Calculation of Detection Probabilities for Automated Change Detection

A general model is presented for calculating detection and falsealarm probabilities for the automated change detector. The model is then applied to determine PD'PF for the ?target-no target? type change; the resulting PD and PF are compared to the one-channel case.     

Recursive Methods for Computing Detection Probabilities

Recursive methods are drived for computing detection probabilities for general fluctuating targets in Gaussian noise. For the generalized chi-square family of fluctuating targets, very simple and convenient recursive algrithms result. The methods are also extended to cell-averaging CFAR. Although the detection probability is expressed iw: terms of an infinite series, a convenient expression is derived for the resulting error when the series is truncated. Cell-averaging CFAR results are computed for nonfluctuating, Swering case I, and Swerling case II fluctuating targets.     

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.     

Calculating Detection Probabilities for Systems Employing Noncoherent Integration

Cumulative probability distributions that occur in radar and sonar detection problems are calculated directly from the characteristic function by using a Fourier series. The error in the result is controlled by two parameters which can be adjusted to suit the application. The technique is applied to the problem of determining the detection performance of consecutive discrete Fourier transforms (DFTs) for a narrowband Gaussian signal with a rectangular spectrum. Since the characteristic function is used directly in its product form this technique does not suffer from the numerical problems associated with the partial fraction approach. The technique can handle many different problems in a single computational structure making it a valuable tool in system performance studies.     

Adaptive Detection Probabilities for Fluctuating Target Models in Nonhomogeneous Gaussian Noise

Under the assumption that the average noise power may vary from cell to cell, new, more easily computed expressions are given for the probability of detecting a fluctuating target by means of a cell-averaging CFAR test. The generalized chi-square family of fluctuating targets is considered with the Swerling I and III models given as special cases.     

Evaluating Radar Detection Probabilities by Steepest Descent Integration

The probability of detection for radars employing noncoherent integration and a fixed threshold or cell-averaging constant false alarm rate (CA-CFAR) processor is computed by numerical contour integration in the complex plane. The technique is applied to both nonfluctuating and chi-squared fluctuating targets. A bound on the truncation error allows for a simple stopping rule for the numerical integration. The method has applicability to many problems in radar detection theory.     

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.     

Mean-Level Detection of Nonfluctuating Signals

Analysis of the performance of a mean-level threshold in the detection of nonfluctuating signals is performed. Formulas for the probability of detection are derived and a simple recursive method that can be used for computations is described. Binary integration is discussed, and it is shown that the loss in sensitivity due to the use of an adaptive threshold followed by binary integration is only a fraction of a decibel when compared with optimum binary integration. Binary integration results are given for both fluctuating and nonfluctuating signals.     

Detection with Distributed Sensors

The extension of classical detection theory to the case of distributed sensors is discussed, based on the theory of statistical hypothesis testing. The development is based on the formulation of a decentralized or team hypothesis testing problem. Theoretical results concerning the form of the optimal decision rule, examples, application to data fusion, and open problems are presented.     

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.     

Detection Performance of Soft-Limited Phase-Coded Signals

General analytic expressions are developed for the soft-limited digital pulse compressor (matched filter). This theoretical development is then used for the hardware realization of a two-channel (I,Q), 3-bit-limited digital pulse compressor with a compression ratio of 255: 1. The realized hardware uses state of the art integrated circuit devices. An experimental laboratory setup is described. This setup is used to study hard-limited versus 3-bit-limited matched-filter performance characteristics with the data in the following areas: 1) constant false alarm rate (CFAR) characteristics as a function of threshold settings and noise levels; 2) single target detection characteristics as a function of input signal-to-noise ratio (SNR); and 3) two target performance characteristics: a) the amplitude of a weaker target as a function of target ratio and target overlap; and b) the detection characteristics of a weaker target as a function of weaker target SNR, strong target SNR, and target overlap.     

Detection Performance of Hard-Limited Phase-Coded Signals

The performance of a complex phase-coded waveform digital processor with hard-limiting constant false-alarm rate (CFAR) is presented. Processing losses relative to ideal matched-filter performance are computed and verified by hardware measurement. The losses considered include the consequences of hard limiting, envelope algorithm implementation, range cusping, and the associated effects of code length, IF filter bandwidth, and in-phase and quadrature channel phase offset. The range resolution properties of two closely spaced targets are also considered.     

Approximate Evaluation of Detection Probabilities in Radar and Optical Communications

Cumulative probability distributions such as occur in radar detection problems are approximated by a new version of the saddlepoint method of evaluating the inverse Laplace transform of the moment-generating function. When the number of radar pulses integrated is large, the approximation of lowest order yields good accuracy in the tails of the distributions, yet requires much less computation than standard recursive methods. Greater accuracy can be achieved upon summing the residual series by converting it to a continued fraction. The method is applied to evaluating the error-function integral and the Mth-order Q function, and to approximating the inverse of the chi-squared distribution. Cumulative distributions of discrete random variables, needed for determining error probabilities in optical communication receivers that involve counting photoelectrons, can be approximated by a simple modification of the method, which is here applied to the Laguerre distribution.     

