Monopulse DOA estimation of two unresolved Rayleigh targets

This paper provides for new approaches to the processing of unresolved measurements as two direction-of-arrival (DOA) measurements for tracking closely spaced targets rather than the conventional single DOA measurement of the centroid. The measurements of the two-closely spaced targets are merged when the target echoes are not resolved in angle, range, or radial velocity (i.e., Doppler processing). The conditional Cramer Rao lower bound (CRLB) is developed for the DOA estimation of two unresolved Rayleigh targets using a standard monopulse radar. Then the modified CRLB is used to give insight into the boresight pointing for monopulse DOA estimation of two unresolved targets. Monopulse processing is considered for DOA estimation of two unresolved Rayleigh targets with known or estimated relative radar cross section (RCS). The performance of the DOA estimator is studied via Monte Carlo simulations and compared with the modified CRLB     

Radar measurement extraction in the presence of sea-surface multipath

In the presence of sea-surface multipath monopulse radar signals from a low elevation target have three alternative paths in addition to the direct (radar-to-target) path due to reflections from the sea surface. The specular reflection causes significant signal fading. The diffuse reflection causes an approximately constant bias to the in-phase component of the monopulse ratio, which is the standard extractor of the direction of arrival (DOA) in the monopulse processing. The diffuse reflection also causes higher standard deviation to the in-phase component of the monopulse ratio. We propose a maximum likelihood (ML) angle extraction technique for low elevation targets of known average signal strength having a Rayleigh fluctuation. The results show that this method reduces the error of the estimated angle compared with the conventional monopulse ratio estimator. Subsequently, the ML angle extractor is modified for the unknown average signal strength case. This modified angle extractor has only a small performance degradation compared with the known average signal strength case, but it performs much better than the monopulse ratio based estimator. An algorithm to calculate the accuracy of the estimated angle (or height) is also presented. This angle extractor reduces the root-mean-square error (RMSE) by more than 50% in the signal processing stage when used in a low flying target tracking scenario. The same algorithm can be used to track sea skimmers.     

Statistical description of monopulse parameters for trackingRayleigh targets

The conditional probability density function (pdf) is developed for each monopulse measurement of a Rayleigh target by conditioning the pdf of the complex monopulse ratio on the measured amplitude of the sum signal. The conditional pdf is used to develop the conditional Cramer-Rao Lower Bound (CRLB) for any unbiased estimator of the direction-of-arrival (DOA). Conditional maximum likelihood (CML) and conditional method of moments (CMM) estimators of the DOA are developed along with estimates of the variances associated with the monopulse ratio and DOA estimate. Using simulation results, the performances of the CML and CMM estimators of the DOA are compared with the performance of standard monopulse ratio and the performances of the variance estimators are also studied     

Monopulse-radar tracking of swerling III-IV targets using multiple observations

This paper proposes a novel statistical prediction of monopulse errors (Levanon, 1988) for a radar Swerling III-IV target embedded in noise or noise jamming where multiple observations are available. First, the study of the maximum likelihood estimator (MLE) of the complex monopulse ratio for a Swerling III-IV target embedded in spatially white noise allows us to extend the use of the MLE practical approximate form introduced by Mosca (1969) for Swerling 0-I-II cases. Afterward, we derive analytical formulas for both the mean and variance of the MLE in approximate form conditioned by the usual detection step performed on the sum channel of a monopulse antenna. Last, we provide a comparison of target direction of arrival (DOA) estimation performance based on monopulse ratio estimation as a function of the Swerling model in the context of a multifunction radar.     

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.     

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.     

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.     

Multiple radar targets estimation by exploiting induced amplitude modulation

This work deals with the problem of estimating complex amplitudes, Doppler frequencies, and directions of arrival (DOA) of multiple targets present in the same range-azimuth resolution cell of a surveillance radar. The maximum likelihood (ML) and the asymptotic (large sample size) ML (AML) estimators are derived. To reduce the computational complexity of the maximization of the nonlinear two-dimensional criterion function of the AML estimator, we propose a computationally efficient algorithm based on the RELAXation method. It allows decoupling the problem of jointly estimating the parameters of the signal components into a sequence of simpler problems, where the parameters of each component are separately and iteratively estimated. The proposed method overcomes the resolution limitation of the classical monopulse technique and resolves multiple targets exhibiting an arbitrarily small difference in azimuth as long as their Doppler frequencies differ at least by the inverse of the number of integrated pulses, provided that enough signal-to-noise ratio (SNR) per pulse is available. The performance of the proposed AML-RELAX estimator is numerically investigated through Monte Carlo simulation and Cramer-Rao lower bound (CRLB) calculation.     

