Radar detection in clutter

Clutter is defined as any unwanted radar return. The presence of clutter in a range/Doppler cell complicates the detection of a target return signal in that cell. In order to quantify the effect of clutter on the probability of detection, we must first specify sets of models suitable for representing the clutter and target. The simplest and most common model for clutter is based on the gamma density. We include two additional models, the NCG and NCGG clutter models for low grazing angles. They are motivated by physical arguments, the latter of which can accommodate the well-known phenomenon of speckle. Using one of these models for clutter together with one of several models for targets, we determine, in a range/Doppler cell, expressions for probabilities of detection of a target in the presence of clutter. It is important to control the probability of false alarms. The presence of clutter in a cell necessitates an increase in the detection threshold setting in order to control false alarms, thus lowering the probability of detection. If the clutter level is unknown, then we need to take measurements of the clutter and use it to adjust the threshold. The more clutter samples we take, the better the estimate of the clutter level and the less is the resulting detection loss. Using the expressions for the probability of detection in clutter, we can quantify the detection loss for a pair of commonly used constant false-alarm rate (CFAR) techniques and investigate how the loss varies with different parameter values, especially with regard to the number of clutter samples taken to estimate the clutter level.     

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     

采用现在点射击方式的反舰导弹捕捉概率计算模型

采用前置点射击方式的反舰导弹,在计算射击诸元时,需要目标运动参数,但采用现在点射击方式的反舰导弹,在计算射击诸元时,不测定目标运动要素,不计算导弹自控飞行时间内目标的运动。因此,必须要建立采用现在点射击方式的反舰导弹的捕捉概率计算模型。在把反舰导弹飞向目标过程中的主要误差综合为目标指示精度和侧向偏移两类误差基础上,把目标机动范围、目标指示精度误差作为圆分布来处理,利用解析方法,建立不同误差条件下反舰导弹捕捉概率的计算模型。对高亚声速反舰导弹的捕捉概率进行了仿真,按照捕捉概率的战术标准,得到了对反舰导弹不同发射距离条件下几个参数的要求。     

Clutter Map CFAR Analysis

An analysis of the probability of target detection for a clutter map CFAR using digital exponential filtering has been performed. General performance equations are derived. The probability of detection versus signal-to-noise ratio is plotted for a false alarm probability of 1.E-06 for several weight values. The CFAR loss is plotted for a detection probability of 0.9 and false alarm probabilities of 1.E-06 and 1.E-08.     

Multi-target state estimation and track continuity for the particle PHD filter

Particle filter approaches for approximating the first-order moment of a joint, or probability hypothesis density (PHD), have demonstrated a feasible suboptimal method for tracking a time-varying number of targets in real-time. We consider two techniques for estimating the target states at each iteration, namely k-means clustering and mixture modelling via the expectation-maximization (EM) algorithm. We present novel techniques for associating the targets between frames to enable track continuity.     

Probablity of Detection for ICW Radars

Eclipsing of received signals is analyzed for Interrupted Continuous Wave (ICW) radars. A probability density for the Signal to Noise Ratio (SNR) at the Doppler filter output is derived which incorporates eclipsing effects and a fluctuating target cross section model. The probability of detection as a function of SNR is calculated for typical ICW parameters and the magnitude of the detection loss due to eclipsing is assessed     

Performance of Predictors with Non-Gaussian Inputs

The trajectory of a maneuvering aircraft can be described by piecewise-constant-coefficient second-order polynomials which constitute a non-Gaussian process at the input of a linear fire control predictor. Consequently, the ?on- target? probability which is determined by the predictor output cannot be analytically evaluated. Using this a priori assumption for this type of target trajectory, the structure of a finite-time polynomial filter is determined. By using the ?go-no-go? characteristic of the loss function, the smoothing time of the predictor can be optimized to yield the highest possible ?on-target? probability. The results obtained constitute lower bounds whose validity is verified by digital simulation of the system. This shows that, on the average, they are 15 percent below the exact values. The simulation program is also used in a comparative study, with a conventional predictor and a Wiener-type predictor. The results demonstrate that the finite time polynomial predictor is markedly superior to both systems for a wide range of parameters and their combinations.     

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.     

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。     

Contiguous pulse binary integration analysis

The probability of detecting m or more pulses contiguously-that is, in a row-from a pulse train of n pulses is determined when the detection of each pulse is an independent Bernoulli trial with probability p. While a general closed-form expression for this probability is not known, we present an analytical procedure that gives the exact expression for the probability of interest for any particular case. We also present simple asymptotic expressions for these probabilities and develop bounds on the probability that the number of pulses that must be observed before m contiguous detections is greater than or less than some particular number. We consider the implications for binary integration in radar and electronic warfare problems     

Predicting an upper bound on SAR ATR performance

We present a method for predicting a tight upper bound on performance of a vote-based approach for automatic target recognition (ATR) in synthetic aperture radar (SAR) images. In such an approach, each model target is represented by a set of SAR views, and both model and data views are represented by locations of scattering centers. The proposed method considers data distortion factors such as uncertainty, occlusion, and clutter, as well as model factors such as structural similarity. Firstly, we calculate a measure of the similarity between a given model view and each view in the model set, as a function of the relative transformation between them. Secondly we select a subset of possible erroneous hypotheses that correspond to peaks in similarity functions obtained in the first step. Thirdly, we determine an upper bound on the probability of correct recognition by computing the probability that every selected hypothesis gets less votes than those for the model view under consideration. The proposed method is validated using MSTAR public SAR data, which are obtained under different depression angles, configurations, and articulations     

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     

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.     

