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.     

High Range-Resolution Monopulse Tracking Radar

High range-resolution monopulse (HRRM) tracking radar which maintains wide instantaneous bandwidth through both range and angle error sensing channels provides range, azimuth, elevation, and amplitude for each resolved part of the target. The three-dimensional target detail can be used to improve and extend radar performance in several ways: for improved precision of target location, for target classification and recognition, to counter repeater-type ECM, to improve low-angle multipath tracking, to resolve multiple targets, as a miss-distance measurement capability, and for improved tracking in chaff and clutter. These have been demonstrated qualitatively except for the ECCM to repeater ECM and low-altitude tracking improvement. Initial results from an experimental HRRM radar with 3-ns pulse length show resolution of aircraft into its major parts and precise location of each resolved part accurately in range and angle. Realtime closed-loop tracking is performed on aircraft in flight using high-speed sampled, digitized, and processed HRRM range and angle video data. Clutter rejection capability is also demonstrated.     

Improved Three Subaperture Method for Elevation Angle Estimation

The three subaperture method is a technique for estimating the arrival angles of two targets located in the main beam of a radar. The problem of estimating the arrival angle of a target in the presence of multipath is considered, and it is shown how the accuracy of the three subaperture method can be improved by making use of the information that the amplitude of the direct ray is larger than that of the reflected ray.     

Frequency Diversity in Low-Angle Radar Tracking

Elevation angle errors due to sea-reflected multipath are evaluated theoretically for a radar operating in an off-boresight monopulse tracking mode. The computer simulation accounts only for specular reflection. Angle estimates at three frequencies are assumed to be available. It is shown that one can improve upon a simple average of the three indicated angles by unequally weighting them according to rank (lowest, middle, or highest). Some sample computations show that there is an optimum difference between the three frequencies.     

Multipath Limitations on Low-Angle Radar Tracking

This paper investigates the problem of tracking targets at a low elevation angle in the presence of specular and diffuse multipath. Quantitative estimates are derived of the elevation angles, and hence, range, at which targets of specified height can be accurately tracked. A parametric approach is followed in which the long-standing uncertainty of how terrain forward-scatters at low grazing angles is recognized at the outset. Particular attention is given to the effects of target motion which permit rejection of multipath components falling outside the radar tracker's passband. The results are presented in a form which can be readily applied to a spectrum of radar trackers with differing requirements. The limited experimental ental data on the specular and diffuse scattering parameters for several generic types of terrain are applied to estimate the significance of multipath under different situations and to indicate specific areas in which additional experimental data are critically needed.     

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     

Multipath Angle Error Reduction Using Multiple-Target Methods

The usual methods of reducing multipath angle errors in monopulse tracking radar achieve only limited success because they do not attack the root of the problem. A more correct approach is to accept the multipath signal as a second target and utilize a two-target signal processor which angle tracks both wavefronts. The processor will decouple the return signals so that relatively interference-free data on both waves are obtained. In this paper a signal processor for separating signal from (N - 1) multipath components is developed. The processor is then specialized to the case of only one multipath signal and evaluated by a computer simulation. Data show that large improvements are possible as compared to the usual monopulse tracking system. In particular, the usual large bias errors at low elevation angles are eliminated. Tracking precision compares favorably with the theoretically best possible for two-target tracking systems.     

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。     

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.     

直达与非直达环境中的多目标解耦直接定位方法

针对直达（LOS）与非直达（NLOS）环境中的定位问题,提出了一种波形已知条件下的单阵地多目标直接定位（DPD）算法。该算法针对发射时间已知和未知两种情况,利用多径信号到达角度与时延关于障碍物（或反射体）、观测站与目标位置参数的数学关系,建立了三维目标位置的最大似然（ML）函数,无需估计测量参数,避免了传统两步定位方法所需的非直达径识别与数据关联。为了克服多目标定位中的高维非线性优化问题,该算法利用独立波形信息将多目标定位解耦为对各个目标单独求解。通过对目标函数有效近似,算法在发射时间已知和未知两种情况下均仅需三维网格搜索,比相应的两步定位方法具有更低的计算量。此外,基于多径定位场景,推导了发射时间已知和未知两种情况下的位置估计克拉美罗界（CRB）。仿真结果表明：算法的定位性能能够逼近相应的克拉美罗界,比传统两步定位方法和子空间直接定位算法具有更高的定位精度。     

