Bias compensation and tracking with monopulse radars in the presence of multi path

The problem of tracking targets in the presence of reflections from sea or ground is addressed. Both types of reflections (specular and diffuse) are considered. Specular reflection causes large peak errors followed by an approximately constant bias in the monopulse ratio, while diffuse reflection has random variations which on the average generate a bias in the monopulse ratio. Expressions for the average error (bias) in the monopulse ratio due to specular and diffuse reflections and the corresponding variance in the presence of noise in the radar channels are derived. A maximum maneuver-based filter and a multiple model estimator are used for tracking. Simulation results for five scenarios, typical of sea skimmers, with Swerling III fluctuating radar cross sections (RCSs) indicate the significance and efficiency of the technique developed in this paper-a 65% reduction of the rms error in the target height estimate.     

Maximum likelihood angle extractor for two closely spaced targets

In a scenario of closely spaced targets special attention has to be paid to radar signal processing. We present an advanced processing technique, which uses the maximum likelihood (ML) criterion to extract from a monopulse radar separate angle measurements for unresolved targets. This processing results in a significant improvement, in terms of measurement error standard deviations, over angle estimators using the monopulse ratio. Algorithms are developed for Swerling I as well as Swerling III models of radar cross section (RCS) fluctuations. The accuracy of the results is compared with the Cramer Rao lower bound (CRLB) and also to the monopulse ratio technique. A novel technique to detect the presence of two unresolved targets is also discussed. The performance of the ML estimator was evaluated in a benchmark scenario of closely spaced targets - closer than half power beamwidth of a monopulse radar. The interacting multiple model probabilistic data association (IMMPDA) track estimator was used in conjunction with the ML angle extractor     

Exact Detection Probability for Partially Correlated Rayleigh Targets

The detection probability PD of a radar receiver which postdetection integrates N pulses of an expqnentially correlated signal from a Rayleigh target in thermal noise is determined. At the limiting correlation coefficients, p = 1 and p = 0, the analysis yields, respectively, the well known Swerling case 1 and case 2 formulas. The effect of partial (0 ? p ? 1) correlation is exhibited in a set of curves of PD versus signal-to-noise ratio, X, for various N and p. Additional curves compare the exact fluctuation loss determined from the above analysis with an approximate expression universally employed by radar system engineers.     

Angle estimation for two unresolved targets with monopulse radar

Most present-day radar systems use monopulse techniques to extract angular measurements of sunbeam accuracy. The familiar "monopulse ratio" is a very effective means to derive the angle of a single target within a radar beam. For the simultaneous estimation of the angles of two closely-spaced targets, a modification on the monopulse ratio was derived in (Blair and Pearce, 2001), while (Sinha et al., 2002) presented a maximum likelihood (ML) technique via numerical search. In this paper it is shown that the ML solution can in fact be found explicitly, and the numerical search of ((Sinha et al., 2002) is unnecessary. However, the ML solution requires the signal to noise ratio (SNR) for each target to be known, and hence we generalize it so it requires only the relative SNR. Several versions of expectation maximization (EM) joint angle estimators are also derived, these differing in the degree to which prior information on SNR and on beam pattern are assumed. The performances of the different direction-of-arrival (DOA) estimators for unresolved targets are studied via Monte Carlo, and it is found that most have similar performance: this is remarkable since the use of prior information (SNR, relative SNR, beam pattern) varies widely between them. There is, however, considerable performance variability as a function of the two targets' off-boresight angles. A simple combined technique that fuses the results from different approaches is thus proposed, and it performs well uniformly.     

Adaptive digital beamforming for angle estimation in jamming

A radar digital beamforming (DBF) architecture and processing algorithm is described for nulling the signal from a mainlobe electronic jammer and multiple sidelobe electronic jammers while maintaining monopulse angle estimation accuracy on the target. The architecture consists of a sidelobe jamming (SLJ) cancelling adaptive array (AA) followed by a mainlobe jamming (MLJ) canceller. A mainlobe maintenance (MLM) technique or constrained adaptation during the sidelobe cancellation process is imposed so that the results of the SLJ cancellation process do not distort the subsequent mainlobe cancellation process. The SLJ signals and the MLJ signals are thus cancelled sequentially in separate processes. This technique was developed for improving radar processing in determining the angular location of a target, and specifically for improving the monopulse technique by maintaining the accuracy of the target echo monopulse ratio in the presence of electronic jamming by adaptive suppression of the jamming signals before forming the monopulse sum and difference beams     

Thermal Noise in Amplitude Comparison Monopulse Systems

In this paper we consider the problem of estimation of angle of arrival in an Amplitude Comparison Monopulse antenna arrangement with the explicit inclusion of internally generated thermal, i.e., receiver, noise as an interference to the desired measurement. A pulsed type radar is assumed, and an ideal (i.e., point) radar target is postulated. This latter restriction is made so that consideration of the effects of target scintillation, glint, or other external random phenomena can be excluded from our treatment of the problem. In this context, a maximum likelihood analysis is made to determine the form of the estimate of angle of arrival, and the probability density function (pdf) of this quantity is computed. The form of the estimate is found to be a ratio of Gaussian variables quite like that used in conventional monopulse signal processing. The pdf obtained for the estimate is believed to be new, and it serves to emphasize the bias and indeterminate variance effects associated with this type of nonlinear signal processing. Some useful approximations to the pdf are discussed, and a unit of precision for the estimate is defined.     

