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DEVELOPMENT OF SYNTHETIC APERTURE RADAR FOR IMAGING APPLICATION
CHAPTER ONE
INTRODUCTION
1.1 Background of the study
Carl A. Wiley,[49] a mathematician at Goodyear Aircraft Company in Litchfield Park, Arizona, invented synthetic aperture radar in June 1951 while working on a correlation guidance system for the Atlas ICBM program. In early 1952, Wiley, together with Fred Heisley and Bill Welty, constructed a concept validation system known as DOUSER (“Doppler Unbeamed Search Radar”). During the 1950s and 1960s, Goodyear Aircraft (later Goodyear Aerospace) introduced numerous advancements in SAR technology, many with the help from Don Beckerleg.
Independently of Wiley’s work, experimental trials in early 1952 by Sherwin and others at the University of Illinois’ Control Systems Laboratory showed results that they pointed out “could provide the basis for radar systems with greatly improved angular resolution” and might even lead to systems capable of focusing at all ranges simultaneously.
In both of those programs, processing of the radar returns was done by electrical-circuit filtering methods. In essence, signal strength in isolated discrete bands of Doppler frequency defined image intensities that were displayed at matching angular positions within proper range locations. When only the central (zero-Doppler band) portion of the return signals was used, the effect was as if only that central part of the beam existed. That led to the term Doppler Beam Sharpening. Displaying returns from several adjacent non-zero Doppler frequency bands accomplished further “beam-subdividing” (sometimes called “unfocused radar”, though it could have been considered “semi-focused”). Wiley’s patent, applied for in 1954, still proposed similar processing. The bulkiness of the circuitry then available limited the extent to which those schemes might further improve resolution.
The principle was included in a memorandum authored by Walter Hausz of General Electric that was part of the then-secret report of a 1952 Dept. of Defense summer study conference called TEOTA (“The Eyes of the Army”), which sought to identify new techniques useful for military reconnaissance and technical gathering of intelligence. A follow-on summer program in 1953 at the University of Michigan, called Project Wolverine, identified several of the TEOTA subjects, including Doppler-assisted sub-beamwidth resolution, as research efforts to be sponsored by the Department of Defense (DoD) at various academic and industrial research laboratories. In that same year, the Illinois group produced a “strip-map” image exhibiting a considerable amount of sub-beamwidth resolution.
A more advanced focused-radar project was among several remote sensing schemes assigned in 1953 to Project Michigan, a tri-service-sponsored (Army, Navy, Air Force) program at the University of Michigan’s Willow Run Research Center (WRRC), that program being administered by the Army Signal Corps. Initially called the side-looking radar project, it was carried out by a group first known as the Radar Laboratory and later as the Radar and Optics Laboratory. It proposed to take into account, not just the short-term existence of several particular Doppler shifts, but the entire history of the steadily varying shifts from each target as the latter crossed the beam. An early analysis by Dr. Louis J. Cutrona, Weston E. Vivian, and Emmett N. Leith of that group showed that such a fully focused system should yield, at all ranges, a resolution equal to the width (or, by some criteria, the half-width) of the real antenna carried on the radar aircraft and continually pointed broadside to the aircraft’s path.
The required data processing amounted to calculating cross-correlations of the received signals with samples of the forms of signals to be expected from unit-amplitude sources at the various ranges. At that time, even large digital computers had capabilities somewhat near the levels of today’s four-function handheld calculators, hence were nowhere near able to do such a huge amount of computation. Instead, the device for doing the correlation computations was to be an optical correlator.
It was proposed that signals received by the traveling antenna and coherently detected be displayed as a single range-trace line across the diameter of the face of a cathode-ray tube, the line’s successive forms being recorded as images projected onto a film traveling perpendicular to the length of that line. The information on the developed film was to be subsequently processed in the laboratory on equipment still to be devised as a principal task of the project. In the initial processor proposal, an arrangement of lenses was expected to multiply the recorded signals point-by-point with the known signal forms by passing light successively through both the signal film and another film containing the known signal pattern. The subsequent summation, or integration, step of the correlation was to be done by converging appropriate sets of multiplication products by the focusing action of one or more spherical and cylindrical lenses. The processor was to be, in effect, an optical analog computer performing large-scale scalar arithmetic calculations in many channels (with many light “rays”) at once. Ultimately, two such devices would be needed, their outputs to be combined as quadrature components of the complete solution.
Fortunately (as it turned out), a desire to keep the equipment small had led to recording the reference pattern on 35 mm film. Trials promptly showed that the patterns on the film were so fine as to show pronounced diffraction effects that prevented sharp final focusing.[47]
That led Leith, a physicist who was devising the correlator, to recognize that those effects in themselves could, by natural processes, perform a significant part of the needed processing, since along-track strips of the recording operated like diametrical slices of a series of circular optical zone plates. Any such plate performs somewhat like a lens, each plate having a specific focal length for any given wavelength. The recording that had been considered as scalar became recognized as pairs of opposite-sign vector ones of many spatial frequencies plus a zero-frequency “bias” quantity. The needed correlation summation changed from a pair of scalar ones to a single vector one.
