This paper develops the theory for waveform-diverse moving-target synthetic-aperture radar. We assume that
the targets are moving linearly, but we allow an arbitrary flight path and (almost) arbitrary waveforms. We
consider the monostatic case, in which a single antenna phase center is used for both transmitting and receiving.
This work addresses the use of waveforms whose duration is sufficiently long that the targets and/or platform
move appreciably while the data is being collected.
We develop a linearized imaging theory that combines the spatial, temporal, and spectral aspects of scattered
waves. We consider the case of fixed sensors and a general distribution of objects, each undergoing linear
motion; thus the theory deals with imaging distributions in phase space. We derive a model for the data that is
appropriate for any waveform, and show how it specializes to familiar results when the targets are far from the
antennas and narrowband waveforms are used.
We develop a phase-space imaging formula that can be interpreted in terms of filtered backprojection or
matched filtering. For this imaging approach, we derive the corresponding point-spread function. We show
that special cases of the theory reduce to: a) Range-Doppler imaging, b) Inverse Synthetic Aperture Radar
(isar), c) Spotlight Synthetic Aperture Radar (sar), d) Diffraction Tomography, and e) Tomography of Moving
Targets. We also show that the theory gives a new SAR imaging algorithm for waveforms with arbitrary ridge-like
Conventional Synthetic Aperture Radar combines high range resolution waveforms collected from disparate directions/locations to form an image in range and cross-range. If the radar bandwidth is narrow, then range resolution will suffer and the overall image will be degraded. (This necessarily happens when the radar's carrier frequency is small, for instance.) There is, however, a complementary imaging mode in which very narrow frequency-domain pulses are collected by a platform in relative motion with the target and combined to form an image. Such systems rely on Doppler frequency shift measurements (instead of range information). For various practical reasons, this kind of imaging has not been well examined, but there are situations where the scheme is useful (in principle).
We develop the theory of radar imaging from data measured by a moving antenna emitting a single-frequency waveform. We show that, under a linearized (Born) scattering model, the signal at a given Doppler shift is due to a superposition of returns from stationary scatterers on a cone whose axis is the flight velocity vector. This cone reduces to a hyperbola when the scatterers are known to lie on a planar surface. In this case, reconstruction of the scatterer locations can be accomplished by a tomographic inversion in which the scattering density function is reconstructed from its integrals over hyperbolas. We give an approximate reconstruction formula and analyze the resolution of the resulting image. We provide a numerical shortcut and show results of numerical tests in a simple case.
We show how to apply the techniques of microlocal analysis to the Potter-Moses attributed scattering center model, which is based on the
Geometrical Theory of Diffraction (GTD). The microlocal methods enable us to determine how scattering centers will appear in the radar data. We show also how to extend the model to some multiple-scattering events, and we apply the microlocal techniques to the extended model.
To many contemporary radar engineers the term "radar imaging" has come to be synonymous with "scattering center localization." Radar image-based target classification and identification, for example, is typically interpreted as a library look-up process in which the position and strength of target scattering centers is matched to a set of known template signatures. But the ability to accurately estimate scatterer position and strength is severely hampered by low image resolution and noise contamination. In addition, inverse synthetic aperture radar images often also require costly preprocessing steps (such as polar reformatting) to assure adequate accuracy. We describe a simple method, based on subspace fitting techniques, that can be applied to the position and strength estimation problem in this time-constrained and data-limited environment. The scheme is robust against noise corruption and allows for super-resolved estimates of all (or some) of the scatterers. Examples based on both real and synthetic data are presented.
We consider the problem of identification of airborne objects from high-range-resolution radar data. We use high-frequency asymptotics to show that certain features of the object-correspond to identifiable features of the radar data. We study the cases of single scattering and scattering from re-entrant structures such as ducts. This work suggests a method for target identification that circumvents the need to create an intermediate radar image from which the object's characteristics are to be extracted. As such, this scheme may be applicable to efficient machine-based radar identification programs.
Traditional methods in image processing have not enjoyed an easy transition to radar data because most of these techniques are phase insensitive and generalizations have often not led to unique results. The desire to develop image reconstruction algorithms which are not `phase blind' has well-recognized resolution and superresolution consequences since these algorithms are typically based upon complex Fourier techniques. In addition, standard radar imaging methods have employed a linear `weak scatterer' target model to make a simple connection between target and scattered field--a model that is not always appropriate and which can cause deleterious image artifacts. Clearly, the accuracy of follow-on model appraisal requires more than simple `resolution' analysis. Recently, several important ideas have been developed which help to bridge the gap between algorithmic image resolution `enhancement' processing and usual radar image appraisal methods. We present a coordinated overview of some of the more promising of the techniques, including nonlinear Backus-Gilbert restoration and complex target modeling.
The 'weak scatterer' approximation is usually inappropriate for re-entrant target structures, and ISAR images based on this approximation often display unwanted 'artifacts' which can complicate image interpretation. Last year, we presented an image restoration method which can be used to mitigate these artifacts without significant impact on neighboring image components and demonstrated its application using anechoic chamber data [SPIE Proc., Radar Processing, Technology, and Applications II, vol. 3161, pp. 9 - 19 (1997)]. Since then, we have further examined this novel filtering technique and applied it to measured ISAR data. In addition, duct shape-specific parameters can be recovered using this analysis, and we have looked at the possibility of applying these to the problem of radar-based target classification. Our presentation will review the past theory and present results of our investigations over the past year.
The standard ISAR high-frequency weak-scatterer model is inappropriate to targets with inlets and cavities, and images created under this model assumption often display artifacts associated with these structures. Since inlets and cavities (typically) make a strong contribution to the radar field scattered from aircraft targets, these artifacts often confound the image interpretation process and considerable effort has been spent in recent years to model, isolate, and remove these sources of error. Many of the more complete and accurate scattering models require extensive knowledge about the cavity/inlet shape and size and, moreover, are numerically intensive -- features that make them unsuitable for many imaging applications. We examine an older (and less accurate) model based on a weak-scattering modal expansion of the structure which appears to be well-suited to ISAR imaging. In addition, the analysis shows how cavity/inlet shape-specific information may be estimated from an ordinary ISAR image.
The problem of image analysis when the image is complex- valued is becoming increasingly important in problems where the complex nature of the scattering mechanism cannot be ignored. Such problems include automatic target recognition and cross-section reduction. Traditional approaches have sought to apply standard methods in intensity-based imaging to these problems by discarding the inherent phase content. Other methods have been developed but are often ad hoc and insufficiently motivated. We will examine this problem and some of the recent approaches suggested for its solution.
Small radar detection and tracking systems--in particular, radar guided missile systems--are of great utility because of their all-weather performance and their long range capabilities. A major drawback with these systems results from the relatively simple data that they collect and the difficulty in using these data for target classification and identification purposes. We are investigating a technique which employs the statistics of the tracking data used by many missile seekers and which creates a cross-range target structure map that can be expressed as a function of the target's down-range extent. These data consist of ordinary angle-of-arrival measurements collected from a small burden and may hold the potential to be used for automatic (machine-based) target classification in realistic (time and data limited) environments.