Beam resource scheduling for a VHF-MIMO radar network in low-angle tracking

The low-angle tracking in multipath interference is a challenging problem for the Very High Frequency (VHF) radar. The colocated Multi-Input Multi-Output (MIMO) technique can remedy such a defect. In this paper, a Joint Beam-Target Assignment and Power Allocation (JBTAPA) strategy is proposed for the VHF-MIMO radar network tracking low-angle targets. The core of the JBTAPA strategy is to improve the worst tracking accuracy among multiple targets by assigning appropriate beams to targets and allocating the power resource in each beam using the feedback information in the tracking cycle. Taking into account the transmit multipath and receive multipath, we derive the Cramér-Rao Lower Bound (CRLB) on angle estimate, which is then incorporated in the Predicted Conditional CRLB (PC-CRLB). A more accurate and consistent lower bound is provided as the optimization metric since the PC-CRLB is based on the most recently realized measurements. A two-stage-based technique is proposed to solve the JBTAPA problem, which is originally NP-hard. Simulation results verify the effectiveness and efficiency of the proposed method. The results also imply that the target reflectivity plays one of the important roles in resource allocation.     

ISAR imaging of targets at low elevation angles

The problem of inverse synthetic aperture radar (ISAR) image reconstruction of targets at low elevation angle is considered. In this geometric condition the main causes affecting the reconstructed ISAR image are the multipath effect due to the reflection of the Earth's surface and the angular motions of the target produced by external action like wind, fast maneuvering, and sea waves as in the case of ships. The aim of this work is to analyze the effects that the multipath and the target angular motions jointly produce on the ISAR image. The results show that multipath generates some artifacts in the image whereas the target oscillations undergo a spatial-dependent blurring of the point spread function of the ISAR system. These theoretical results are validated by presenting some numerical examples relevant to aircrafts and ships in rectilinear or circular motion. A wide discussion on possible solutions of this problem is made in the conclusion     

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     

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     

A Multistage Processing Algorithm for Disturbance Removal and Target Detection in Passive Bistatic Radar

The paper examines the problem of cancellation of direct signal, multipath and clutter echoes in passive bistatic radar (PBR). This problem is exacerbated as the transmitted waveform is not under control of the radar designer and the sidelobes of the ambiguity function can mask targets including those displaced in either (or both) range and Doppler from the disturbance. A novel multistage approach is developed for disturbance cancellation and target detection based on projections of the received signal in a subspace orthogonal to both the disturbance and previously detected targets. The resulting algorithm is shown to be effective against typical simulated scenarios with a limited number of stages, and a version with computational savings is also introduced. Finally its effectiveness is demonstrated with the application to real data acquired with an experimental VHF PBR system.     

Low-Angle Radar Tracking in the Presence of Multipath

This paper is concerned with the problem of tracking radar targets in the low-angle regime where conventional tracking radars encounter difficulty due to the presence of a surface-reflected ray. Starting with a classical maximum-likelihood analysis of the problem of two closely spaced targets, two different techniques are evolved which are theoretically capable of dealing with the multipath problem. The expected accuracy has been studied both analytically and by means of computer simulations. Experimental programs have demonstrated the feasibility of both techniques. The paper also includes a discussion of certain alternative solutions to the problem.     

基于落角约束的超声速导弹制导方案研究

针对超声速导弹具有落角约束条件下的制导问题,提出了一种新的设计方案.首先,在中制导俯冲过程中,采用攻击预先设定的虚拟目标方案,达到期望的中制导末端性能指标;然后,开始末制导俯冲段,雷达开机实时攻击实际目标,使导弹在需用过载和导引头框架角约束条件下,以期望落角命中目标.仿真结果表明,该制导律具有期望的性能要求,易于工程实现.     

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.     

Experimental Results of the Complex Indicated Angle Techique for Multipath Correction

The complex indicated angle technique, applicable to monopulse radars, is being investigated as a means of overcoming the serious degradation of elevation measurement caused by multipath when the target is within a beamwidth or so of the horizon. This technique makes use of the quadrature-phase component of the normalized difference signal, as well as the in-phase component. Results of analysis and computer simulation have been published previously. This paper reports results of a test program using a slightly modified AN/FPS-16 monopulse tracking radar and a simulated target. The results to date indicate a potential for high accuracy, though there are limitations as to the applications for which the technique appears feasible. A computer program has been developed to perform the elevation estimate and to resolve ambiguities.     

Radar Performance with Multipath Using the Complex Angle

The complex angle (CA) method for resolving a low angle target from its multipath signal is evaluated in the presence of system noise. It is shown that standard deviation improvements of around 3-to-1 can be achieved at a 20-dB signal-to-noise power ratio relative to a normal monopulse system without the CA. It is also shown that the CA method is unbiased, giving bias improvements of as much as 100 times relative to normal monopulse. Evaluation of the assumptions in the technique shows very little sensitivity to knowledge of the reflecting surface's conductivity or dielectric constant. However, the method is somewhat sensitive to knowledge of surface roughness.