Optimum detection and location estimation of target lines in the range-time space of a search radar

The average likelihood ratio detector is derived as the optimum detector for detecting a target line with unknown normal parameters in the range-time data space of a search radar, which is corrupted by Gaussian noise. The receiver operation characteristics of this optimum detector is derived to evaluate its performance improvement in comparison with the Hough detector, which uses the return signal of several successive scans to achieve a non-coherent integration improvement and get a better performance than the conventional detector. This comparison, which is done through analytic derivations and also through simulation results, shows that the average likelihood ratio detector has a better performance for different SNR values. This result is justified by showing the disadvantages of the Hough method, which are eliminated by the optimum detector. To have an estimate for the location of the detected target line in the optimum detection method as the Hough method, which detects and localizes the target lines simultaneously, we present the maximum a posteriori probability estimator. The estimation performance of the two methods is then compared and it is shown that the maximum a posteriori probability estimator localizes the detected target lines with a better performance in comparison with the Hough method.     

Spatially distributed target detection in non-Gaussian clutter

Two detection schemes for the detection of a spatially distributed, Doppler-shifted target in non-Gaussian clutter are developed. The non-Gaussian clutter is modeled as a spherically invariant random vector (SIRV) distribution. For the first detector, called the non-scatterer density dependent generalized likelihood ratio test (NSDD-GLRT), the detector takes the form of a sum of logarithms of identical functions of data from each individual range cell. It is shown under the clutter only hypothesis, that the detection statistic has the chi-square distribution so that the detector threshold is easily calculated for a given probability of false alarm P_F. The detection probability P_D is shown to be only a function of the signal-to-clutter power ratio (S/C)_opt of the matched filter, the number of pulses N, the number of target range resolution cells J, the spikiness of the clutter determined by a parameter of an assumed underlying mixing distribution, and P_F. For representative examples, it is shown that as N, J, or the clutter spikiness increases, detection performance improves. A second detector is developed which incorporates a priori knowledge of the spatial scatterer density. This detector is called the scatterer density dependent GLRT (SDD-GLRT) and is shown for a representative case to improve significantly the detection performance of a sparsely distributed target relative to the performance of the NSDD-GLRT and to be robust for a moderate mismatch of the expected number of scatterers. For both the NSDD-GLRT and SDD-GLRT, the detectors have the constant false-alarm rate (CFAR) property that P_F is independent of the underlying mixing distribution of the clutter, the clutter covariance matrix, and the steering vector of the desired signal     

An Alternative Method for Analyzing the Double Threshold Detector

An alternative method for analyzing the performance of a double threshold or M-out-of-N detector is discussed. Detection performance for the suggested method is based on the probability that a return crosses the threshold for the Mth time (a detection is declared) on the kth return or look. It is shown that this formulation has many advantages, as compared with the conventional method of analysis which employs the binomial probability distribution, since the upper limit N is not contained in the resulting probability expressions. It is shown that the probability of detection obtained by the alternate method is the same as that obtained if the detection method were analyzed as a Markov chain with M+1 states. Use of the method results in simple expressions for the mean and variance of the number of looks before detection, provides an alternative way of estimating the probability of a threshold crossing, and leads to computationally simple bounds for the probability of false alarm.     

Local SNR considerations in decentralized CFAR detection

We consider the decentralized detection problem, involving N sensors and a central processor, in which the sensors transmit unquantized data to the fusion center. Assuming a homogeneous background for constant false-alarm rate (CFAR) analysis, we obtain the performances of the system for the Swerling I and Swerling III target models. We demonstrate that a simple nonparametric fusion rule at the central processor is sufficient for nearly optimum performance. The effect of the local signal-to-noise ratios (SNRs) on the performances of the optimum detector and two suboptimum detectors is also examined. Finally, we obtain a set of conditions, related to the SNRs, under which better performance may be obtained by using decentralized detection as compared with centralized detection     

A Suboptimum Rank Test for Nonparametric Radar Detection

The optimum rank detector structure, in the Neyman-Pearson sense and under Gaussian noise conditions, is approximated by a suboptimum structure that depends on an adjustable parameter. This new rank detector, which operates on radar video signal, includes other well-known detectors as particular cases. The asymptotic relative efficiency (ARE) of the proposed rank detector is computed, with its maximum value the ARE of the locally optimum rank detector (LORD). The detection probability versus signal-to-noise ratio, and the effects of interfering targets are also calculated by Monte-Carlo simulations for different parameter values.     

