Maximum-Likelihood Detection of Unresolved Radar Targets and Multipath

Interference in the form of multipath or uncooperative targets can seriously degrade the angle-of-arrival estimation accuracy of mutiplebeam processors. In this paper, the generalized likelihood ratio test is used to derive a test to detect the presence of interference for multiple beam processors. The detector performance is then analyzed in detail with respect to its dependence on signal-to-noise ratio (SNR), signal-to-interference ration (SIR), and on the relative phase between the target and interfering signals. It is shown that good detection performance can be obtained unless the phase difference between the target and interference signals is either in or out of phase.     

Complex Indicated Angles Applied to Unresolved Radar Targets and Multipath

The off-axis angle indicated by a conventional monopulse radar is only the real part of a "complex indicated angle." The presence of unresolved targets or multipath distorts the real part (causing an erroneous angle indication) and also produces an imaginary part, which can easily be measured by processing the normally unused quadrature-phase component of the difference signal. Under certain conditions the angles, amplitude ratio, and relative phase of two unresolved targets can theoretically be determined by meas urements of the complex indicated angle on two pulses separated by a short interval. In the special case of multipath, known relationships between the unresolved target and image theoretically permit determination of target elevation with a single pulse.     

Radar Track Acquisition Range

The track acquisiton range of a track-while-scan radar is defined as the range at which the cumulative probability of M detections in N scans is 90 percent. Track acquisition ranges for 2 out of 3, 2 out of 4, and 3 out of 4 detection criteria are presented for Swerling 0, 1, and 3 target models.     

Estimation of Velocity Moments of Radar Targets

The Doppler-velocity spectrum of a coherent burst of radar pulses after reflection from the wake of a reentry body is considered. Time-domain estimators of the mean-wake velocity and velocity spread in a particular range cell are given in terms of the echo of a coherent N-pulse burst. These formulas yield values equivalent to common frequency-domain estimators, but, for short bursts (N < 50), are computationally faster than their frequency-domain counterparts.     

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.     

Synthetic Aperture Imaging Radar and Moving Targets

This paper considers the effects of slowly moving targets as they appear in the output of an airborne coherent side-looking synthetic aperture imaging radar. The image of a moving reflector is described, and two approaches to airborne moving target indication (AMTI) are summarized. It is shown that the effects of target movement are decreased as the radar scan rate is increased, and are increased as the (Doppler processed) compression ratio is increased.     

Angular Tracking of Two Closely Spaced Radar Targets

Bounds on the accuracy of unbiased estimates of the angular coordinates of a target, in the presence of a nearby interfering target, have previously been determined. These bounds allow for the angular resolution of two CW targets to an extent limited only by the signal-to-noise ratio (SNR). An SNR of 40 dB will allow two targets to be resolved at less than one-fifth beamwidth (?/2 X) separation, for most values of target relative phase angles. The maximum-likelihood estimator for this problem, based on the outputs of a plane circular array of receiving elements, is found and simplified. An analog realization of the two-target maximum-likeli-hood processor is presented. This realization has the simple form of two single-target trackers each tracking one of the targets, linked by a decoupling network which accounts for the interference produced in each by the presence of a second target, when the targets are separated by less than a beamwidth. Results of an analog-computer simulation of the system are given and discussed. Finally an application to the finite-size single-target problem is given.     

Raster Scan Track of a Radar Scatterer Ensemble

A method is discussed for tracking the radar cross-section centroid of an ensemble of scatterers, using a raster scan observation technique. Estimation of the mean-squared dimensions of the ensemble is also considered. A maximum permissible beam separation is defined for the scan. Expressions for the bias and variance of the centroid estimates are given. Advantages of the approach are that individual scatterers need not be resolvable, and that the number of beams is independent of the number of scatterers.     

一种基于修正Hough变换的航迹起始算法

为了在重杂波区内检测出运动的目标,提出了一种修正的Hough变换算法用于初始航迹的建立。与传统的算法相比,修正算法充分利用目标的运动学信息,选取了更为合适的变换参量,仅利用较少拍数的量测就可以完成起始,能够在检测概率较高的环境下具有良好的起始性能。计算机仿真结果表明,算法能够克服传统算法的多拍扫描,大大缩短实际的计算量和起始时间,实现对航迹起始的在线改进。     

Measurement of Distributed Targets with the Random Signal Radar

A model of a distributed target as a collection of independent, Poisson distributed point scatterers or scattering centers in a range-velocity target space is introduced and is characterized by a deterministic function called the ?scatterer density function.? This function is the density of the point scatterers in the range-velocity space and can be estimated in a relatively straightforward manner by any radar having adequate resolution in both range and velocity and no ambiguities in the region occupied by the distributed target. The use of the random signal radar with a correlator receiver is considered here and the statistical properties of the correlator output, when the return signal is from a distributed target, are derived. It is shown that the spectral density is simply related to the scatterer density function. The technique is illustrated by an example in which the target is a tornado modeled as a cylinder with constant angular velocity. The example suggests that is a possible to remotely estimate the radar cross section per unit volume as a function of distance from the center of the tornado.     

Maximum Likelihood Elevation Angle Estimates of Radar Targets Using Subapertures

The maximum likelihood estimates of the elevation angles of two closely spaced targets within the beamwidth is considered. For an array divided into three subapertures, a simple, closed form solution is found whose accuracy compares favorably to the maximum likelihood estimate which uses all the individual elements. Simulation results are presented for the case of a radar target located over a smooth reflecting surface.     

Design of Truncated Sequential Tests for Rapidly Fading Radar Targets

Curves and equations are presented from which the exact performance of truncated sequential tests can be determined for one important case: the biased square-law detector for the detection of rapidly fading targets. The method of generating functions is used to derive probability distributions for sample size. It is shown how these probability distributions can be used to determine truncation errors and the effects of multiple-resolution elements. Sample calculations are performed to determine the effects of a particular truncation procedure.     

Probability Density of the Maximum Likelihood Elevation Estimate of Radar Targets

The probability density of the maximum likelihood estimate of elevation angle of a radar target in the presence of multipath is calculated. For detectable signals that have low signal-to-noise ratios, the density is a mixture of a Gaussian density and a delta function at the horizon.     

目标指示精度对跟踪雷达截获概率的影响

在分析压制干扰对目标指示精度影响的基础上,研究了目标指示精度对跟踪雷达截获目标概率的影响,将跟踪雷达截获目标的过程分为落入目标探测区域及发现目标两个过程,建立了相应的评价指标与模型,对模型进行了在不同的干扰及抗干扰条件下进行了仿真验证。     

Natural Resonances of Radar Targets Via Prony's Method and Target Discrimination

The dominant complex natural resonances of radar targets are obtained via Prony's method applied to calculated and measured back-scattered ramp response waveforms. Subject targets are spheres, simple wire models of straight and swept wing aircraft, and realistic models of modern fighter aircraft. It is demonstrated that when the backscattered ramp response waveforms are obtained via Fourier synthesis of limited spectral range harmonic scattering data, some resonance locations at variance with those obtained from reaction integral equation search procedures are obtained. It is also shown, however, that the Prony deduced resonances can be used successfully in predictor-correlator target discrimination.     

Tracking Performance of a Monopulse Radar in the Presence of Multiple Targets

The equations derived by A. J. Rainal for the probability density function of the angle error output of a monopulse radar excited by a Gaussian signal and Gaussian thermal noise are generalized to include the presence of multiple targets. The examples given demonstrate the radar's behavior for various combinations of target and noise parameters.