Search radar detection and track with the Hough transform. III.Detection performance with binary integration

For pt.II see ibid., vol. 30, no 1, (Jan. 1994). This paper considers how well a Hough transform detector with binary integration improves the performance of a typical surveillance radar. For Hough transform detection, binary integration offers some advantages over noncoherent integration when multiple targets appear in range-time space or when the detector receives signals with a wide range of power. We derive expressions for P_F and P_D for a Hough transform binary integrator and apply the expressions to a typical surveillance radar. The results show that for the case considered, the binary Hough integrator improves the power budget of the radar by about 3 dB for a nonfluctuating target and 1 dB for a highly fluctuating target     

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.     

Hybrid integration method for highly maneuvering radar target detection based on a Markov motion model

To detect highly maneuvering radar targets in low signal-to-noise ratio conditions, a hybrid long-time integration method is proposed, which combines Radon-Fourier Transform (RFT), Dynamic Programming (DP), and Binary Integration (BI), named RFT-DP-BI. A Markov model with unified range-velocity quantification is formulated to describe the maneuvering target’s motion. Based on this model, long-time hybrid integration is performed. Firstly, the whole integration time is divided into multiple time segments and coherent integration is performed in each segment via RFT. Secondly, non-coherent integration is performed in all segments via DP. Thirdly, 2/4 binary integration is performed to further improve the detection performance. Finally, the detection results are exported together with target range and velocity trajectories. The proposed method can perform the long-time integration of highly maneuvering targets with arbitrary forms of motion. Additionally, it has a low computational cost that is linear to the integration time. Both simulated and real radar data demonstrate that it offers good detection and estimation performances.     

The Detection Performance of a Modified Moving Window Detector

The modified moving window detector for binary integration has a shorter window length compared with the ordinary moving window detector because of the addition of a third threshold. When the second threshold is reached, a counter begins to count until the third threshold is reached. A graphical method using a probability chain is developed here to analyze and to calculate the detection performance of this type detector. The detection performances for some practical cases are calculated by computer and are compared with the ordinary moving window detector.     

The Nonparametric Detection of Signals Embedded in Log-Normal Noise

The nonparametric detection of signals embedded in log-normal noise is discussed. The generalized sign (GS), Mann-Whitney (MW), modified Savage (MS), and modified rank squared (MRS) non-parametic detectors are considered and are compared with the mean and trimmed mean (TM) detectors when envelope detection is used. The detection of both nonfluctuating and Rayleigh fluctuating signals is considered.     

Detection analysis of the MX-MLD with noncoherent integration

The detection performance of the maximum mean level detection (MX-MLD) when noncoherent integration is used under both nonfluctuating and chi-square fluctuating target models is analyzed. Finite series are obtained in all cases. Required thresholds and constant false-alarm rate loss curves are presented, with emphasis on the important Swerling case II model     

A recursive method for calculating binary integration detectionprobabilities

The calculation of the probability of detection for a binary integration when the probability of a threshold crossing changes from sample to sample is presented. The significance of the algorithm is that it uses a simple recursion relation which provides a computationally efficient means of performing the calculation     

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.     

Computation of binary integration detection probabilities

Efficient algorithms are described for computing the probability of detection for a binary integration when the probability of a threshold crossing changes from sample to sample. A binary integrator is exceeded (a hit occurs) in a sequence of N trials and declares a detection if the number of hits is at least as large as some number M, where O>     

Detection Results for Scanning Radars Employing Feedback Integration

A method is presented for the calculation of the detection probabilities for a scanning radar employing feedback integration. An equation is developed for the optimum feedbacd value? the equation holds for small and large sample sizes and for fluctuating and nonfluctuating targets. Then, a value for the antenna beam-shape factor is given which enables one to calculate detection probabilities.     

