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.     

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.     

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.     

Multipath Tracking Errors in Elevation-Scanning and Monopulse Radars

The tracking performance of elevation- scanning and monopulse radars in the presence of multipath propagation are compared. The key difference between these two generic types of radars is the way they respond to moving targets. There are no significant differences between their responses to pure specular multipath, nor to diffuse multipath for targets on radial courses. However, they are found to respond quite differently to the diffuse com ponent for low-altitude crossing targets. For these conditions the tracking errors for elevation-scanning radars may be several times those for monopulse radars.     

A Modified Monopulse Technique for Radar Tracking with Low-Angle Multipath

In this paper a new monopluse technique for reducing radar multipath angle-tracking errors is proposed. The solution is achieved by using two monopulse antennas at different heights. The available signals allow one to control the antenna-height diversity so that the elevation angle control signal is not affected by reflected-wave components. The size of the antenna system may be reduced by properly using phase shifters. A possible configuration of such a system is considered and some practical data on the antenna-height diversity are discussed.     

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     

Resolution of Closely Spaced Optical Targets Using MLE and MEM

The capabilities of the maximum likelihood estimator (MLE) and the maximum entropy method (MEM) in resolving closely spaced optical point targets are compared using Monte Carlo simulation results for two different examples. It is found that the MEM is very sensitive to the noise and that the MLE performs better than the MEM in both examples.     

Multipath Fluctuation Effects in Track-While-Scan Radar

A theoretical model of diffuse multipath reflections from rough surfaces is applied to the prediction of multipath power distribu tions in radar coordinates: elevation angle, time delay, and Dop pler frequency. These distributions are used to predict radar tracking errors in elevation angle, for both monopulse and scan ning antenna systems, and typical results are presented. These show a small increase in tracking error for scanning systems, on radially approaching targets, caused by sensitivity of these trackers to amplitude scintillation of the composite direct-plus multipath signal. Effects of knife-edge diffraction and of vegetation ion are briefly considered.     

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.     

雷达低空目标俯仰角跟踪的C2算法研究

在单脉冲测角体制下,由于多径回波信号的干扰,极大地降低了雷达低空目标仰俯角跟踪精度,甚至丢失目标。通过对多路径反射环境模型分析,得出了岸、海基单脉冲雷达低空目标跟踪时仰俯角测量误差的产生原因,提出将传统的多目标分辨算法(C2算法)应用于低角多径环境下目标俯仰角的跟踪测量,并在不同多径反射环境下对不同高度、不同飞行速度和飞行方向的目标进行了仿真,得到良好的仿真结果,表明该算法可较大地提高俯仰角跟踪测量精度。通过对仿真结果的分析,验证了该算法在低空目标跟踪中的有效性和可行性。     

基于模拟器的单脉冲雷达幅相修正方法研究

以某型单脉冲测量雷达为研究对象,深入分析研究幅相一致性修正的必要性和修正原理,通过理论分析与公式推导,经过大量的试验验证,提出一种基于目标模拟的单脉冲测量雷达无塔幅相修正方法。该方法实现后,已成功应用于该型单脉冲测量雷达,解决了传统幅相修正方法受外界因素影响大的技术难题,同时降低了建造成本和维护难度,取得了良好的军事和经济效益。     

相关系数ARMA(p,q)序列分析方法

本文提出相关系数ARMA(p,q)序列分析方法。相关系数ARMA(p,q)序列是从非平稳序列中分离出的一类工程上常见且便于研究的时间序列,在模式识别、故障诊断、信号处理、自动控制和结构响应分析等领域有着广泛的应用。传统的相关函数ARMA(p,q)序列仅是它的一个特例。文中建立了相关系数ARMA(p,q)序列的条件极大似然估计和精确极大似然估计,前者在样本较大时简单便于工程应用,后者则在样本较小时仍具有较高的精度,它们通过时域的全程分析,充分利用样本信息确定相关系数ARMA(p,q)序列的均值函数、方差函数和相关系数函数。在此基础上可进行高精度的频谱分析。     

Maximum likelihood azimuth estimation applied to SSR/IFF systems

A conventional (nonmonopulse) secondary surveillance radar (SSR) is significantly cheaper than a monopulse SSR but exhibits much greater azimuthal error, especially when some of the replies are missing. Estimation techniques and their performance are discussed with special reference to SSR applications, and a novel estimator for conventional SSR is described. The proposed technique is a close approximation of the maximum-likelihood estimator (MLE), taking into account the receiver characteristics as well as the missed replies. Estimator performance obtained by analysis and computer simulation is compared with that of conventional estimators that are based on the leading and trailing edges of binary sequences and shows significantly improved accuracy     

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     

Further Results on Multipath Angle Error Reduction Using Multiple-Target Methods

The two-target technique proposed by the author in an earlier paper [1] for reducing radar multipath angle tracking errors has been simulated on a digital computer assuming an actual closed-loop system. When tracking with noise, the technique provides angle error performance which compares quite favorably with the expected performance given in [1] Furthermore, the large bias errors usually encountered in normal monopulse systems at low elevation angles are removed. Results of typical tracks are given, both for the method of [1], and for a modified version of the method which applies primarily to shipboard radar systems. Some results on loss of lock are also presented.     

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.     

Thermal Noise Errors in DF Monopulse Systems Having Log Amplifiers

An analysis of the effects of thermal noise on the accuracy of direction finding (DF) monopulse systems which employ logarithmic amplifiers is presented. Numerical results are presented which indicate that a simple model may be used to compute rms thermal errors for a wide range of signal levels. Analytical results obtained in the limit of large signal-to-noise ratios are compared with standard results used to analyze monopulse systems employing automatic gain control (AGC) circuitry instead of log amplifiers.     

A multipath data association tracker for over-the-horizon radar

A new algorithm, multipath probabilistic data association (MPDA), for initiation and tracking in over-the-horizon radar (OTHR) is described. MPDA is capable of exploiting multipath target signatures arising from discrete propagation modes that are resolvable by the radar. Nonlinear measurement models exhibiting multipath target signatures in azimuth, slant range, and Doppler are used. Tracking is performed in ground coordinates and therefore depends on the provision of estimates of virtual ionospheric heights to achieve coordinate registration. Although the propagation mode characteristics are assumed to be known, their correspondence with the detections is not required to be known. A target existence model is included for automatic track maintenance. Numerical simulations for four resolvable propagation modes are presented that demonstrate the ability of the technique to initiate and maintain track at probabilities of detection of 0.4 per mode in clutter densities for which conventional probabilistic data association (PDA) has a high probability of track loss, and suffers from track bias. A nearest neighbor version of MPDA is also presented     

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.