攻击移动目标的末制导导弹命中概率评估方法

针对攻击移动目标的末制导导弹的命中概率评估问题,深入分析了影响导弹精度的各类误差源,研究了目标机动特性对末制导雷达捕获概率的影响,提出了打击任意形状目标的命中概率计算模型。以慢速移动目标——舰船为例进行了仿真分析,结果表明提出的命中概率评估方法能够有效融合多源信息,评估结论符合工程实际。     

Adaptive Detection Algorithms for Multiple-Target Situations

The performance of a mean-level detector is considered for the case where one or more interfering target returns are present in the set of cells used in estimating the clutter-plus-noise level. A serious degradation of detection probability is demonstrated for all of the single-pulse Swerling target fluctuation models (i. e., cases 0, 2, and 4). Indeed, for fixed mean radar cross sections of the primary and interfering targets, the probability of detecting the primary target is asymptotic to values significantly less than unity as the signal-to-noise ratios of the returns approach infinity. A class of alternative adaptive detection procedures is proposed and analyzed. These procedures, based on ranking and censoring techniques, maintain acceptable performance in the presence of interfering targets, and require only a minor addition in hardware to a conventional mean-level detector.     

A multipath data association tracker for over-the-horizon radar

A new algorithm, multipath probabilistic data association (MPDA), for initiation and tracking in over-the-horizon radar (OTHR) is described. MPDA is capable of exploiting multipath target signatures arising from discrete propagation modes that are resolvable by the radar. Nonlinear measurement models exhibiting multipath target signatures in azimuth, slant range, and Doppler are used. Tracking is performed in ground coordinates and therefore depends on the provision of estimates of virtual ionospheric heights to achieve coordinate registration. Although the propagation mode characteristics are assumed to be known, their correspondence with the detections is not required to be known. A target existence model is included for automatic track maintenance. Numerical simulations for four resolvable propagation modes are presented that demonstrate the ability of the technique to initiate and maintain track at probabilities of detection of 0.4 per mode in clutter densities for which conventional probabilistic data association (PDA) has a high probability of track loss, and suffers from track bias. A nearest neighbor version of MPDA is also presented     

改进的MMPHD机动目标跟踪方法

基于序列蒙特卡罗方法的经典多模概率假设密度滤波方法及其各种衍生方法,在预测过程中依据多个并行的状态转移模型,通过将大量粒子散布到下一时刻目标所有可能出现的状态空间实现目标状态的捕获,造成计算量大、目标跟踪精度差。为此,提出一种改进的多模粒子概率假设密度机动目标跟踪方法。该方法利用最新量测信息估计目标运动模型概率及模型参数,并将估计得到的目标模型应用到粒子概率假设密度滤波方法的预测过程中生成预测粒子,从而将大部分粒子聚合在目标最可能出现的状态空间邻域中,实现粒子的有效利用。数值仿真表明,所提方法不仅显著地减少了目标丢失个数,而且提高了目标跟踪精度。     

航迹规划中雷达探测空间的生成

从飞机突防习行任务规划出发，综合考虑地球曲率、陆地（或海洋）的反射和杂波干扰、大气折射和吸收损耗等因素的影响，采用临界散射截面法生成了对空警戒雷达在不同地貌、发现概率下，对不同雷达散射截面的目标的探测空间。计算并分析了飞行高度、目标雷达散射截面、发现概率和地貌等因素对雷达探测空间的影响，以便选择低探测概率的飞行走廓，这对制定和实施安全突防飞行策略有实际意义。     

航改燃气轮机燃烧室故障模式、影响及危害性分析

为提高航改燃机燃烧室可靠性及使用安全性,在设计阶段对某型中等功率航改燃气轮机燃烧室进行故障模式、影响及危害性分析(FMECA)。根据燃烧室结构组成,建立硬件层次及可靠性逻辑框图。针对燃烧室机匣、火焰筒、燃油总管、燃油喷嘴、导流罩等零部件进行故障模式分析,指出可能发生故障的原因及其影响,并有针对性地提出改进措施。根据各零部件发生故障的概率及严重程度建立危害性矩阵,找出系统的薄弱环节,得到FMECA表。结果表明:火焰筒壁面掉块及燃油总管焊缝开裂是影响燃烧室性能及使用安全性的主要因素,应采取相应措施降低其发生概率及严重程度,同时指出对于发生概率及严重程度较低的故障可以适当降低其设计成本。运用FMECA表客观地找出系统薄弱环节,为后续燃烧室维护及测试提供参考。     

Moving target detection via airborne HRR phased array radar

We study moving target detection in the presence of temporally and spatially correlated ground clutter for airborne high range resolution (HRR) phased array radar. We divide the HRR range profiles into large range segments to avoid the range migration problems that occur in the HRR radar data. Since each range segment contains a sequence of HRR range bins, no information is lost due to the division and hence no loss of resolution occurs. We show how to use a vector autoregressive (VAR) filtering technique to suppress the ground clutter. Then a moving target detector based on a generalized likelihood ratio test (GLRT) detection strategy is derived. The detection threshold is determined according to the desired false alarm rate, which is made possible via an asymptotic statistical analysis. After the target Doppler frequency and spatial signature vectors are estimated from the VAR-filtered data as if a target were present, a simple detection variable is computed and compared with the detection threshold to render a decision on the presence of a target. Numerical results are provided to demonstrate the performance of the proposed moving target detection algorithm