Calculating Detection Probabilities for Adaptive Thresholds

In calculating detection probabiities for radar and sonar systems it is usually assumed that the threshold required to yield a certain probability of false alarm is known. This is often not the case for real systems and therefore the threshold must be estimated using some measure related to the test statistic. This paper presents a calculation technique that handles estimated (adaptive) thresholds in a general framework that can be applied easily to many detection problems. False alarm and detection probabilities are calculated from the characteristic function of the noise or signal plus noise variate and the characteristic function of the threshold estimate. To illustrate the method the detection performance of overlapped discrete Fourier transforms (DFTs) is calculated for a narrowband Gaussian target signal.     

Multiple-Tone Signals and Detection Probabillities

An analysis technique is presented for multiple-tone signals insystems employing noncoherent integration of a square-law detectoroutput. It is shown how the characteristic function for the teststatistic can be found from the easily determined "coherent"characteristic function defined in the two-dimensional signal space.This result is applied to two detection problems, the detection of multiple-tone signals in Gaussian noise and the detection of a Gaussian signal in multiple-tone plus Gaussian noise interference.The detection curves are compared to an approximation that is often used in practice to estimate performance. It is found that detection performance in the presence of multiple-tone interferences can be significantly different from that in the presence of Gaussian noise alone.     

Fourier Transform and Ambiguity Function of Piecewise Polynomial Functions

A general systematic procedure is described for computing the Fourier transform and the ambiguity function of waveforms that are piecewise polynomial. The procedure can be implemented by hand or programmed for execution by a digital computer. The main advantage of the technique is that integration is replaced by a finite summation. Examples include the computation of characteristic function, moments, and the ambiguity function of an amplitude modulated linear FM signal.     

利用分数阶Fourier域滤波的机载SAR多运动目标检测

 强度相差较大的多运动目标检测是机载合成孔径雷达 ( SAR)技术的一个重点和难点,传统的频域滤波和现代的时频分布方法都无法解决这个问题。首先分析了机载 SAR运动目标回波本质上为线性调频信号,据此提出一种基于分数阶 Fourier域滤波的运动目标检测新方法,并且应用逐次消去的思想有效地解决了强度相差较大的多目标检测问题。仿真的结果验证了算法的有效性。     

分数傅立叶变换用于抑制SAR杂波背景检测慢速动目标

慢速运动目标在时、空、频域上都落入主杂波区。利用单通道SAR图像中静止背景的信息抑制静止杂波,可改善检测动目标的性能。分数傅立叶变换是线性变换,不存在交叉项,采用分数傅立叶变换搜索匹配动目标信号,使其能量汇聚。对称计算旋转角正负对称的分数傅立叶变换,在两个对称的分数傅立叶域中得到两个复信号,这两个复信号中静止背景的模处处相同,而包含动目标的区域,模的幅度有很大差别,计算对称的分数傅立叶域信号对应位置模的差,取绝对值,可对消静止背景,敏锐地检测动目标。实测数据表明本算法有效。     

An efficient 3-D near-field ISAR algorithm

This paper presents a new three-dimensional (3-D) near-field inverse synthetic aperture radar (ISAR) imaging technique. A 3-D ISAR image can be obtained by processing coherently the backscattered fields as a function of the frequency and two rotation angles about axes which are mutually orthogonal. Most of the existing ISAR algorithms are based on the Fourier transform and as such can tolerate only small amounts of wavefront curvature. Wavefront curvature must be taken into account when imaging an object in the near-field. Near-field ISAR imaging of large objects using a direct Fourier inversion may result in images which are increasingly unfocused at points which are more distant from the center of rotation. An algorithm based on an azimuth convolution between a near-field focusing function and the frequency domain backscattered fields is discussed. This convolution is efficiently implemented by using fast Fourier transform (FFT) techniques. Furthermore, in order to further alleviate the computational load of the algorithm, the discrete Fourier transform (DFT) of the focusing function is evaluated by means of the stationary phase method. Experimental results show that this technique is precise and virtually impulse invariant     

Calculating the performance of linear and square-law detectors

A method is presented for calculating the performance of linear and square-law detectors in detection schemes that employ noncoherent integration. The method consists of transforming the coherent characteristic function, which is usually easy to obtain to a noncoherent moment generating function describing the test statistic of a linear or square-law detector. The method provides a single mathematical framework for many signal models (both classical and new) and can be implemented using standard numerical routines. Although the method is not always optimum in terms of computing speed for specific classical models, its common approach for all signal models makes it very efficient in term of learning and implementation times. Classical results as well as results for an extended set of target models consisting of an arbitrary number of constant amplitude random phase returns are presented to demonstrate the technique. It is shown for the signal parameters considered that the performance difference between the linear and square-law detectors is relatively insignificant     