Each zone plate strip has two equal but oppositely signed focal lengths, one real, where a beam through it converges to a focus, and one virtual, where another beam appears to have diverged from, beyond the other face of the zone plate. The zero-frequency (DC bias) component has no focal point, but overlays both the converging and diverging beams. The key to obtaining, from the converging wave component, focused images that are not overlaid with unwanted haze from the other two is to block the latter, allowing only the wanted beam to pass through a properly positioned frequency-band selecting aperture.
Each radar range yields a zone plate strip with a focal length proportional to that range. This fact became a principal complication in the design of optical processors. Consequently, technical journals of the time contain a large volume of material devoted to ways for coping with the variation of focus with range.
For that major change in approach, the light used had to be both monochromatic and coherent, properties that were already a requirement on the radar radiation. Lasers also then being in the future, the best then-available approximation to a coherent light source was the output of a mercury vapor lamp, passed through a color filter that was matched to the lamp spectrum’s green band, and then concentrated as well as possible onto a very small beam-limiting aperture. While the resulting amount of light was so weak that very long exposure times had to be used, a workable optical correlator was assembled in time to be used when appropriate data became available.
Although creating that radar was a more straightforward task based on already-known techniques, that work did demand the achievement of signal linearity and frequency stability that were at the extreme state of the art. An adequate instrument was designed and built by the Radar Laboratory and was installed in a C-46 (Curtiss Commando) aircraft. Because the aircraft was bailed to WRRC by the U. S. Army and was flown and maintained by WRRC’s own pilots and ground personnel, it was available for many flights at times matching the Radar Laboratory’s needs, a feature important for allowing frequent re-testing and “debugging” of the continually developing complex equipment. By contrast, the Illinois group had used a C-46 belonging to the Air Force and flown by AF pilots only by pre-arrangement, resulting, in the eyes of those researchers, in limitation to a less-than-desirable frequency of flight tests of their equipment, hence a low bandwidth of feedback from tests. (Later work with newer Convair aircraft continued the Michigan group’s local control of flight schedules.)
Michigan’s chosen 5-foot (1.5 m)-wide World War II-surplus antenna was theoretically capable of 5-foot (1.5 m) resolution, but data from only 10% of the beamwidth was used at first, the goal at that time being to demonstrate 50-foot (15 m) resolution. It was understood that finer resolution would require the added development of means for sensing departures of the aircraft from an ideal heading and flight path, and for using that information for making needed corrections to the antenna pointing and to the received signals before processing. After numerous trials in which even small atmospheric turbulence kept the aircraft from flying straight and level enough for good 50-foot (15 m) data, one pre-dawn flight in August 1957[56] yielded a map-like image of the Willow Run Airport area which did demonstrate 50-foot (15 m) resolution in some parts of the image, whereas the illuminated beam width there was 900 feet (270 m). Although the program had been considered for termination by DoD due to what had seemed to be a lack of results, that first success ensured further funding to continue development leading to solutions to those recognized needs.
First successful focussed airborne synthetic aperture radar image, Willow Run Airport and vicinity, August 1957. Image courtesy University of Michigan.
The SAR principle was first acknowledged publicly via an April 1960 press release about the U. S. Army experimental AN/UPD-1 system, which consisted of an airborne element made by Texas Instruments and installed in a Beech L-23D aircraft and a mobile ground data-processing station made by WRRC and installed in a military van. At the time, the nature of the data processor was not revealed. A technical article in the journal of the IRE (Institute of Radio Engineers) Professional Group on Military Electronics in February 1961[57] described the SAR principle and both the C-46 and AN/UPD-1 versions, but did not tell how the data were processed, nor that the UPD-1’s maximum resolution capability was about 50 feet (15 m). However, the June 1960 issue of the IRE Professional Group on Information Theory had contained a long article[58] on “Optical Data Processing and Filtering Systems” by members of the Michigan group. Although it did not refer to the use of those techniques for radar, readers of both journals could quite easily understand the existence of a connection between articles sharing some authors.
An operational system to be carried in a reconnaissance version of the F-4 “Phantom” aircraft was quickly devised and was used briefly in Vietnam, where it failed to favorably impress its users, due to the combination of its low resolution (similar to the UPD-1’s), the speckly nature of its coherent-wave images (similar to the speckliness of laser images), and the poorly understood dissimilarity of its range/cross-range images from the angle/angle optical ones familiar to military photo interpreters. The lessons it provided were well learned by subsequent researchers, operational system designers, image-interpreter trainers, and the DoD sponsors of further development and acquisition.
