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。     

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     

航迹规划中反舰巡航导弹的雷达突防能力

在导弹航迹规划中，需要计算导弹突防过程中被雷达发现的概率。为此，在雷达方程中引入雷达系统特征常数以简化雷达方程，从探测概率与信噪比的关系出发，通过一系列的推导并考虑杂波的影响得出探测概率与目标距离的关系，提出在航迹规划中用横距探测概率来表征反舰巡航导弹的雷达突防能力。算例计算结果较为真实，表明该方法有一定应用价值。     

MTI Loss with Coherent Integration of Weighted Pulses

A moving target indicator (MTI) preceding a coherent integrator causes a degradation in the signal-to-noise ratio (SNR). This negative effect can be reduced by weighting of the MTI output pulses before the integration process. Two examples are given which show the improvement in SNR and detection probability as a result of this weighting.     

Frequency-Agile Radar Signal Processing

Modern radars may incorporate pulse-to-pulse carrier frequency modulation to increase probability of detection, to reduce Vulnerability to jamming, and to reduce probability of interception. However, if coherent processing is used for clutter rejection, the frequency of N consecutive pulses must be held constant for N-pulse clutter cancellation or Doppler filtering. If M pulses are transmitted during the time the antenna illuminates a target, there are M/N coherently integrated echoes available for noncoherent integration in the computer or the operator's display to further improve the signal-to-noise ratio (SNR). In this paper, analytical and simulation methods are employed to determine the balance between coherent and noncoherent integration that yields the greatest SNR improvement. Attention is focused upon a model using peak selection of fast Fourier transform (FFT) Doppler channels and is compared to a reference model involving only a single Doppler channel. Curves of detectable SNR as a function of M and N are presented for both models.     

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.     

Radiometric detection of spread-spectrum signals in noise ofuncertain power

The standard analysis of the radiometric detectability of a spread-spectrum signal assumes a background of stationary, white Gaussian noise whose power spectral density can be measured very accurately. This assumption yields a fairly high probability of interception, even for signals of short duration. By explicitly considering the effect of uncertain knowledge of the noise power density, it is demonstrated that detection of these signals by a wideband radiometer can be considerably more difficult in practice than is indicated by the standard result. Worst-case performance bounds are provided as a function of input signal-to-noise ratio (SNR), time-bandwidth (TW) product and peak-to-peak noise uncertainty. The results are illustrated graphically for a number of situations of interest. It is also shown that asymptotically, as the TW product becomes large, the SNR required for detection becomes a function of noise uncertainty only and is independent of the detection parameters and the observation interval     

Distributed Airborne Array Concepts

The improvement in SNR and detection range due to distributing an antenna array throughout the airframe and skin of an aircraft is examined. SNR formulas for three system configurations are presented and compared with that of a conventional, monostatic radar. Examples given in the paper show detection range increases as large as a factor of 4. Three additional potential advantages of the distributed array are an increase in spatial signal processing capability, an improvement in azimuthal resolution, and a potential reduction in transmitter power for fixed radar Performance so as to reduce the probability of intercept.     

Cyclic code shift keying: a low probability of intercept communication technique

A low probability of intercept (LPI), or low probability of detection (LPD) communication technique known as cyclic code shift keying (CCSK) is described. We discuss the basic concepts of CCSK and describe a system based on the use of random or pseudorandom codes for biphase modulation. We use simulation to show that the bit error rate (BER) for CCSK can be closely estimated by using existing equations that apply to M-ary orthogonal signaling (MOS). Also, we show that significantly fewer computations are required for CCSK than for MOS when the number of bits per symbol is the same. We show that using biphase modulation results in waveforms that have a large time-bandwidth product and very low input signal-to-noise ratio (SNR) and thus inherently have an LPI by a radiometer. We evaluate detection by a radiometer and show that LPI can be achieved by using codes of lengths greater than about 2/sup 12/ (i.e., by transmitting more than about 12 bits per symbol). Results illustrate the effect that the CCSK symbol length and error probability, and the radiometer integration time and probability of false alarm (PFA), have on detection by a radiometer. We describe a variation of CCSK called truncated CCSK (TCCSK). In this system, the code of length 2/sup k/ is cyclically shifted, then truncated and transmitted. Although shortened, the truncated code still represents k bits of information, thus leading to an increased data rate. We evaluate radiometer detection of TCCSK and it is shown that the probability of detection is increased compared with the detection of CCSK.     