Radar power multiplier for acquisition of low observables using anESA radar

In this paper the acquisition of a low observable (LO) incoming tactical ballistic missile using the measurements from a surface based electronically scanned array (ESA) radar is presented. We present a batch maximum likelihood (ML) estimator to acquire the missile while it is exo-atmospheric. The proposed estimator, which combines ML estimation with the probabilistic data association (PDA) approach resulting in the ML-PDA algorithm to handle false alarms, also uses target features. The use of features facilitates target acquisition under low signal-to-noise ratio (SNR) conditions. Typically, ESA radars operate at 13-20 dB, whereas the new estimator is shown to be effective even at 4 dB SNR (in a resolution cell, at the end of the signal processing chain) for a Swerling III fluctuating target, which represents a significant counter-stealth capability. That is, this algorithm acts as an effective “power multiplier” for the radar by about an order of magnitude. An approximate Cramer-Rao lower bound (CRLB), quantifying the attainable estimation accuracies and shown to be met by the proposed estimator, is derived as well     

Monopulse Radars Excited by Gaussian Signals

This paper presents the theoretical probability densities of the outputs of both an amplitude-comparison monopulse radar and a phase-comparison monopulse radar when the monopulse radars are excited by Gaussian signals plus Gaussian noises. These probability densities are useful for studying the responses of monopulse radars to noise excitations. For example: Noise excitations arise when the monopulse radars are ?viewing? a noise source or a radar target consisting of randomly moving scatterers. The probability densities also serve as useful approximations for characterizing the outputs of monopulse radars when sinusoidal signals plus Gaussian noises excite the monopulse radars. Some special cases of the probability densities are presented in graphs.     

Model-based multifrequency array signal processing for low-angletracking

Tracking low-altitude targets over the sea is problematic because of interference between the direct and reflected signal. Standard monopulse trackers can experience large errors because of multipath maximum likelihood estimation (MLE) has been used to more accurately estimate the target height in the presence of multipath MLE is a model-fitting technique where the model parameters are chosen to maximize the likelihood function. It is shown that the type of observation model has a large effect on performance. Tracking performance is compared using three different observation models employing varying amounts of a priori information. Results are presented for different array sizes: eight and 32-element arrays and two-element subarrays typical of phase monopulse. Performance is compared with that of standard techniques such as Fourier beamforming and phase monopulse     

Impact of target RCS fluctuations on radar measurement accuracy

The impact of target radar cross section (RCS) fluctuations on the thermal noise limited accuracy of radar measurements of range, range rate, and angle is evaluated for Swerling fluctuation models. The impact is expressed as a modification of the large-signal approximation to the standard deviation σ of measurement error     

Correlation between horizontal and vertical monopulse measurements

Many radar systems use the monopulse ratio to extract angle of arrival (AOA) measurements in both azimuth and elevation angles. The accuracies of each such measurement are reasonably well known: each measurement is, conditioned on the sum-signal return, Gaussian-distributed with calculable bias (relative to the true AOA), and variance. However, we note that the two monopulse ratios are functions of basic radar measurements that are not entirely independent, specifically in that the sum signal is common to both. The effect of this is that the monopulse ratios are dependent, and a simple explicit expression is given for their correlation; this is of considerable interest when the measurements are supplied to a tracking algorithm that requires a measurement covariance matrix. The system performance improvement when this is taken into account is quantified: while it makes little difference for a tracking radar with small pointing errors, there are more substantial gains when a target is allowed to stray within the beam, as with a rotating (track-while-scan) radar or when a single radar dwell interrogates two or more targets at different ranges. But in any case, the correct covariance expression is so simple that there is little reason not to use it. We additionally derive the Cramer-Rao lower bound (CRLB) on joint azimuth/elevation angle estimation and discover that it differs only slightly from the covariance matrix corresponding to the individual monopulse ratios. Hence, using the individual monopulse ratios and their simple joint accuracy expression is an adequate and quick approximation of the optimal maximum likelihood procedure for single resolved targets.     

Detection of Target Multiplicity Using Monopulse Quadrature Angle

The feasibility of using the indicated quadrature angle of arrival of a monopulse radar to discriminate a single target from multiple targets, separated in angle within a radar resolution cell, is investigated. The analysis is performed for steady (fixed) and Rayleigh fluctuating targets which cover a broad range of target characteristics. In both cases, the interfering signals due to noise and clutter in the sum and difference monopulse channels are assumed to be independent, zero-mean Gaussian processes. Detection and false alarm probabilities are evaluated analytically and the receiver operating characteristics are obtained for both fixed and fluctuating target cases. It is shown that multiple targets can be discriminated from a single target condition by integrating the indicated monopulse quadrature angle of arrival from several independent pulses. It is also shown that the probability of detecting multiple targets increases as the fluctuation in the target radar cross section decreases, approaching the fixed amplitude case in the limit.     