In subsequent work the technique’s latent capability was eventually achieved. That work, depending on advanced radar circuit designs and precision sensing of departures from ideal straight flight, along with more sophisticated optical processors using laser light sources and specially designed very large lenses made from remarkably clear glass, allowed the Michigan group to advance system resolution, at about 5-year intervals, first to 15 feet (4.6 m), then 5 feet (1.5 m), and, by the mid-1970s, to 1 foot (the latter only over very short range intervals while processing was still being done optically). The latter levels and the associated very wide dynamic range proved suitable for identifying many objects of military concern as well as soil, water, vegetation, and ice features being studied by a variety of environmental researchers having security clearances allowing them access to what was then classified imagery. Similarly improved operational systems soon followed each of those finer-resolution steps.
Comparison of earliest SAR image with a later improved-resolution one. Additionally, the data-processing light source had been changed from a mercury lamp to a laser. Image data courtesy of University of Michigan and Natural Resources Canada.
Even the 5-foot (1.5 m) resolution stage had over-taxed the ability of cathode-ray tubes (limited to about 2000 distinguishable items across the screen diameter) to deliver fine enough details to signal films while still covering wide range swaths, and taxed the optical processing systems in similar ways. However, at about the same time, digital computers finally became capable of doing the processing without similar limitation, and the consequent presentation of the images on cathode ray tube monitors instead of film allowed for better control over tonal reproduction and for more convenient image mensuration.
Achievement of the finest resolutions at long ranges was aided by adding the capability to swing a larger airborne antenna so as to more strongly illuminate a limited target area continually while collecting data over several degrees of aspect, removing the previous limitation of resolution to the antenna width. This was referred to as the spotlight mode, which no longer produced continuous-swath images but, instead, images of isolated patches of terrain.
It was understood very early in SAR development that the extremely smooth orbital path of an out-of-the-atmosphere platform made it ideally suited to SAR operation. Early experience with artificial earth satellites had also demonstrated that the Doppler frequency shifts of signals traveling through the ionosphere and atmosphere were stable enough to permit very fine resolution to be achievable even at ranges of hundreds of kilometers. The first spaceborne SAR images of Earth were demonstrated by a project now referred to as Quill (declassified in 2012).
After the initial work began, several of the capabilities for creating useful classified systems did not exist for another two decades. That seemingly slow rate of advances was often paced by the progress of other inventions, such as the laser, the digital computer, circuit miniaturization, and compact data storage. Once the laser appeared, optical data processing became a fast process because it provided many parallel analog channels, but devising optical chains suited to matching signal focal lengths to ranges proceeded by many stages and turned out to call for some novel optical components. Since the process depended on diffraction of light waves, it required anti-vibration mountings, clean rooms, and highly trained operators. Even at its best, its use of CRTs and film for data storage placed limits on the range depth of images.
At several stages, attaining the frequently over-optimistic expectations for digital computation equipment proved to take far longer than anticipated. For example, the SEASAT system was ready to orbit before its digital processor became available, so a quickly assembled optical recording and processing scheme had to be used to obtain timely confirmation of system operation. In 1978, the first digital SAR processor was developed by the Canadian aerospace company MacDonald Dettwiler (MDA).[61] When its digital processor was finally completed and used, the digital equipment of that time took many hours to create one swath of image from each run of a few seconds of data.[62] Still, while that was a step down in speed, it was a step up in image quality. Modern methods now provide both high speed and high quality.
Although the above specifies the system development contributions of only a few organizations, many other groups had also become players as the value of SAR became more and more apparent. Especially crucial to the organization and funding of the initial long development process was the technical expertise and foresight of a number of both civilian and uniformed project managers in equipment procurement agencies in the federal government, particularly, of course, ones in the armed forces and in the intelligence agencies, and also in some civilian space agencies.
Since a number of publications and Internet sites refer to a young MIT physics graduate named Robert Rines as having invented fine-resolution radar in the 1940s, persons who have been exposed to those may wonder why that has not been mentioned here. Actually, none of his several radar-image-related patents[63] actually had that goal. Instead, they presumed that fine-resolution images of radar object fields could be accomplished by already-known “dielectric lenses”, the inventive parts of those patents being ways to convert those microwave-formed images to visible ones. However, that presumption incorrectly implied that such lenses and their images could be of sizes comparable to their optical-wave counterparts, whereas the tremendously larger wavelengths of microwaves would actually require the lenses to have apertures thousands of feet (or meters) wide, like the ones simulated by SARs, and the images would be comparably large. Apparently not only did that inventor fail to recognize that fact, but so also did the patent examiners who approved his several applications, and so also have those who have propagated the erroneous tale so widely. Persons seeking to understand SAR should not be misled by references to those patents.
Data collection
A model of a German SAR-Lupe reconnaissance satellite inside a Cosmos-3M rocket.