Nonparametric rank detectors under K-distributed clutter in radar applications

This correspondence deals with a comparative analysis of parametric detectors versus rank ones for radar applications, under K-distributed clutter and nonfluctuating and Swerling II target models. We show that the locally optimum detectors (LODs) (optimum for very low signal-to-clutter ratio (SCR)) under K-distributed clutter are not practical detectors; on the contrary, asymptotically optimum detectors (optimum for high SCR) are the practical ones. The performance analysis of the parametric log-detector and the nonparametric (linear rank) detector is carried out for independent and identically distributed (IID) clutter samples, correlated clutter samples, and nonhomogeneous clutter samples. Some results of Monte Carlo simulations for detection probability (P/sub d/) versus SCR are presented in curves for different detector parameter values.     

Performance analysis of linearly combined order statistic CFARdetectors

Linearly combined order statistic (LCOS) constant false-alarm rate (CFAR) detectors are examined for efficient and robust threshold estimation applied to exponentially distributed background observations for improved detection. Two optimization philosophies have been employed to determine the weighting coefficients of the order statistics. The first method optimizes the coefficients to obtain efficient estimates of clutter referred to the censored maximum likelihood (CML) and best linear unbiased (BLU) CFAR detectors. The second optimization involves maximizing the probability of detection under Swerling II targets and is referred to as the most powerful linear (MPL) CFAR detector. The BLU-CFAR detector assumes no knowledge of the target distribution in contrast to the MPL-CFAR detector which requires partial knowledge of the target distribution. The design of these CFAR detectors and the probability of detection performance are mathematically analyzed for background observations having homogeneous and heterogeneous distributions wherein the trade-offs between robustness and detection performance are illustrated     

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     

A comparison of two adaptive detection schemes

Two schemes for adaptive detection are compared: Kelly's generalized likelihood ratio test (GLRT) and the mean level adaptive detector (MLAD). Detection performance, P_D, is predicted for the two schemes under the assumptions that the input noises are zero-mean complex Gaussian random variables that are temporally independent but spatially correlated; and the amplitude of the desired signal is Rayleigh distributed. P_D is computed as a function of the false alarm probability, the number of input channels, the number of independent samples per channel, and the matched filtered output signal-to-noise (S/N) power ratio. In this analysis the GLRT is shown to have better detection performance than the MLAD. The difference in detection performance increases as one uses fewer input samples. However, the required number of samples necessary to have only a 3 dB detection loss for both detection schemes is approximately the same. This is significant since for the present, the MLAD is considerably less complex to implement than the GLRT     

Decentralized CFAR signal detection

The authors develop the theory of CA-CFAR (cell-averaging constant false-alarm rate) detection using multiple sensors and data fusion, where detection decisions are transmitted from each CA-CFAR detector to the data fusion center. The overall decision is obtained at the data fusion center based on some k out of n fusion rule. For a Swerling target model I embedded in white Gaussian noise of unknown level, the authors obtain the optimum threshold multipliers of the individual detectors. At the data fusion center, they derive an expression for the overall probability of detection while the overall probability of false alarm is maintained at the desired value for the given fusion rules. An example is presented showing numerical results     

Radar Detection of Correlated Targets in Clutter

This paper provides general models of radar echoes from a target. The rationale of the approach is to consider the echoes as the output of a linear dynamic system driven by white Gaussian noise (WGN). Two models can be conceived to generate N target returns: samples generated as a batch, or sequentially generated one by one. The models allow the accommodation of any correlation between pulses and nonstationary behavior of the target. The problem of deriving the optimum receiver structure is next considered. The theory of "estimator-correlator" receiver is applied to the case of a Gaussian-distributed time-correlated target embedded in clutter and thermal noise. Two equivalent detection schemes are obtained (i. e., the batch detector and the recursive detector) which are related to the above mentioned procedures of generating radar echoes. A combined analytic-numeric method has been conceived to obtain a set of original detection curves related to operational cases of interest. Finally, an adaptive implementation of the proposed processor is suggested, especially with reference to the problem of on-line estimation of the clutter covariance matrix and of the CFAR threshold. In both cases detection loss due to adaptation has been evaluated by means of a Monte Carlo simulation approach. In summary, the original contributions of the paper lie in the mathematical formulation of a powerful model for radar echoes and in the derivation of a large set of detection curves.     

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     

Nonparametric Radar Extraction Using a Generalized Sign Test

A nonparametric procedure used in a constant false alarm rate (CFAR) radar extractor for detecting targets in a background of noise with unknown statistical properties is described. The detector is based on a generalization of the well-known two-sample sign test and thus requires a set of reference noise observations in addition to the set of observations being tested for signal presence. The detection performance against Gaussian noise is determined for a finite number of observations and asymptotically, for both nonfluctuating and pulse-to-pulse Rayleigh fluctuating target statistics. It is noted that the performance loss, as compared to the optimum parametric detector, depends critically on the number of reference noise observations available when the number of hits per target is not large. In the same case a much larger loss is also found for a pulse-to-pulse fluctuating target even though the asymptotic loss is the same as for a nonfluctuating target. A comparison is finally made with a detector based on the Mann-Whitney test, which usually is considered to be one of the better nonparametric procedures for the two-sample case.     