非相干Rice杂波中的恒虚警检测

 地杂波的统计特性常常可以用Rice模型来描述,其物理基础是认为地杂波由一些大的固定散射体引起的稳定分量和大量小的随机分布的运动散射体引起的瑞利起伏分量所合成。文献[2]研究了稳定分量不相干时Rice杂波中离散时间最佳检测的估值器——相关器结构,但无显式解,实现有困难。文献[3]导出了Rice杂波中SwerlingⅡ目标的离散时间检测的似然比检测器结构。在此基础上,本文给出了一种修正平方律结构的似然比检测器,并和通常的平方律检测器作了性能比较。     

基于3DT的空时自适应单脉冲参数估计算法

空时自适应处理(STAP)是机载预警雷达抑制杂波和干扰的一项关键技术,而多普勒三通道联合自适应处理(3DT)是适合工程实现的降维(RD)STAP方法。STAP目标检测后还需进一步估计目标的角度参数,因此将自适应单脉冲(AM)技术引入3DT,提出了一种高精度联合估计目标速度与方位空间角的空时自适应单脉冲算法。理论分析与仿真实验结果表明,当目标多普勒频率偏离检测多普勒单元中心频率时,该算法能同时减少目标多普勒跨越损失和空时导引矢量失配损失,进而提高输出信杂噪比(SCNR),改善目标测角精度。     

Monopulse radar based on spatiotemporal correlation of stochastic signals

The theory and technique of angle-of-arrival (AOA) estimation using random-noise or other stochastic transmit waveforms is addressed. The additional uncertainties induced by signal itself and the statistical complexity of the received signals result in major challenges. The statistical properties of the random-noise interferometer and monopulse radar system are studied and compared theoretically using an approximation method. Furthermore, a random-noise coherent correlation receiver (CCR) architecture is proposed. The concept of mean monopulse characteristic curve (MMCC) is introduced. Experimental results using an X-band random-noise monopulse radar system validate the theoretical predictions of random-noise monopulse characteristics and suggest potential applications such as surveillance, imaging, and maneuvering target tracking.     

Radar measurement accuracy for fluctuating targets

The impact of target radar cross-section (RCS) fluctuations on the thermal noise limited accuracy of radar measurements of range, range rate, and angle are evaluated for the Swerling fluctuation models. For large signal-to-noise ratios (SNRs), the accuracy criterion used is the measurement error with the same probability span as the one corresponding to the standard deviation points of the measurement error for the nonfluctuating model.<>     

单脉冲成像算法性能分析

单脉冲技术通过比较单个脉冲多路回波信号的信息实现对目标角度位置的精确测量,广泛运用于跟踪雷达中。在雷达成像中引入单脉冲技术可以显著提高前视这一合成孔径雷达(SAR)与多普勒波束锐化(DBS)成像盲区雷达图像的清晰度。本文着重对单脉冲成像算法的成像效果分析方法进行研究。从单脉冲和差比的概率密度函数出发,提出了目标图像位置失真、分辨率以及图像信噪比3个对图像质量进行衡量的指标。分析了决定这3个指标的系统及外部环境参数,并给出了相应的计算方法。最终通过数值积分以及Monte-Carlo仿真实验对理论分析结果进行了验证。     

Simple Procedures for Radar Detection Calculations

The literature of radar contains results of Rice, Marcum, Swerling, and Schwartz in several families of curves, which permit radar engineersto estimate the signal energy ratio required for a given level of detectionperformance. The variety of radar problems, however, makes itimpractical to construct curves for all combinations of radar and targetparameters. The concept of detector loss is used here to evaluate lossesattributable to integration and collapsing, with an accuracy of ±0.3 dBon steady targets. This is added to a separate fluctuation loss, modifiedfor diversity effects, to obtain results on all Swerling target modelsand also on partially correlated targets. The accuracy of the combinedlosses is ±0.5 dB for a wide range of detection and false-alarm probabilities.Starting from the basic single-sample detection curves, onlythree additional graphs are needed to find the energy ratio for givendetection performance in any of these cases. Examples are given whichshow the ease with which different radar options may be compared asto performance on an arbitrary type of target.     

Monopulse Estimation of the Centroid of an Ensemble of Radar Scatterers

The use of data obtained by a monopulse radar to estimate the location of the radar cross-section centroid of an ensemble of scatterers is discussed. Both dish and phased-array antenna radars are treated. Expressions for the bias and variance of the centroid estimates are presented, including the effects of the radar receiver and beam pattern characteristics, receiver noise, and the video waveform sampling granularity, as well as the target properties. The monopulse tracking approach discussed here is contrasted with a raster scan approach presented previously.