Highly accurate data can be collected by aircraft overflying the terrain in question. In the 1980s, as a prototype for instruments to be flown on the NASA Space Shuttles, NASA operated a synthetic aperture radar on a NASA Convair 990. In 1986, this plane caught fire on takeoff. In 1988, NASA rebuilt a C, L, and P-band SAR to fly on the NASA DC-8 aircraft. Called AIRSAR, it flew missions at sites around the world until 2004. Another such aircraft, the Convair 580, was flown by the Canada Center for Remote Sensing until about 1996 when it was handed over to Environment Canada due to budgetary reasons. Most land-surveying applications are now carried out by satellite observation. Satellites such as ERS-1/2, JERS-1, Envisat ASAR, and RADARSAT-1 were launched explicitly to carry out this sort of observation. Their capabilities differ, particularly in their support for interferometry, but all have collected tremendous amounts of valuable data. The Space Shuttle also carried synthetic aperture radar equipment during the SIR-A and SIR-B missions during the 1980s, the Shuttle Radar Laboratory (SRL) missions in 1994 and the Shuttle Radar Topography Mission in 2000.
The Venera 15 and Venera 16 followed later by the Magellan space probe mapped the surface of Venus over several years using synthetic aperture radar.
Titan – Evolving feature in Ligeia Mare (SAR; 21 August 2014).
Synthetic aperture radar was first used by NASA on JPL’s Seasat oceanographic satellite in 1978 (this mission also carried an altimeter and a scatterometer); it was later developed more extensively on the Spaceborne Imaging Radar (SIR) missions on the space shuttle in 1981, 1984 and 1994. The Cassini mission to Saturn used SAR to map the surface of the planet’s major moon Titan, whose surface is partly hidden from direct optical inspection by atmospheric haze. The SHARAD sounding radar on the Mars Reconnaissance Orbiter and MARSIS instrument on Mars Express have observed bedrock beneath the surface of the Mars polar ice and also indicated the likelihood of substantial water ice in the Martian middle latitudes. The Lunar Reconnaissance Orbiter, launched in 2009, carries a SAR instrument called Mini-RF, which was designed largely to look for water ice deposits on the poles of the Moon.
Titan – Ligeia Mare – SAR and clearer despeckled views.
The Mineseeker Project is designing a system for determining whether regions contain landmines based on a blimp carrying ultra-wideband synthetic aperture radar. Initial trials show promise; the radar is able to detect even buried plastic mines.
SAR has been used in radio astronomy for many years to simulate a large radio telescope by combining observations taken from multiple locations using a mobile antenna.
The National Reconnaissance Office maintains a fleet of (now declassified) synthetic aperture radar satellites commonly designated as Lacrosse or Onyx.
In February 2009, the Sentinel R1 surveillance aircraft entered service in the RAF, equipped with the SAR-based Airborne Stand-Off Radar (ASTOR) system.
The German Armed Forces’ (Bundeswehr) military SAR-Lupe reconnaissance satellite system has been fully operational since 22 July 2008.
As of January 2021, multiple commercial companies have started launching constellations of satellites for collecting SAR imagery of Earth.[64]
A technique closely related to SAR uses an array (referred to as a “phased array”) of real antenna elements spatially distributed over either one or two dimensions perpendicular to the radar-range dimension. These physical arrays are truly synthetic ones, indeed being created by synthesis of a collection of subsidiary physical antennas. Their operation need not involve motion relative to targets. All elements of these arrays receive simultaneously in real time, and the signals passing through them can be individually subjected to controlled shifts of the phases of those signals. One result can be to respond most strongly to radiation received from a specific small scene area, focusing on that area to determine its contribution to the total signal received. The coherently detected set of signals received over the entire array aperture can be replicated in several data-processing channels and processed differently in each. The set of responses thus traced to different small scene areas can be displayed together as an image of the scene.
In comparison, a SAR’s (commonly) single physical antenna element gathers signals at different positions at different times. When the radar is carried by an aircraft or an orbiting vehicle, those positions are functions of a single variable, distance along the vehicle’s path, which is a single mathematical dimension (not necessarily the same as a linear geometric dimension). The signals are stored, thus becoming functions, no longer of time, but of recording locations along that dimension. When the stored signals are read out later and combined with specific phase shifts, the result is the same as if the recorded data had been gathered by an equally long and shaped phased array. What is thus synthesized is a set of signals equivalent to what could have been received simultaneously by such an actual large-aperture (in one dimension) phased array. The SAR simulates (rather than synthesizes) that long one-dimensional phased array. Although the term in the title of this article has thus been incorrectly derived, it is now firmly established by half a century of usage.
While operation of a phased array is readily understood as a completely geometric technique, the fact that a synthetic aperture system gathers its data as it (or its target) moves at some speed means that phases which varied with the distance traveled originally varied with time, hence constituted temporal frequencies. Temporal frequencies being the variables commonly used by radar engineers, their analyses of SAR systems are usually (and very productively) couched in such terms. In particular, the variation of phase during flight over the length of the synthetic aperture is seen as a sequence of Doppler shifts of the received frequency from that of the transmitted frequency. It is significant, though, to realize that, once the received data have been recorded and thus have become timeless, the SAR data-processing situation is also understandable as a special type of phased array, treatable as a completely geometric process.
