Tracker and signal processing for the benchmark problem with unresolved targets

Radar signal processing is particularly important in tracking closely spaced targets and targets in the presence of sea-surface-induced multipath. Closely spaced targets can produce unresolved measurements when they occupy the same range cell of the radar. These issues are the salient features of the benchmark problem for tracking unresolved targets combined with radar management, for which this paper presents the only complete solution to date. In this paper a modified version of a recently developed maximum likelihood (ML) angle estimator, which can produce two measurements from a single (unresolved) detection, is presented. A modified generalized likelihood ratio test (GLRT) is also described to detect the presence of two unresolved targets. Sea-surface-induced multipath can produce a severe bias in the elevation angle measurement when the conventional monopulse ratio angle extractor method is used. A modified version of a recently developed ML angle extractor, which produces nearly unbiased elevation angle measurements and significantly improves the track accuracy, is presented. Efficient radar resource allocation algorithms for two closely spaced targets and targets flying close to the sea surface are also presented. Finally, the IMMPDAF (interacting multiple model estimator with probabilistic data association filter modules) is used to track these targets. It is found that a two-model IMMPDAF performs better than the three-model version used in the previous benchmark. Also, the IMMPDAF with a coordinated turn model works better than the one using a Wiener process acceleration model. The signal processing and tracking algorithms presented here, operating in a feedback manner, form a comprehensive solution to the most realistic tracking and radar management problem to date.     

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.     

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.     

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.     

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.     

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 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     

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.     

Unresolved Rayleigh target detection using monopulse measurements

When the returns from two or more targets interfere (i.e., the signals are not resolved in the frequency or time domains) in a monopulse radar system, the direction-of-arrival (DOA) estimate indicated by the monopulse ratio can wander far beyond the angular separation of the targets. Generalized maximum likelihood (GML) detection of the presence of unresolved Rayleigh targets is developed with probability density functions (pdfs) conditioned on the measured amplitude of the target echoes. The Neyman-Pearson detection algorithm uses both the in-phase and quadrature portions of the monopulse ratio and requires no a priori knowledge of the signal-to-noise ratio (SNR) or DOA of either target. Receiver operating characteristic (ROC) curves are given along with simulation results that illustrate the performance and application of the algorithm     

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     

KUPS: Knowledge-Based Ubiquitous and Persistent Sensor Networks for Threat Assessment

We propose a knowledge-based ubiquitous and persistent sensor network (KUPS) for threat assessment, in which "sensor" is a broad characterization. It refers to diverse data or information from ubiquitous and persistent sensor sources such as organic sensors and human intelligence sensors. Our KUPS for threat assessment consists of two major steps: situation awareness using fuzzy logic systems (FLSs) and threat parameter estimation using radar sensor networks (RSNs). Our FLSs combine the linguistic knowledge from different intelligent sensors, and our proposed maximum-likelihood (ML) estimation algorithm performs target radar cross section (RCS) parameter estimation. We also show that our ML estimator is unbiased and the variance of parameter estimation matches the Cramer-Rao lower bound (CRLB) if the radar pulses follow the Swerling II model. Simulations further validate our theoretical results.     

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.     

Self-calibrating SSR monopulse receiver

An extension of the monopulse technique for estimating the target azimuth in a secondary surveillance radar (SSR) is considered. The idea is to associate in pairs monopulse measurements coming from the amplitude processor (AP) at the dwell time processing level. This allows the automatic compensation of the bias errors due to the misalignments in the receiver channels, thus eliminating the necessity for periodic system calibration. This dual-pulse technique also allows for the practical use of the dot product receiver as a modification of the AP receiver. This, in turn, implies that the variance of each dual-pulse estimate is uniformly maintained at the monopulse maximum-likelihood level over the whole off-boresight angle (OBA) range     

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。     

机载雷达中的单脉冲技术

 本文总结机载雷达中单脉冲技术的研究和应用,着重讨论幅度比较系统的关键技术,给出有关数据。 机载雷达中的单脉冲技术着眼于抗干扰性能和特殊应用。这些应用包括空对地测距、角分辨力改进、地形防撞。本文阐述了这些特殊应用。     

反向交叉眼对单脉冲雷达干扰效果分析及仿真验证

交叉眼干扰被认为是对单脉冲雷达干扰最有效的方式之一。基于雷达方程建立了隔离平台回波下的两点源反向交叉眼干扰模型，推导了交叉眼干扰欺骗角一般性公式，研究了干扰机发射天线间距、干扰平台旋转角和干扰机相对雷达之间距离等参数变化对角度欺骗效果的影响，并依据单脉冲雷达接收机获取角度的信息处理流程，建立了单脉冲雷达接收机仿真模型，对交叉眼数学模型的正确性和局限性进行了分析。研究结果表明：单脉冲雷达越靠近两点源交叉眼干扰机中心线、干扰机两发射天线间距越大、与干扰机距离越近时，角度欺骗效果越好；单脉冲雷达的欺骗角度随着与干扰机距离的接近呈指数式增大；数学模型和仿真模型计算的单脉冲雷达角度误差最大值随干扰机天线与雷达天线中心连线的夹角的增大呈指数化增长。研究可为交叉眼干扰工程设计作参考。     

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.     

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.