Phase-Shift-Keyed Signal Detection with Noisy Reference Signals

This paper derives and graphically illustrates the performance characteristics of Phase-Shift-Keyed communication systems where the receiver's phase reference is noisy and derived from the observed waveform by means of a narrow-band tracking filter (a phase-locked loop). In particular, two phase measurement methods are considered. One method requires the transmission of an auxiliary carrier (in practice, this signal is usually referred to as the sync subcarrier). This carrier is tracked at the receiver by means of a phase-locked loop, and the output of this loop is used as a reference signal for performing a coherent detection. The second method is self-synchronizing in that the reference signal is derived from the modulated data signal by means of a squaring-loop. The statistics (and their properties) of the differenced-correlator outputs are derived and graphically illustrated as a function of the signal-to-noise ratio existing in the tracking filter's loop bandwidth and the signal-to-noise ratio in the data channel. Conclusions of these results as well as design trends are presented.     

Detection of Known Signals in Nonstationary Noise

The basic design of a nonlinear, time-invariant filter is postulated for detecting signal pulses of known shape imbedded in nonstationary noise. The noise is a sample function of a Gaussian random process whose statistics are approximately constant during the length of a signal pulse. The parameters of the filter are optimized to maximize the output signal-to-noise ratio (SNR). The resulting nonlinear filter has the interesting property of approximating the performance of an adaptive filter in that it weights each frequency band of each input pulse by a factor that depends on the instantaneous noise power spectrum present at that time. The SNR at the output of the nonlinear filter is compared to that at the output of a matched filter. The relative performance of the nonlinear system is good when the signal pulses have large time-bandwidth products and the instantaneous noise power spectrum is colored in the signal pass band.     

使用吊放声纳的直升机应召搜潜发现概率

建立了目标航速为瑞利分布条件下的目标位置分布模型,按照这个模型,研究了使用吊放声纳进行单机应召搜潜的搜索概率的计算方法,并给出了基于圆形搜索方式的不同参数条件下的搜索发现概率的部分计算结果。     

Maximum Likelihood Energy Detection of Mary Orthogonal Signals

The literature on energy detection is extended by applying it to the processing of M'ary orthogonal communication signals of arbitrary time-bandwidth product. Guassian noise channel transition probabilities are derived for maximum likelihood energy detection, modified to the extent of including an erasure threshold. Relations and computational techniques are described for determining the symbol erasure and error probabilities for general signal alphabet sizes (M) and time-bandwidth products. When time of arrival is known exactly and Doppler is negligible, gible, it is determined that energy detection is inferior to noncoherent matched filter detection. For time-bandwidth products of the order of 100 and error probabilities around 10 3, a loss of about 5 dB occurs which is attributable to a lack of knowledge of the detail signal structure. However, for problems where time of arrival and/ or Doppler are unknown, energy detection will perform nearly as well as matched filter detection of, for example, spread spectrum signals, and is also simpler to implement. General energy detection performance curves are given in terms of required signal energy for specific error and erasure probabilities, as a function of M'ary and time-bandwidth product.     

Detection of Narrowband Signals Using Time-Domain Adaptive Filters

The detection performance of a conventional narrowband analyzer is compared with two adaptive processor mechanizations based on the Widrow least mean squares algorithm. Comparisons are based on both analysis and extensive digital simulation. With a narrowband signal in stationary, white background noise, the performance of the three systems is shown to be essentially the same. With nonstationary background noise, the performance of the conventional system degrades by an amount proportional to the processing time-bandwidth product. The adaptive systems appear to be less sensitive to the nonstationary background, resulting in a potential performance advantage relative to the conventional system.     

基于检测前跟踪的超视距雷达微弱目标检测方法

天波超视距雷达（over-the-horizonradar,OTHR）通过快速傅立叶变换（FFr）实现相干积累,再利用常规的方法进行目标检测。但这种方法在弱目标、低信噪比的情况下效果并不好。本文提出了一种基于检测前跟踪（track-before-detect,TBD）的OTHR弱目标检测方法,利用数学形态学对每帧弱目标回波信号进行滤波,再通过动态规划方法进行检测。仿真结果表明,该方法能够有效地提高OTHR对弱目标的检测能力,运算效率高,实用性强。     

On the Limitations of Random Sensor Placement for Distributed Signal Detection

We consider the design of a sensor network for detecting an emitter which if present is known to be located in an interval but whose exact position is unknown. We seek to minimize the total system power consumption subject to detection performance constrains by carefully choosing the thresholds and positions of the sensors. Toward this goal, we propose an iterative algorithm for the optimization problem. Numerical results are given to provide insights into the design of such networks. We show that random sensor placement can perform poorly, in contrast to what many currently believe.