The core of both the SAR and the phased array techniques is that the distances that radar waves travel to and back from each scene element consist of some integer number of wavelengths plus some fraction of a “final” wavelength. Those fractions cause differences between the phases of the re-radiation received at various SAR or array positions. Coherent detection is needed to capture the signal phase information in addition to the signal amplitude information. That type of detection requires finding the differences between the phases of the received signals and the simultaneous phase of a well-preserved sample of the transmitted illumination.
Every wave scattered from any point in the scene has a circular curvature about that point as a center. Signals from scene points at different ranges therefore arrive at a planar array with different curvatures, resulting in signal phase changes which follow different quadratic variations across a planar phased array. Additional linear variations result from points located in different directions from the center of the array. Fortunately, any one combination of these variations is unique to one scene point, and is calculable. For a SAR, the two-way travel doubles that phase change.
Comparison of the array-signal phase variation across the array with the total calculated phase variation pattern can reveal the relative portion of the total received signal that came from the only scene point that could be responsible for that pattern. One way to do the comparison is by a correlation computation, multiplying, for each scene element, the received and the calculated field-intensity values array element by array element and then summing the products for each scene element. Alternatively, one could, for each scene element, subtract each array element’s calculated phase shift from the actual received phase and then vectorially sum the resulting field-intensity differences over the array. Wherever in the scene the two phases substantially cancel everywhere in the array, the difference vectors being added are in phase, yielding, for that scene point, a maximum value for the sum.
The equivalence of these two methods can be seen by recognizing that multiplication of sinusoids can be done by summing phases which are complex-number exponents of e, the base of natural logarithms.
However it is done, the image-deriving process amounts to “backtracking” the process by which nature previously spread the scene information over the array. In each direction, the process may be viewed as a Fourier transform, which is a type of correlation process. The image-extraction process we use can then be seen as another Fourier transform which is a reversal of the original natural one.
It is important to realize that only those sub-wavelength differences of successive ranges from the transmitting antenna to each target point and back, which govern signal phase, are used to refine the resolution in any geometric dimension. The central direction and the angular width of the illuminating beam do not contribute directly to creating that fine resolution. Instead, they serve only to select the solid-angle region from which usable range data are received. While some distinguishing of the ranges of different scene items can be made from the forms of their sub-wavelength range variations at short ranges, the very large depth of focus that occurs at long ranges usually requires that over-all range differences (larger than a wavelength) be used to define range resolutions comparable to the achievable cross-range resolution.
Synthetic-aperture radar (SAR) is a form of radar that is used to create two-dimensional images or three-dimensional reconstructions of objects, such as landscapes.[1] SAR uses the motion of the radar antenna over a target region to provide finer spatial resolution than conventional stationary beam-scanning radars. SAR is typically mounted on a moving platform, such as an aircraft or spacecraft, and has its origins in an advanced form of side looking airborne radar (SLAR). The distance the SAR device travels over a target during the period when the target scene is illuminated creates the large synthetic antenna aperture (the size of the antenna). Typically, the larger the aperture, the higher the image resolution will be, regardless of whether the aperture is physical (a large antenna) or synthetic (a moving antenna) – this allows SAR to create high-resolution images with comparatively small physical antennas. For a fixed antenna size and orientation, objects which are further away remain illuminated longer – therefore SAR has the property of creating larger synthetic apertures for more distant objects, which results in a consistent spatial resolution over a range of viewing distances.
To create a SAR image, successive pulses of radio waves are transmitted to “illuminate” a target scene, and the echo of each pulse is received and recorded. The pulses are transmitted and the echoes received using a single beam-forming antenna, with wavelengths of a meter down to several millimeters. As the SAR device on board the aircraft or spacecraft moves, the antenna location relative to the target changes with time. Signal processing of the successive recorded radar echoes allows the combining of the recordings from these multiple antenna positions. This process forms the synthetic antenna aperture and allows the creation of higher-resolution images than would otherwise be possible with a given physical antenna.
As of 2010, airborne systems provide resolutions of about 10 cm, ultra-wideband systems provide resolutions of a few millimeters, and experimental terahertz SAR has provided sub-millimeter resolution in the laboratory.[citation needed
1.2 Statement of the problem
The wish for humans to explore nature is the core for the development and survival of the human race. Since the space race began in the 1950s with the launch of Sputnik, we have used spacecrafts to explore our planet’s closest surroundings. These explorations have given us a better understanding of how dependent we are on the surrounding atmosphere, for instance the ozone
layer, and how important it is to supervise it. Radar and especially Synthetic Aperture Radar (SAR) systems are very important for the continuous supervision of the Earth climate and they are also crucial as sensors capable of high-resolution mapping of space bodies.
1.3 Synthetic Aperture Radar
Synthetic Aperture Radar
In SAR systems as well as in traditional radar, both monostatic and bistatic configurations are possible. In this section, a monostatic SAR system is assumed.
