Detection of Slow Fluctuating Targets with Frequency Diversity Channels

In this paper an exact closed-form expression for the radar detection probability is derived and results are plotted for a frequency diversity radar receiver. The receiver model performs post-detection integration on all received pulses in all diversity channels. The target model assumed is the slow fluctuating Rayleigh-distributed (Swerling case I target) scatterer. Each of the M frequency diverse channels receives N amplitude-correlated returns to give a total of NM post square-law detection integrations. The tabulated data falls between the two extreme cases, that for which all the returns are amplitude-correlated and that for which each return is independent. The plotted results fall close to the figures obtained through simple empirical relationships.     

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.     

False alarm analysis of the envelope detection GO-CFAR processor

The greatest of constant false alarm rate processor (GO CFAR) is a useful architecture for adaptively setting a radar detection threshold in the presence of clutter edges. The GO CFAR input is often the envelope detected in-phase (I) and quadrature (Q) channels of the baseband signal (x_e=√(I²+Q²)). This envelope detection can also be approximated using x=a max{|I|,|Q|}+b min{|I|,|Q|} which requires less complex hardware (a and b are simple multiplying coefficients). The envelope GO CFAR processor and several envelope approximation GO CFAR processors are compared in terms of the probability of false alarm (PFA) performance. Closed-form expressions which describe the PFA performance are given and their accuracy evaluated. It is shown that for all cases, the PFA is proportional to the number of reference cells n for small threshold multiplier T and inversely proportional to n for large T. A region of intersection occurs where the PFA is the same for two different values of n. For example, at T'=1.68 in the |I|+|Q| GO CFAR (a=1, b=1) the PFA for n=1 is equal to the optimal n=∞ fixed-threshold PFA (PFA=0.112)     

Evaluating a multiple-hypothesis multitarget tracking algorithm

The performance evaluation of multiple-hypothesis, multitarget tracking algorithm is presented. We are primarily interested in target-detection/track-initiation capabilities as measures of performance. Through Monte Carlo simulations, a multiple-hypothesis tracking algorithm was evaluated in terms of 1) probability of establishing a track from target returns and 2) false track density. A radar was chosen as the sensor, and a general multiple-hypothesis, multitarget tracking algorithm was used in the Monte Carlo simulations. The simulation results predict the probability of establishing a track from returns of a target as well as the false track density per scan volume per unit time. The effects of the target radar cross section and the radar power, measured through the mean signal-to-noise ratio (SNR) were studied, as were the effects of detection threshold and track quality threshold. Computational requirements were also investigated     

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.     

Scanning, Tracking, and Mapping State Variable Estimation Algorithms

Recursive state equation estimation algorithms are derived to determine optimal estimation error covariance and state estimate for a linear dynamic system, driven by time-varying and positionverying (or angle-varying) functions whose a priori covariance are described. Retracing the same trajectory with the system measuring device causes the position varying function to repeat and can significantly reduce estimation errors. Applications for these algorithms include improving accuracy of a position dependent quantity to be mapped, or recursively processing radar or sonar data from repeating scans over the same area. Three types of return path patterns are considered: 1) multiple independent returns, 2) reverse returns, and 3) cyclical returns.     

Adaptive Correlation Regions for Alpha-Beta Tracking Filters

The design of correlation regions for track-while-scan systems is examined, assuming the requirement to maintain a constant probability of successful correlation. Starting with the assumption of independent and Gaussian-distributed range and azimuth errors in the sensor and assuming a constant-coefficient isotropic ?-? tracking filter, it is shown how the correlation region design must include such factors as sensor errors, timing jitter, tracking errors, and the asynchronous operation of the tracking function with respect to the sensor measurements. For a maneuvering target, it is shown that the size of the correlation region must be equal to the sum of the radius used for the straight-line case plus the magnitude of any tracking bias which results from deviation from the straight-line trajectory assumed in the tracking filter. An upper bound is derived for the magnitude of the bias which could reasonably be expected in typical maneuvers. By specifying the size of the correlation region on a constant probability basis, it is possible to obtain better discrimination against false targets and improved detection of maneuvers by sensing the development of tracking biases.     

Second time around radar return suppression using PRI modulation

A technique for suppressing second-time-around radar returns using pulse-repetition interval (PRI) modulation is presented and analyzed. It is shown that a staggered PRI radar system can offer considerable improvement over a nonstaggered radar system in rejecting second-time-around returns which cause false alarms. This improvement is a function of detector implementation (noncoherent integrator or binary integrator), the number of staggered PRIs, the quiescent false alarm number, the Swerling number of the false return, the transmitted signal power, the second-time-around noise power, and the quiescent noise power of the radar. Small changes in transmitted signal power can be traded off with the quiescent false alarm number to suppress the bogus return significantly. In addition, for a noncoherent integrator, all other parameters being equal, if the second-time-around return is a Swerling case II or IV target, then there is an optimum number of staggered PRIs that can be chosen to minimize the likelihood of its detection. It is also shown that the binary integrator significantly reduces the number of second-time-around return detections when compared with the noncoherent integrator. However, there is an accompanying loss of detection     

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.     

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 Gaussian Targets: The Track-on-Jam Problem

When a radar with amplitude comparison monopulse arithmetic encounters signals from multiple Gaussian sources it will "point" to the centroid of the incident radiation. The probability density function (pdf) of the monopulse ratio when N independent samples of difference and sum signals are processed in a maximum likelihood receiver is derived. For finite jam-to-noise ratio the estimate has a bias which is independent of N. The variance in the estimate does however depend upon N. Central moments of order less than or equal 2N - 2 exist and are given by a simple formula. Plots of the pdf and its bias and variance for various jam-to-noise ratios, locations of the centroid with respect to the boresight direction, and number of samples processed are presented in the accompanying figures.     