基于短时傅里叶变换的Duffing振子微弱信号检测

研究了Duffing振子信号检测过程中混沌、间歇混沌和大周期状态的时频特征,提出了一种基于检测统计量的任意频率信号检测方法。通过对系统不同状态下的输出序列进行短时傅里叶变换(STFT)发现,等幅线和三维时频分布能够体现出不同状态的显著差异,且可以完全区分出每一种状态。从构造统计量的易实现性出发,用三维时频分布中的幅时曲线作为衡量不同状态的依据,并将不同频率对应的幅时曲线的均值最大量作为检测统计量,该统计量的计算可以借助快速傅里叶变换(FFT)操作提高时效性。在此基础上,引入频率控制单元,给出了任意频率信号的检测方法步骤,方法的关键是将检测统计量最大值处所在的频率作为待测信号频率范围的一个端点,另一个端点为毗邻的两个检测统计量值较大者所在频率点。实验给出了不同状态的检测统计量范围,进而以此范围为判据,实现了振子对任意频率信号的检测,说明了方法的可行性,为Duffing振子信号检测问题的研究提供了一种新的思路。     

Simulation of Permanent Magnet Generator/Rectifier Combination

Permanent magnet generators are often used as the pilot exciters of three-stage generating units to provide an efficient and reliable source of electrical power. No external power supply is then necessary, and the problems associated with brushwear and with arcing at the rubbing contacts are eliminated. A technique is presented here by which the performance of a permanent magnet generator, when combined with a rectifier-fed d.c. load at its output terminals, may be accurately and efficiently computed. The machine model takes into account the magnetization characteristic of the permanent magnet rotor and involves only parameters which can be determined from terminal measurements on the machine at standstill. Both computed and measured characteristics for an experimental machine are presented, and a comparison of these characteristics shows that the model can predict accurately all the major characteristics of the machine, as well as its detailed internal performance, when supplying a typical resistiveinductive load.     

基于固有模态函数频域熵的目标检测算法

为提高海杂波中慢速目标的检测性能,提出了一种基于固有模态函数(IMF)频域熵的目标检测算法。该算法对原始信号经 EMD分解后得到的固有模态函数采用 Fourier变换,自动地提取其各个分量的频域能量,以此获得 IMF能量分布特点,再运用信息熵的方法构建检验统计量,并将其输入非参量检测器中进行目标检测。研究结果表明,相比于海杂波、海尖峰,慢速目标的能量分布更为分散,熵值更大,对比频域广义符号(GS)检测算法,所提 方法检测性能更优,适用于慢速目标检测。     

适用于BOC(m,n)信号的无模糊捕获技术

针对二进制偏移载波(BOC)调制信号自相关多峰特性引起的信号捕获模糊性问题,提出了一种子相关相乘边峰消除技术(CMSCT)。根据BOC子相关函数的特性,通过将不同子相关函数相乘获得边峰消除能力,并且为了充分利用接收信号,进一步提高捕获性能,提出了相应的优化算法。分析对比了提出算法的实现复杂度和基于恒虚警率准则的峰值发现概率,对Galileo E1C中频采样信号的处理结果表明:提出的边峰消除方法有效解决了捕获模糊性问题。     

一种多分量chirp信号阵列检测新方法

提出了一种多分量chirp信号检测与参数估计的新方法。该方法利用天线阵列的空间特性,通过阵列平均在分数阶傅里叶域中引入加权函数来降低噪声、抑制不同源信号之间的相互干扰。和单阵元方法相比,文中方法大大提高了多分量chirp信号检测和参数估计的性能,仿真结果证明了方法的有效性。     

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.     