The basic principle of SAR is the collection of radar echoes from a hypothetical stationary ground scene as the SAR system moves along a straight flight track, called the synthetic aperture. The longer the synthetic aperture is, the larger the integration angle will be. For a point in the middle of the SAR scene, the synthetic aperture covers a certain viewing angle, and this angle is called the integration angle. The resolution in a final SAR image is a function of the integration angle, signal bandwidth and centre frequency only. This makes the resolution independent of the distance from the scene. That means that a satellite imaging a scene on the ground from long distance can obtain the same resolution as an aircraft imaging the same area from very short distance. This can be contrasted with optical sensors that are limited by the resolution in the viewing angle.
In the same way as for each radar echo, pulse compression is used, but this time to compress the signal along the synthetic aperture. As the SAR platform moves along a hypothetical straight flight track, the radar emits and receives pulses. Considering one target of interest, the difference between pulses will be determined by the attenuation of the signal from the path loss and the antenna pattern as well as by the change in distance to the target. Based on this, the pulse-compressed signal before SAR processing is
(4)
where the range to a target is a function of t, so-called slowtime, and is given by
. Here, X0 and Y0 are the azimuth and slant-range
coordinates for the target. Slowtime is the azimuth time vector, which relates to the movement of the SAR platform during illumination of the scene of interest. Based on this pulse-compressed data, many algorithms that are able to obtain a SAR image have been proposed. Among algorithms performing well even for large integration angles, Range Migration(RMA)[7] and Global Backprojection(GBP)[8] should be mentioned. Consequently, their basic functions are presented later in the introduction.
1.4 Nature and Importance Radar
The main sensors used in remote sensing that create 2-D mappings of the ground are active sensors such as radar and LIDAR or passive sensors such as IR sensors, optical cameras and radiometers. Out of these sensors, the radiometer and the radar are least sensitive to bad weather conditions such as cloud and rain. In order to use a camera, not only good weather is needed, but also sunlight to illuminate the ground.
The abbreviation radar comes from RAdio Detection And Ranging and the basic principle of radar is to illuminate an object with the help of electromagnetic (EM) radiation and analyze the received response. In order to radiate EM waves, a transmitter and an antenna are needed. The transmitter generates and amplifies a signal. The signal goes from the transmitter to an antenna which radiates EM waves that contain the signal from the transmitter. In order to later receive an echo, another antenna is needed which is
1
(a) Bistatic setup (b) Monostatic setup
Figure 1: Two different configurations of a basic radar system. For the bistatic system, there are two antennas and they are separated by a distance B, here called a baseline.
connected to a receiver. The receiver uses a detector to detect the incoming signal by means of e.g. a matched filter. Such a system with one transmitter, one transmitting antenna, one receiver and one receiving antenna is called a bistatic radar system. It is possible, however, that the transmitter and receiver share one common antenna; such a system is called a monostatic system. In Fig. 1a and 1b, the bistatic and monostatic radar configurations are shown respectively. Another radar configuration is the multistatic setup that make use of many transmitters and receivers that together form a radar network. A kind of multi static radar systems are passive bistatic or passive multistatic systems. In passive systems, the echoed signals from one or many third part transmitters are used. This can, for instance, be GPS or TV signals.
Radar systems were introduced in the beginning of the 20th century, however, it was not used widely until the 1930s, when the military realized the usefulness of this technology. Most of the continued development of radar has also been conducted by the military and in Sweden some famous radar systems have been developed, including ERIEYE, PS-05/A, GIRAFFE, ARTHUR, LORA and CARABAS-II. Data from CARABAS-II and LORA has been used in the work presented in this thesis.
Fully coherent radar needs very precise oscillators. Therefore, the system has precise knowledge of the transmitted signal and with the use of GPS information it can get good information about the position of the transmitter and receiver. Since the wave speed in air is well known, and also the position of the transmitter and receiver, the flight time, and therefore also the distance the wave has traveled from transmitter to receiver can be precisely measured.
The most common type of radar is probably the one that incoherently transmits short pulses. This type of system uses a magnetron to generate a pulse which has a large power over short time. For long-distance surveillance high-performance systems, it is more common to transmit a wide-band pulse over a long time and afterwards perform pulse compression. In these radars, it is common to use chirp waveforms. In order to obtain a good range resolution, the transmitted signal is saved and later convolved with the received signals, something referred to as pulse compression. A standard chirp signal can be written as
(1)
where τ is fast-time, φ0 an arbitrary phase, k is the chirp rate, fc is the
center frequency and Tp is the pulse length.
For a monostatic systems, the received echo signal from an object at the distance R will be
(2)
After convolving sr (τ) with its matched filter namely (st (−τ))∗, where ∗ denotes complex conjugation, the pulse compressed signal spc (τ) can be determined. This signal can be shown to be
The windowed sinc function has a much better resolution in range compared to sr (τ). We say that we have compressed the signal energy to a short time duration. The way to obtain good resolution in elevation and azimuth for a radar is by creating very narrow beams.
