多基地航空搜潜建模与仿真

利用主动吊放声纳与被动浮标组成多基地航空声纳对目标进行搜索,可节约搜索时间,有效提高搜潜效率。针对已知目标的大概航向,在有限范围内确定目标存在区的情况下,建立了多基地搜潜范围模型、单机吊放声纳和浮标的主/被动联合多基地搜潜模型、潜艇运动模型,仿真分析了潜艇初始航向、海洋环境噪声、搜索样式等因素对联合搜索概率的影响。结果表明,潜艇初始航向角度对单机吊放声纳和浮标的联合搜索概率影响较小,海洋环境噪声的变化对单机吊放声纳和浮标的联合搜索概率影响较大。     

Calculation of Probability of Detection with Target Scintillation

This paper presents a computational method for the calculation of probability of detection using measured radar target cross-section data. The described method can also be used for probability of detection calculations when the radar target cross section follows a specified probability density function. Using the computational procedure of the paper, a number of curves are generated which can be used for probability of detection calculations with exponential and Gaussian radar target cross-section distributions. The results obtained using theoretical distributions are compared with the corresponding results using actual target cross-section measurements. The results of computer runs are compared to the corresponding values in the literature where available.     

Passive ranging of a low observable ballistic missile in agravitational field

In this paper we present an estimation algorithm for tracking the motion of a low-observable target in a gravitational field, for example, an incoming ballistic missile (BM), using angle-only measurements. The measurements, which are obtained from a single stationary sensor, are available only for a short time. Also, the low target detection probability and high false alarm density present a difficult low-observable environment. The algorithm uses the probabilistic data association (PDA) algorithm in conjunction with maximum likelihood (ML) estimation to handle the false alarms and the less-than-unity target detection probability. The Cramer-Rao lower bound (CRLB) in clutter, which quantifies the best achievable estimator accuracy for this problem in the presence of false alarms and nonunity detection probability, is also presented. The proposed estimator is shown to be efficient, that is, it meets the CRLB, even for low-observable fluctuating targets with 6 dB average signal-to-noise ratio (SNR). For a BM in free flight with 0.6 single-scan detection probability, one can achieve a track detection probability of 0.99 with a negligible probability of false track acceptance     

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.     

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。     

声纳浮标阵目标搜索优化布放算法

为提高声纳浮标阵的目标搜索效率,文章首先建立目标运动模型和累积搜索概率的计算方法,然后提出了基于多点随机搜索、分区分支界定和遗传算法的浮标阵优化布放方法。仿真结果表明：这3种优化方法均优于传统布放方法,多点随机搜索算法性能最差但适合短时间制定布放策略;分区分支界定算法适合优化较少参数的浮标阵形,保证能找到最优点;对于较...     

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