Adaptive False Alarmrm Regulation in Double Threshold Radar Detection

In practical situations the false alarm probability in double threshold radar detection, sometimes known as binary integration with sliding window detection, is dependent on the nonstationarity and azimuthal correlation of the clutter which is present. Control of the false alarm probability can be achieved, to a certain extent, by the adjustment of the second threshold in the detection process. In this study two adaptive control techniques which are based on the statistical characteristics of the data are compared. Comparing the results for a technique based on first-order statistics with one based on second-order statistics, it is shown that the second-order, or correlation sensitive, technique can give a reduction of 30 to 45 percent in the false alarm probability with no corresponding loss in the detection probability. An interesting aspect of the results is the fact that the effects of the size of the sample area and the bias in the correlation estimator are clearly evident.     

Binary integration of fluctuating targets

The detection performance of a binary integrator (M-out-of-N detector) against nonfluctuating, slowly fluctuating, and quickly fluctuating targets is given. Since the solution for the slowly fluctuating target is numerically intensive, a simpler approximate solution is developed. This approximation is very accurate and is valid even when the noise power varies from pulse to pulse within a single antenna scan     

Fluctuating Target Detection in Clutter Using Sidelobe Blanking Logic

In an earlier paper, Maisel [6] considered two-channel detection systems using a sidelobe blanking logic when a nonfluctuating target was present. This paper is an extension of the earlier work to include fluctuating targets. The Swerling I, II, III, and IV models are considered when single-pulse detection is of interest. An adaptive threshold procedure is also briefly discussed whereby the probability of false alarm at any given resolution cell is maintained constant, even though the input clutter level may vary from cell to cell or from beam position to beam position. Useful data are presented for detection probabilities in the range 0.5 to 0.9, for false alarm probabilities in the range 104 to 10-8, and for a false detection probability of 0.1 for a sidelobe target yielding an apparent signal to total noise power density ratio of 13.0 dB in the main beam receiver.     

Asynchronous distributed detection

Binary parallel distributed-detection architectures employ a bank of local detectors to observe a common volume of surveillance, and form binary local decisions about the existence or nonexistence of a target in that volume. The local decisions are transmitted to a central detector, the data fusion center (DEC), which integrates them to a global target or no target decision. Most studies of distributed-detection systems assume that the local detectors are synchronized. In practice local decisions are made asynchronously and the DFC has to update its global decision continually. In this study the number of local decisions observed by the central detector within any observation period is Poisson distributed. An optimal fusion rule is developed and the sufficient statistic is shown to be a weighted sum of the local decisions collected by the DFC within the observation interval. The weights are functions of the individual local detector performance probabilities (i.e., probabilities of false alarm and detection). In this respect the decision rule is similar to the one developed by Chair and Varshney for the synchronized system. Unlike the Chair-Varshney rule, however, the DFC's decision threshold in the asynchronous system is time varying. Exact expressions and asymptotic approximations are developed for the detection performance with the optimal rule. These expressions allow performance prediction and assessment of tradeoffs in realistic decision fusion architectures which operate over modern communication networks     

Lock threshold deterioration induced by antenna vibration and signal coupling effects in hypersonic vehicle carrier tracking system of Ka band

The envelope of a hypersonic vehicle is affected by severe fluctuating pressure, which causes the airborne antenna to vibrate slightly. This vibration mixes with the transmitted signals and thus introduces additional multiplicative phase noise. Antenna vibration and signal coupling effects as well as their influence on the lock threshold of the hypersonic vehicle carrier tracking system of the Ka band are investigated in this study. A vibration model is initially established to obtain phase noise in consideration of the inherent relationship between vibration displacement and electromagnetic wavelength. An analytical model of the Phase-Locked Loop(PLL), which is widely used in carrier tracking systems, is established. The coupling effects on carrier tracking performance are investigated and quantitatively analyzed by imposing the multiplicative phase noise on the PLL model. Simulation results show that the phase noise presents a Gaussian distribution and is similar to vibration displacement variation. A large standard deviation in vibration displacement exerts a significant effect on the lock threshold. A critical standard deviation is observed in the PLL of Binary Phase Shift Keying(BPSK) and Quadrature Phase Shift Keying(QPSK) signals. The effect on QPSK signals is more severe than that on BPSK signals. The maximum tolerable standard deviations normalized by the wavelength of the carrier are 0.04 and 0.02 for BPSK and QPSK signals,respectively. With these critical standard deviations, lock thresholds are increased from à12 andà4 d B to 3 and à2 d B, respectively.     