基于点集合并的修正Hough变换TBD算法

在低信噪比条件下,基于Hough变换的检测前跟踪算法是进行强杂波背景下目标航迹检测的一种手段。本文针对Hough变换后一个目标产生多条可能航迹以及航迹内可能存在杂波点的问题,提出了一种基于能量最大点和点集合并的修正Hough变换检测前跟踪算法。该算法利用量测点时序、能量信息及目标速度先验信息对Hough变换后点迹进行关联和剔除,能够有效的对目标原始航迹进行回溯。针对高斯噪声背景下的飞行目标,仿真结果表明该算法能够对微弱目标进行有效检测,在目标数目、杂波密度、信噪比发生变化的条件下仍能保持较高的检测概率。     

从探测概率的角度评价飞机的隐身性能

采用雷达散射截面(RCS)均值来衡量飞机的隐身性能并不能给出足够充分的信息,从信号检测概率的角度来衡量飞机的可探测性可以提供更完整的信息。本文从探测概率的角度详细分析了4种典型隐身飞机RCS起伏数据与虚警概率、探测概率、探测距离、信噪比(SNR)等参数间的关系,并给出了完整的推导过程,采用此方法可以对任意飞机目标在给定雷达参数下的可探测性进行准确计算。一般在雷达性能评估中需要用到RCS起伏模型,本文对飞机目标回波信号进行检测分析时采用数值计算方法,信号的概率密度函数(PDF)直接来源于原始回波起伏信号,避免了模型拟合带来的回波特性失真,且不会产生大的计算误差。通过对比分析计算结果发现:单脉冲检测下回波信号均值中值比越大,回波取值范围越小,则信号的检测概率越小,其中均值中值比一般相差3倍以上时可以得到明显不同的检测概率;在快起伏假设下,非相参积累检测的积累脉冲数Nin即便较小,也能得到较大的信噪比增益,此增益可能大于Nin。     

A noncoherent adaptive detection technique

An adaptive detection technique suitable for both stationary and nonstationary noise environments based upon a generalized likelihood ratio test (GLRT) formulation is presented. The detector, which is statistically equivalent to a special form of the Wilks's lambda test, noncoherently combines the information contained in a pulse train of arbitrary length for decision-making purposes. The probability density function of the test under the noise only hypothesis is shown to be central χ². Under the signal plus noise hypothesis, an exact statistical characterization of the test cannot be obtained, and, therefore, a Chernoff bound is derived. Results in terms of the probability of detection versus signal-to-noise ratio (SNR) obtained from Monte Carlo simulation, the Chernoff bound, and the optimal matched filter case are examined. The performance of the noncoherent detector is shown to be a function of the covariance matrix estimate and the number of data samples     

Phase-Coded Interrupted CW Signals and Processors

High resolution radars require signals with large time-bandwidth product such as CW signal and coherent pulse train (CPT). We discuss a phase-coded interrupted CW (ICW) signal which is the combination of CW signal and CPT. Phase codes used here are with perfect periodic autocorrelation. The periodic ambiguity function of ICW signals is studied including single-carrier signal and multi-carrier signal. It is interesting that the gate function has different effects on two signals and contributes to a multi-carrier ICW signal which yields nearly perfect autocorrelation. Meanwhile we also suggest an efficient receiver approach to ICW signals, which can reduce the computational burden of the processor and utilize the good properties of P3 and P4 codes.     