1.5 Moving targets in SAR
In a SAR image, the image of a moving target is typically effected in two ways, namely through defocusing and by shifting its position. For a moving target, its phase information in the SAR image is modified, compared to that of a stationary target, in a way determined by target motion parameters. This fact is utilized in this thesis. An illustrative example, produced by moving targets in SAR imagery, is the one produced by trains when imaged by spaceborne SAR systems. In [14] the train appears to move parallelly to the train track. In very high resolution SAR, such as UWB SAR, that makes use of long integration times, the moving target will have its energy spread out in a curved shape, either as a parabola or a hyperbola [15]. The papers in this thesis focus on moving targets and their effects on SAR images.
1.6 Model for radar echo signal
For detectability and low false alarm rate, it is important to model a received radar echo and a SAR image with and without a moving target present. This means that we have to have an appropriate model for the target, the clutter and the noise. In the first two papers of this thesis, it is for simplicity assumed that the radar echo is described by (8)
x = s + c + n (8)
where, as presented in Paper IV, x is the radar echo, s the moving target signal, c the clutter signal and n is the noise. Clutter in this case refers to everything in the echo that is not noise and not a moving target. This can be anything that reflects the radar signal, such as grass, water, trees, roads, houses, power lines etc.
Furthermore, it is generally assumed that the SAR processing is a linear system, i.e. if the radar echo is the sum of moving target signal, clutter signal and noise, then the SAR image is the sum of the SAR image of the moving target, the SAR image of the clutter and the SAR image of the noise as in (9) hx (Xp,Yp) = hs (Xp,Yp) + hc (Xp,Yp) + hn (Xp,Yp) (9)
where h(Xp,Yp) is the SAR image at the azimuth image coordinate Xp and
slant range image coordinate Yp.
This model assumes that the return echo from the moving target is independent of the clutter, i.e. anything surrounding the moving target. This would mean that as the target moves e.g. along a road, where for certain angles the moving target is obstructed by trees or houses, the radar echo must not be affected by the trees of the houses. As this cannot be true, the return echo cannot be considered independent of the clutter and the model is not true. However, within signal processing, most models are of the form given in (8), mainly due to simplicity when implementing filtering which in our case has the purpose to filter out the noise and clutter from the radar echo and only keep the moving target. In the following subsection, several methods for such filtering is presented.
1.7 Moving Target dynamics model
In general, movement in a 2-D surface such as flat ground can be described by a polynomial function in slow time, t.
(10)
where v is speed, a is acceleration, ξ and η speed components in azimuth and slant range and t0 the time instant where the distance between the target and the platform is minimal. As the time for SAR data collation is usually short, it is throughout the research in this thesis assumed that there are no target accelerations giving (11). There are cases in this thesis where the collection times are not short, in which one can argue about the validity of the model, as for VHF SAR data using CARABAS-II [16]. Having wavelengths between 3 and 15 meter causes only very large targets to give reflections. A large target is heavy and thus cannot accelerate very quickly. Also, the vibrations for the moving vehicles do not not cause severe signal loss, since the vibration amplitude is small in comparison to signal wavelength. This may explain why the approximation of no accelerations still give the good results in Part II.
| ξ (t) | = | ξ0 + vξ (t − t0) | |
| η (t) | = | η0 + vη (t − t0) | |
| ζ (t) | = | 0 | (11) |
1.8 Increasing Detectability of Moving Targets
In order to extract parameters and image moving targets in SAR images, one must detect and localize the target. This is done by applying signal processing algorithms that increase the detectability. Such algorithms can be divided into different categories, for instance based on the number of channels used:
- Single-channel
- Dual-channel
Figure 5: Standard setup for a 4-channel along track SAR system used for moving target detection, with the baseline of length B.
Multi-channel
In Fig. 5, a standard SAR setup for the detection of moving targets is shown. The two antennas alternate as transmitters and both antennas are connected to the receiver. In multi-channel systems, more antennas are mounted in along track direction.
Single-channel methods
One antenna on a SAR platform is most common and therefore much effort has been put into being able to detect moving targets for single-channel SAR,[14][22]. Firstly, as mentioned at the start of the section, moving targets appear smeared in a SAR image, for low bandwidth systems it appears just as a line, similar to taking a photo of a car in the night, where the lights become lines. Knowing the speed and direction of movement for the moving target it can be focused, by reprocessing the data according to the target dynamic properties. This is called moving target focusing. By focusing the target, it becomes more prominent in the image in comparison to the original SAR image, thus increasing the detectability. Secondly, the phase information of a smeared moving target in a SAR image is in azimuth direction a chirp, i.e. the phase information increases or decreases quadratically. This is only true for moving targets. Trying to find such chirps in a SAR image is a method to detect moving targets. Such methods can employ, for instance, time-frequency analysis. Thirdly, as the platform and the target move, several medium resolution images can be generated. For each of these images, the target has moved a short distance in between. This effect can be used by applying change detection using, most easily, only subtraction of two images. Another method used for detecting targets involves on a patch-by-patch basis processing the SAR image [22]. For each patch the image is multiplied with its own conjugate. If a moving target is present, it will focus as its so-called residual phase or chirp will be compensated by multiplying with the conjugate. This is based on the same idea as for detecting a chirp. Finally, the total opposite of trying to detect the moving target by finding it in the image is trying to find its shadow. As was mentioned in the beginning of this section, a moving target is smeared and displaced in the SAR image. However, on the original place of the target, a shadow can be seen, since the target blocked the background behind it. Thus, trying to detect these shadows is also a way to detect moving targets.