Radar detection in clutter

Clutter is defined as any unwanted radar return. The presence of clutter in a range/Doppler cell complicates the detection of a target return signal in that cell. In order to quantify the effect of clutter on the probability of detection, we must first specify sets of models suitable for representing the clutter and target. The simplest and most common model for clutter is based on the gamma density. We include two additional models, the NCG and NCGG clutter models for low grazing angles. They are motivated by physical arguments, the latter of which can accommodate the well-known phenomenon of speckle. Using one of these models for clutter together with one of several models for targets, we determine, in a range/Doppler cell, expressions for probabilities of detection of a target in the presence of clutter. It is important to control the probability of false alarms. The presence of clutter in a cell necessitates an increase in the detection threshold setting in order to control false alarms, thus lowering the probability of detection. If the clutter level is unknown, then we need to take measurements of the clutter and use it to adjust the threshold. The more clutter samples we take, the better the estimate of the clutter level and the less is the resulting detection loss. Using the expressions for the probability of detection in clutter, we can quantify the detection loss for a pair of commonly used constant false-alarm rate (CFAR) techniques and investigate how the loss varies with different parameter values, especially with regard to the number of clutter samples taken to estimate the clutter level.     

Contiguous pulse binary integration analysis

The probability of detecting m or more pulses contiguously-that is, in a row-from a pulse train of n pulses is determined when the detection of each pulse is an independent Bernoulli trial with probability p. While a general closed-form expression for this probability is not known, we present an analytical procedure that gives the exact expression for the probability of interest for any particular case. We also present simple asymptotic expressions for these probabilities and develop bounds on the probability that the number of pulses that must be observed before m contiguous detections is greater than or less than some particular number. We consider the implications for binary integration in radar and electronic warfare problems     

Optimal radar threshold determination in Weibull clutter andGaussian noise

A technique is presented for determining the ideal detection threshold when Gaussian noise and Weibull distributed clutter returns are present on a radar receiver and neither is dominant. Quantitative data is presented for several clutter types and false alarm probabilities     

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.     

Determination of Failure Thresholds in Hybrid Navigation

A systematic approach for the determination of failure thresholds for hybrid navigation systems is described. Cost functions which reflect the importance assigned to the consequences of false and missed alarms are minimized. The false alarm probability is obtained as a function of the threshold magnitude by observing the statistical behavior of the instrument outputs in the normal operating mode. The missed alarm probability is obtained by determining the sensitivity of navigation error performance to instrument error sources. Two cost functions are considered. To illustrate this method, failure detection and identification (FDI) thresholds are determined for the Space Shuttle Approach and Landing Test flight.     

A Detection Algorithm for Optical Targets in Clutter

There is active interest in the development of algorithms for detecting weak stationary optical and IR targets in a heavy opticalclutter background. Often only poor detectability of low signal-to-noise ratio (SNR) targets is achieved when the direct correlation method is used. In many cases, this is partly obviated by using detection with correlated reference scenes [1, 2].This paper uses the experimentally justified assumption that most optical clutter can be modeled as a whitened Gaussian randomprocess with a rapidly space-varying mean and a more slowlyvarying covariance [2]. With this assumption, a new constant falsealarm rate (CFAR) detector is developed as an application of the classical generalized maximum likelihood ratio test of Neyman and Pearson. The final CFAR test is a dimensionless ratio. This test exhibits the desirable property that its probability of a false alarm(PFA) is independent of the covariance matrix of the actual noiseencountered. When the underlying noise processes are complex intime, similar considerations can yield a sidelobe canceler CFARdetection criterion for radar and communications. Performance analyses based on the probability of detection (PD)versus signal-to-noise ratio for several given fixed false alarm probabilities are presented. Finally these performance curves are validated by computer simulations of the detection process which use real image data with artificially implanted signals.     

Threshold Control for Automatic Detection in Radar Systems

In automatic detection in radar systems an estimate of background clutter power is used to set the detection threshold. Usually detection cells surrounding the cell under test for the presence of a target are used to estimate the clutter power. In the research reported herein, the target location is taken to be uncertain and thus returns from a target could corrupt this clutter power estimate. It is shown how the threshold should be varied to compensate for the resulting degradation in detection performance. The threshold control procedure is based on a priori information about target location that could be supplied by the radar's tracking system. In addition, a simple procedure for calculating detection and false alarm probabilities for Swerling II target models is presented.     

复杂航迹和起伏地形条件下机载聚束SAR 空变运动补偿

 运动补偿是雷达平台机动飞行条件下合成孔径雷达(SAR)实现精确聚焦成像的前提,而如何精确实现运动误差的空变补偿(误差补偿随目标距离、方位和高度位置的变化而变化)目前还存在很大的挑战。本文提出了一种新的三阶运动补偿方法,能够有效解决复杂雷达航迹和地形起伏条件下运动误差的空变补偿问题。该方法首先以场景中心为参考进行空不变运动补偿,然后以多个子场景中心为参考进行空变运动补偿,最后再利用极坐标格式算法(PFA)统一补偿每个像素的空变误差。仿真数据处理结果验证了本文方法的有效性。     

Frequency-Agility Processing to Reduce Radar Glint Pointing Error

A technique to reduce radar pointing errors due to glint using frequency agility and amplitude weighting is presented. The reduction in rms tracking error is developed into an equation dependent upon the original glint tracking error, ?g, and the number of returns weighted, N. The rms tracking error is thereby reduced approximately by a factor of N. Finally, the equation formulated allows one to evaluate the reduction in glint error versus the number of frequencies chosen for frequency agility.