Difference beam aided target detection in monopulse radar

The classical detection step in a monopulse radar system is based on the sum beam only,the performance of which is not optimal when target is not at the beam center. Target detection aided by the difference beam can improve the performance at this case. However, the existing difference beam aided target detectors have the problem of performance deterioration at the beam center, which has limited their application in real systems. To solve this problem, two detectors are proposed in this paper. Assuming the monopulse ratio is known, a generalized likelihood ratio test(GLRT) detector is derived, which can be used when targeting information on target direction is available. A practical dual-stage detector is proposed for the case that the monopulse ratio is unknown. Simulation results show that performances of the proposed detectors are superior to that of the classical detector.     

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     

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。     

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     

两种自适应方向图峰值副瓣控制方法比较

自适应阵列（或称自适应波束形成）目前已广泛应用到雷达、声纳和通信领域中用来抑制各种干扰（有意的干扰，杂波干扰和多用户干扰等）。在雷达应用中，为了减轻脉冲欺骗式干扰或旁瓣目标并利用单脉冲雷达来准确测量目标波达方向．要求自适应方向图具有低副瓣和稳定的主瓣形状。在实际应用中，各种失配误差将降低自适应阵列的性能．这些误差包括由于目标的波达方向不精确引起的信号指向误差，由通道失配和位置扰动引起的阵列校准误差和由小样本教引起的协方差矩阵估计误差。在此情况下，自适应波束形成的性能大大下降（干扰抑制性能变差。主瓣失真和高的副瓣）。已提出了一种基于二次约束的集成峰值副瓣控制（integrated peak sidelobe control，简称IPSC）方法。该方法可以精确地控制峰值副瓣电平并产生具有稳定的主瓣形状的自适应方向图。研究IPSC中目标信号的影响和信号消除方案以进一步提高IPSC的性能。并将IPSC方法和最新提出的基于二阶锥规划（second-order cone programming，简称SOCP）的分布式峰值副瓣控制（distfibuted peak sidelobe control，简称为DPSC）新方法在性能上进行了比较。仿真结果表明。在干扰抑制性能和方向图控制质量方面IPSC比DPSC性能优越。此外IPSC比DPSC计算高效。     

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.     

Monopulse-radar angle tracking in noise or noise jamming

In many monopulse radars, feedback in the angle-tracking servo system is taken to be directly proportional to the monopulse ratio. In those radars, monopulse measurements are conditioned on simultaneous occurrences of receiver sum-channel video exceeding a detection threshold: if a detection fails to occur, the measurement is ignored, and the angle-tracking servo is made to coast. Such conditioning is shown to be necessary in order that the noise power be finite in the servo feedback. The conditional mean value and conditional variance of the monopulse ratio are derived and quantified in terms of threshold level as well as signal-to-noise ratio. The formulation permits the noise covariance between receiver difference and sum channels to be complex rather than only real-valued, so that the sources of noise jamming are not required to be positioned in the receiving-antenna mainlobe and to be copolarized with the antenna response there. Nonfluctuating and Rayleigh-fluctuating target cases are considered and compared, and fluctuation loss is quantified     

单脉冲跟踪雷达多目标检测算法性能分析

对2种检测单脉冲雷达主波束内是否存在2个不可区分目标的算法进行了推广,将其应用到波束内可能存在N个不可区分的目标,并仿真了波束内存在3个目标时的检测性能。仿真表明,在总信噪比相同时,3个目标的检测概率不一定大于2个目标的检测概率,处于方位向上间距最大的2个目标的信噪比对整个检测概率影响较大。     

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.     

The Effect of Jamming on Monopulse Accuracy

An expression is applied for the probability density function (pdf) of the monopulse ratio when skin echoes from a passive target are contaminated by interference from a jammer. The analysis is valid for arbitrary signal-to-jam ratio and arbitrary locations of the target and jammer in the beam. For an on-axis skin target and a stand-off jammer at an off-axis location, the "pulling" effect of the jammer and the accuracy of the angle estimate are compared with the approximations currently employed in radar performance analysis. The pdf of the monopulse ratio for large and for small signal-to-jam ratios is presented, showing that the pdf is bimodal at small signal-to-jam ratio.     

Monopulse tracking of Rayleigh targets: a simple approach

A simple derivation of the probability distribution of the monopulse ratio is presented. The derivation is based upon a conditional distribution and considers both Rayleigh targets and simple non-Rayleigh cases. The mean is obtained almost without calculation. The variance expression is given completely general noise and glint interpretation. Analytical expressions for angle error mean and spread, including noise, target width, and unresolved targets, are presented as functions of antenna position, in simple and comprehensive diagrams