Frequency-hopping signal detection using partial band coverage

The performance of a channelized radiometer in detecting a frequency-hopping signal is analyzed for a variable number of parallel radiometers not necessarily covering the entire hopping band. The full band may not be covered because of an attempt to avoid interfering signals, limited radiometer resources, lack of knowledge of the band frequency location, or combinations of these factors. The analysis provides for calculation of the value of the signal-to-noise ratio (SNR) required to achieve a given probability of detection for a specified false-alarm rate, assuming an observation interval equivalent to N hops using either a fixed or a moving observation window. The dependence of the probability of detection on a misalignment of the detector observation intervals with the hop transitions is also analyzed. Numerical results are presented and discussed. Applied to a typical slow-hopping VHF radio, the results imply that a 150-hop transmission can be detected by a channelized radiometer covering half the hopping band when the SNR is about 2 dB     

单脉冲跟踪雷达多目标检测算法性能分析

对2种检测单脉冲雷达主波束内是否存在2个不可区分目标的算法进行了推广,将其应用到波束内可能存在N个不可区分的目标,并仿真了波束内存在3个目标时的检测性能。仿真表明,在总信噪比相同时,3个目标的检测概率不一定大于2个目标的检测概率,处于方位向上间距最大的2个目标的信噪比对整个检测概率影响较大。     

Decision-Directed Detector for Overlapping PCM/NRZ Signals

A decision-directed (DD) technique for the detection of overlapping PCM/NRZ signals in the presence of white Gaussian noise is investigated. The performance of the DD detector is represented by probability of error PE versus input signal-to-noise ratio (SNR). To examine how much improvement in performance can beachieved with this technique, PE's with and without DD feedback are evaluated in parallel. Further, analytical results are compared with those found by Monte Carlo simulations. The results are shown in good agreement.     

Radar detection and preclassification based on multiple hypothesis

This work presents a single-scan-processing approach to the problem of detecting and preclassifying a radar target that may belong to different target classes. The proposed method is based on a hybrid of the maximum a posteriori (MAP) and Neyman-Pearson (NP) criteria and guarantees the desired constant false alarm rate (CFAR) behavior. The targets are modeled as subspace random signals having zero mean and given covariance matrix. Different target classes are discriminated based on their different signal subspaces, which are specified by their corresponding projection matrices. Performance is investigated by means of numerical analysis and Monte Carlo simulation in terms of probability of false alarm, detection and classification; the extra signal-to-noise power ratio (SNR) necessary to classify once target detection has occurred is also derived.     

Relay selection based on MAP estimation for cooperative communication with outdated channel state information

In this paper, we consider an amplify-and-forward (AF) cooperative communication system when the channel state information (CSI) used in relay selection differs from that during data transmission, i.e., the CSI used in relay selection is outdated. The selected relay may not be actually the best for data transmission and the outage performance of the cooperative system will deteriorate. To improve its performance, we propose a relay selection strategy based on maximum a posteriori (MAP) estimation, where relay is selected based on predicted signal-to-noise ratio (SNR). To reduce the computation complexity, we approximate the a posteriori probability density of SNR and obtain a closed-form predicted SNR, and a relay selection strategy based on the approximate MAP estimation (RS-AMAP) is proposed. The simulation results show that this approximation leads to trivial performance loss from the perspective of outage probability. Compared with relay selection strategies given in the literature, the outage probability is reduced largely through RS-AMAP for medium-to-large transmitting powers and medium-to-high channel correlation coefficients.     

基于均匀性判定规则的统计MIMO雷达多通道融合检测技术

针对统计MIMO雷达各观测通道统计特性不一致的情况,提出了一种多通道融合检测技术。该技术利用均匀性判定规则,选择一组均匀的、"被认为是具有较高信杂噪比"的局部检验统计量来构建全局检验统计量,即新的检测器。给出了新检测器的设计步骤和均匀性判定规则,并利用全概率公式证明了新检测器的虚警概率与每一操作步骤中过门限概率的关系,从而为仿真得出检测门限提供了理论基础。仿真结果表明,在不同通道间信噪比分布类型条件下,新检测器的检测性能具有较强的稳健性,且与不同条件下性能最优的检测器相比,其性能损失很小。