Modified Generalized Sign Test Processor for 2-D Radar

The modified generalized sign test processor is a nonparametric, adaptive detector for 2-D search radars. The detector ranks a sample under test with its neighboring samples and integrates (on a pulse-to-pulse basis) the ranks with a two-pole filter. A target is declared when the integrated output exceeds two thresholds. The first threshold is fixed and yields a 10-6 probability of false alarm when the neighboring samples are independent and identically distributed. The second threshold is adaptive and maintains a low false-alarm rate when the integrated neighboring samples are correlated and when there are nonhomogeneities, such as extraneous targets, in the neighboring cells. Using Monte Carlo techniques, probability of false-alarm results, probability of detection curves, and angular accuracy curves have been generated for this detector. The detector was built and PPI photographs are used to indicate the detector's performance when the radar is operated over land clutter.     

无需辅助数据的分布式目标自适应检测器

在非高斯背景和没有辅助数据的条件下,研究了高分辨率雷达分布式目标的自适应检测问题.首先采用有序检测理论和协方差矩阵的迭代估计方法粗略估计散射点集合,进一步利用迭代估计方法获得协方差矩阵的近似最大似然估计,提出了无需辅助数据的自适应检测器(ADWSD).ADWSD在非高斯背景下具有近似恒虚警率特性,且检测性能远好于修正的...     

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.     

Weak Signal Detection in Non-Gaussian Noise of Unknown Level

An adaptive threshold detector to test for the presence of a weak signal in additive non-Gaussian noise of unknown level is discussed. The detector consists of a locally optimum detector, a noise level estimator, and a decision device. The detection threshold is made adaptive according to the information provided by the noise level estimator in order to keep a fixed false-alarm probability. Asymptotic performance characteristics are obtained indicating relationships among the basic system parameters such as the reference noise sample size and the underlying noise statistics. It is shown that, as the reference noise sample size is made sufficiently large, the adaptive threshold detector attains the performance of a corresponding locally optimum detector for detecting the weak signal were the noise level known.     

Optimum and mismatched detection against K-distributed plusGaussian clutter

We derive the optimum radar receiver to detect fluctuating and non-fluctuating targets against a disturbance which is modeled as a mixture of coherent K-distributed and Gaussian-distributed clutter. In addition, thermal noise, which is always present in the radar receiver, is considered. We discuss the implementation of the optimum coherent detector, which derives from the likelihood ratio test under the assumption of perfectly known disturbance statistics, and evaluate its performance via a numerical procedure, when possible, and via Monte Carlo simulation otherwise. Moreover, we compare the performance of the optimum detector with those of two detectors which are optimum for totally Gaussian and totally K-distributed clutter respectively, when they are fed with such a mixed disturbance. We conclude that, though the optimum detector has a larger computational cost, it provides sensibly better detection performance than the mismatched detectors in a number of operational situations. Thus, there is a need to derive suboptimum target detectors against the mixture of disturbances which trade-off the detection performance and the implementation complexity     

Cascaded detector for multiple high-PRF pulse Doppler radars

A postdetection design methodology for a multiple high-pulse-repetition frequency (PRF) pulse Doppler radar has been developed. The postdetection processor consists of an M out of N detector where range and target ambiguities are resolved, followed by a square-law detector which enhances the minimum signal-to-noise (S/N) power-ratio per pulse burst performance. For given probabilities of false alarm and detection, formulas are derived from which the three thresholds associated with the cascaded detector can be found. Fundamental tradeoffs between the minimum S/N required, number of ghosts, and the number of operations (NOPs) that the cascaded detector must perform are identified. It is shown that the NOPs and the number of ghosts increase and the minimum S/N required decreases as the binary M out of N detector passes more detections to the square-law detector     

Detection Performance in Clutter with Variable Resolution

Experiments were conducted to determine the influence of background clutter on target detection criteria. The experiment consisted of placing observers in front of displayed images on a TV monitor. Observer ability to detect military targets embedded in simulated natural and manmade background clutter was measured when there was unlimited viewing time. Results were described in terms of detection probability versus target resolution for various signal to clutter ratios (SCR). The experiments were preceded by a search for a meaningful clutter definition. The selected definition was a statistical measure computed by averaging the standard deviation of contiguous scene cells over the whole scene. The cell size was comparable to the target size. Observer test results confirmed the expectation that the resolution required for a given detection probability was a continuum function of the clutter level. At the lower SCRs the resolution required for a high probability of detection was near 6 line pairs per target (LP/TGT), while at the higher SCRs it was found that a resolution of less than 0.25 LP/TGT would yield a high probability of detection. These results are expected to aid in target acquisition performance modeling and to lead to improved specifications for imaging automatic target screeners.