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.     

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.     

Correspondence

Extraction of elevation information with phased array search radar in the presence of specular reflection from sea surface is presented. Specular reflection from sea causes large peak errors in the measurement of low elevation angle. An algorithm based on complex indicated angle is derived to reduce specular reflection component. From the complex indicated angle and the exactly known or approximately known data, the authors can generate a specular reflection error finding function (SREFF). SREFF clearly indicates where the measurements are much affected by the specular reflection in the complex indicated angle data     

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.     

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.     

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。     

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.     

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.     

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.     

Reconstruction of Target Reflecting Surface Using Differential Geometry

A procedure based on the envelope concept of differential geometry is described that permits the reconstruction of the contour of a smooth, moving, conducting target, satisfying the geometrical optics approximation. The target reflections are assumed to be specular in nature with either one reflection point or multiple resolvable reflection points. The time variation of the range to the reflection point of the target (assumed derivable from a high-resolution radar) and the general motion of the target (assumed derivable from tracking or trajectory information) are employed to reconstruct the contour of that portion of the assumed target surface that is illuminated by the radar. The reconstruction is accomplished by the simultaneous solution of two nonlinear differential equations which are derived using the envelope concept of differential geometry. Several reconstruction examples based on computer analysis are presented which indicate the results obtainable using this method.     

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     

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.     

Reduction of Radar Tracking Errors with Frequency Agility

Frequency agility with random frequency in each pulse gives an improvement in radar angle tracking with a monopulse radar. With a conical-scan tracking radar, the glint error is reduced but fading error can be increased, and the net result must be studied in each case. A theory, usable for calculating angle tracking errors with a frequency agile radar, is given, and two examples showing the error reduction are presented. According to the theory, one part of the glint or fading spectra is ``smeared out' to half the pulse repetition frequency. Another part, the size of which depends on the degree of correlation between pulses, keeps the form of the original spectrum.     

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.     

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。     

Monopulse Radar Angle Tracking Accuracy with Sum Channel Limiting

The variance of angle tracking error is found for an amplitude-comparison form of monopulse radar when the sum channel contains a limiter prior to the angle error detector. The error expression is valid for any shape of transmitted pulse and any duration of range tracking gate but does assume matched filters in signal processing channels. The procedures used are rigorous and an example of results is worked out for the special case of a rectangular transmitted pulse envelope. It is shown, for rectangular pulses, that achievable angle tracking error variance with sum channel limiting is not more than 2.22 dB larger than the theoretical minimum for any processor and not more than 1.29 dB larger than a similar signal processor that uses a "linear" angle error detector. Results apply for large single-pulse signal-to-noise ratio.     

Multiple Target Effects on Monopulse Signal Processing

Analysis of a typical amplitude-comparison monopulse angle-tracking radar shows that gain variation and bias in the radar error signal can occur under certain conditions involving multiple targets. The general behavior depends on the Doppler separation of the targets relative to system bandwidths; for a specific situation, the gain variation and bias are functions of the relative strengths of the targs. The analysis is shown to be consistent with experimental observations.     

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.     

Radar Tracking of Low-Altitude Targets

The antenna elevation control signal and the associated staticequilibrium equations are analyzed for the case of tracking of lowaltitude targets for both monopulse and conical-scanning radar. Three possible equilibrium positions of the radar antenna under static operating conditions are ascertained. The static solutions suggest certain dynamic solutions that are likely to arise under practical conditions. The extreme values of the pointing error are shown in graphical form.     

Multiple Gaussian Targets: The Track-on-Jam Problem

When a radar with amplitude comparison monopulse arithmetic encounters signals from multiple Gaussian sources it will "point" to the centroid of the incident radiation. The probability density function (pdf) of the monopulse ratio when N independent samples of difference and sum signals are processed in a maximum likelihood receiver is derived. For finite jam-to-noise ratio the estimate has a bias which is independent of N. The variance in the estimate does however depend upon N. Central moments of order less than or equal 2N - 2 exist and are given by a simple formula. Plots of the pdf and its bias and variance for various jam-to-noise ratios, locations of the centroid with respect to the boresight direction, and number of samples processed are presented in the accompanying figures.