Quickest detection for sequential decentralized decision systems

Quickest detection procedures are techniques used to detect sudden or abrupt changes (also called disorders) in the statistics of a random process. The goal is to determine as soon as possible that the change occurred, while at the same time minimizing the chance of falsely signaling the occurrence of a disorder before the change. In this work the distributed quickest detection problem when the disorder occurs at an unknown time is considered. The distributed local detectors utilize a simple summing device and threshold comparator, with a binary decision at the output. At the fusion center, the optimal maximum likelihood (ML) procedure is analyzed and compared with the more practical Page procedure for quickest detection. It is shown that the two procedures have practically equivalent performance. For the important case of unknown disorder magnitudes, a version of the Hinkley procedure is also examined. Next, a simple method for choosing the thresholds of the local detectors based on an asymptotic performance measure is presented. The problem of selecting the local thresholds usually requires optimizing a constrained set of nonlinear equations; our method admits a separable problem, leading to straightforward calculations. A sensitivity analysis reveals that the resulting threshold settings are optimal for practical purposes. The issue of which sample size to use for the local detectors is investigated, and the tradeoff between decision delay and communication cost is evaluated. For strong signals, it is shown that the relative performance deteriorates as the sample size increases, that is, as the system cost decreases. Surprisingly, for the weak signal case, lowering the system cost (increasing the sample size) does not necessarily result in a degradation of performance     

Distributed binary integration

A distributed radar detection system that employs binary integration at each local detector is studied. Local decisions are transmitted to the fusion center where they are combined to yield a global decision. The optimum values of the two thresholds at each local processor are determined so as to maximize the detection probability under a given probability of false alarm constraint. Using an important channel model, performance comparisons are made to determine the integration loss     

分布式接收宽带多目标信号盲检测迭代处理方法

随着软硬件技术的飞速发展和宽带接收机的广泛使用,频谱检测向着高瞬时带宽的方向发展,传统基于信道化处理的频谱检测方法存在搜索速度慢、处理效率低下的问题。文章提出了 1种新的分布式接收宽带多目标信号盲检测迭代处理方法,在无须预先知道信号数目及信号频谱位置的情况下,能够实现特定虚警概率多信号盲检测,具备较高的灵活性和稳健性。首先,在对信号特征进行分析的基础上,通过构造线性模型,将分布式接收多目标信号检测转化为线性模型求解问题进行处理;然后,基于贝叶斯多参数联合求解模型,在对未知参数先验分布进行合理假设的基础上,推导了各未知参数变分分布及信号检测门限的解析表达式,采用变分分布软信息迭代的方式实现多传感器信号、多参数联合估计,并利用每次迭代参数估计结果,对信号检测门限进行更新,通过置零操作实现预设虚警概率下的多信号盲检测;最后,通过仿真实验对所提方法性能进行了分析,并与相关方法进行了对比。仿真结果表明,所提方法能够有效利用多路接收信号信息,实现宽带未知多目标信号的盲检测,有效提升短数据下的算法处理效能,与现有方法相比,在接收单元数目较多以及信噪比较低时具有明显优势。     

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.     

Detection Probabilities for Log-Normally Distributed Signals

The amplitude and power of a large family of radio signals are observed to have log-normal probability density functions. Among these are signals propagated through random inhomogeneous media, a notable example being low frequency atmospheric radio noise. Of greater importance are certain radar targets that have been observed to have essentially log-normal density functions. Both ships and space vehicles may fall into this category. Curves of probability of detection vs. signal-to-noise ratio for the case of log-normal signals in Gaussian noise have been computed and are presented in this paper. The curves apply for square-law detection with varying degrees of postdetection linear integration. Both fully correlated and completely uncorrelated fluctuating signals are considered. It is shown that for log-normal signal distributions having large variances, the probability of detection differs significantly from that obtained using curves based on an assumed Rayleigh signal distribution.