Adaptive detection schemes in compound-Gaussian clutter

Radar detection of coherent pulse trains embedded in compound-Gaussian disturbance with partially known statistics is discussed. We first give a thorough derivation of two recently proposed adaptive detection structures. Next, we derive a different detection scheme exploiting the assumption that the clutter is wide-sense stationary. Resorting to the theory of circulant matrices, in fact, we demonstrate that the estimation of the structure of the clutter covariance matrix can be reduced to the estimation of its eigenvalues, which in turn can be (efficiently) done via fast Fourier transform codes. After a thorough performance assessment, mostly carried on via computer simulations, the results show that the newly proposed detector achieves better performance than the two previously introduced adaptive detectors. Moreover, a sensitivity analysis shows that, even though this detector does not strictly guarantee the constant false alarm rate property with respect to the clutter covariance matrix, it is robust, in the sense that its performance is only slightly affected by variations in the clutter temporal correlation     

Evaluating the Detectability of Gaussian Stochastic Signals by Steepest Descent Integration

It is shown how to compute the detection probability of certain signals by numerical integration of the Laplace inversion integral involving the characteristic function or the moment-generating function of the detection statistic. The contour of integration is taken as the path of steepest descent of the integrand and is determined numerically as the integration proceeds. The method is applied to calculating the performance of the optimum detector of a Gaussian stochastic signal in white noise when the signals actually present have a different average s.n.r. from that assumed in the design. Results are presented for narrowband signals with Lorentz and rectangular spectral densities. The detectability of the former is shown to be more sensitive than that of the latter to the value of the design s.n.r. The relative disadvantage of the threshold detector, also assessed by this method, is smaller for signals with a rectangular than for those with a Lorentz spectral density.     

A Coarse Search Correlation Tracker for Image Registration

A high-speed compact digital correlation tracker which determines the frame-to-frame translational motion between two images is presented. By combining a similarity detection approach with the correlation coefficient in a parallel pipelined architecture, effective tracking rates comparable to conventional fast Fourier transform (FFT) techniques can be achieved. Examples of the tracker's performance using simulated data and image data acquired by an active infrared radar are given.     

Maximum likelihood track-before-detect with fluctuating targetamplitude

An important problem in target tracking is the detection and tracking of targets in very low signal-to-noise ratio (SNR) environments. In the past, several approaches have been used, including maximum likelihood. The major novelty of this work is the incorporation of a model for fluctuating target amplitude into the maximum likelihood approach for tracking of constant velocity targets. Coupled with a realistic sensor model, this allows the exploitation of signal correlation between resolution cells in the same frame, and also from one frame to the next. The fluctuating amplitude model is a first order model to reflect the inter-frame correlation. The amplitude estimates are obtained using a Kalman filter, from which the likelihood function is derived. A numerical maximization technique avoids problems previously encountered in “velocity filtering” approaches due to mismatch between assumed and actual target velocity, at the cost of additional computation. The Cramer-Rao lower bound (CRLB) is derived for a constant, known amplitude case. Estimation errors are close to this CRLB even when the amplitude is unknown. Results show track detection performance for unknown signal amplitude is nearly the same as that obtained when the correct signal model is used     

Model-based multifrequency array signal processing for low-angletracking

Tracking low-altitude targets over the sea is problematic because of interference between the direct and reflected signal. Standard monopulse trackers can experience large errors because of multipath maximum likelihood estimation (MLE) has been used to more accurately estimate the target height in the presence of multipath MLE is a model-fitting technique where the model parameters are chosen to maximize the likelihood function. It is shown that the type of observation model has a large effect on performance. Tracking performance is compared using three different observation models employing varying amounts of a priori information. Results are presented for different array sizes: eight and 32-element arrays and two-element subarrays typical of phase monopulse. Performance is compared with that of standard techniques such as Fourier beamforming and phase monopulse     

Hough transform for long chirp detection

The online detection of a very long and weak chirp signal is studied. The signal has an extremely slowly decreasing frequency, and is corrupted by white Gaussian noise and possibly also by powerful tones. By exploring and comparing candidate methods, it is found that the Hough transform (HT) detector appears to be most suitable given constraints on computational load and detectability. The analytical and the simulational performance of the HT detector are obtained and compared with the analytical performance of the generalized likelihood ratio test (GLRT), which is assumed to be optimal. Applying a suitable threshold for the HT can increase speed dramatically while preserving performance. We have found that both dithering (taking varied frequency shifts for fast Fourier transforms (FFTs)) and increasing the FFT length can reduce the minimum detectable frequency slope with nearly no additional computation     

一种新的某涡扇发动机地面检测设备

针对某涡扇发动机，本文介绍了AYF型地面检测设备的系统组成，结构、特点和功能，该设备技术先进，性能良好，功能完善，具有一定的军事意义和经济效益。