Dual and multi-channel methods
Adding a second channel strongly increases the ability to suppress the clutter. There are a couple of standard methods in which two channels can be used, including for instance the Displaced Phase Centre Antenna (DPCA) [14], Along-track Interferometry (ATI) [14], Adaptive DPCA (ADPCA) and Space Time Adaptive Processing (STAP) [20]. In all of these methods, two or more antennas are places on the platform along the flight direction. Having more than one antenna, the model given in (8) must be extended. First of all, it is assumed that the antennas are placed equidistantly in the flight direction. For simplicity it is also assumed that each antenna acts as transmitter and receiver separately and that all antennas and receivers are identical. Given these conditions, the signal of the k’th antenna at the azimuth position x0 is given by
(12).
x
where t is slow time.
Now we make the assumption that the clutter does not change during the small time differences , which is typically much less than 0.1 seconds, and we assume that noise is a stationary random process. This allows us to rewrite (12) to (13).
n (13)
The DPCA method assumes that as the platform moves, the pulse repetition frequency is chosen by, where N is any positive integer, vp the platform speed and d the distance between the antennas.
Using the same sub-aperture for both antennas to generate an image, the two antenna signals can be subtracted for each aperture position, then applying SAR processing to generate an image. Alternatively, two images are formed and then the two images subtracted. If some target moves, and the antenna channels are identical, then the difference of the channels is decided only by the movement of the target. If the two signals are then subtracted from each other, the moving target signal is the only information left in the signal. In reality there are always imperfections which reduce the effectiveness of DPCA, such as e.g. antennas not having the same antenna pattern, receiver characteristics, etc. Moreover, in reality there is always noise present. The noise will not be suppressed in the DPCA, rather the SNR worsens. The DPCA method can be written mathematically as
x1 − x2 1 · x1 + (−1) · x2
= = (14) x1 + x2 x1 + x2
Combining (13) with (14) gives
s
p
y = (15)
x1 + x2
where n0 is a random process. This shows that even though SNR was lost,
the Signal to Clutter Ratio (SCR) gain is very significant.
Similarly as for DPCA, subtraction of two channels is the central part for ATI. But instead of calculating the difference of the measurements or the images, the difference of the phase of the signals are calculated. This is conducted by multiplying the first signal with the conjugate of the second signal as presented in (16).
y (16)
In this equation, ◦ refers to the Hadamard product, or element-wise multiplication.
Adding adaptivity to the filtering is usually made using either ADPCA or STAP. ADPCA is an extension of DPCA in which the coefficients for combining the two channels are adaptively updated, instead of always set to 1 and -1. The coefficients are calculated based on the covariance matrix of the clutter between the two channels. How often the coefficients are updated is an implementation choice.
STAP takes ADPCA much further, allowing for K number of channels and each fast time sample of the measurements vectors to have a filter coefficient, i.e. in the case of two channels, instead of 2 coefficients as with DPCA, it allows for 2M coefficients if M is the number of fast time samples. STAP has the ability just as DPCA to suppress clutter, but it can also be used for suppressing for instance jammers. Also, in STAP in contrast to DPCA, the SNR is not degraded as much. STAP filtering can be described by (17)
y = Xwk ◦ xk (17)
k
where xk is a vector of range samples from antenna k and wk are filter coefficients for antenna k. This means that the filtered signal is a weighted sum of the k channels in which each sample also has a different filter coefficient. Thus, the filter has many more coefficients than the DPCA. We can choose
w1
w
..
and
x1
x = x2
…
and then the optimal coefficients for w are found to be
w = C−1u (18)
in which C is the clutter and noise covariance matrix, and u is the steering vector which depends on moving target dynamics parameters. The adaptive part of STAP refers to that the optimal coefficients changes depending on the clutter and noise statistics. These statistics changes depending on, for instance, time, range and angle. In the thesis in Part II, STAP filtering is used. However, x,w,u and C are defined a little differently.
5.4 Imaging of Moving Targets
As explained for the single-channel methods, focusing of the target according to target dynamic properties is possible. Since imaging of a moving target and estimation of moving target parameters are very closely linked, the reader is here introduced to the concept of focusing of moving targets and the important parameter NRS, which also will help in understanding the last section in the introduction.
If it is possible to exactly know the movement of the target during the SAR data collection time, then it is possible to focus the target to obtain an image of the target appearing as if it would be stationary, thus producing a normal SAR image of the target.
Based on the model for a moving target (11), and the model for the platform movement given by
| ξp (t) | = | ξ0 + vp (t − t0) | (19) |
| ηp (t) | = | 0 | (20) |
| ζp (t) | = | h | (21) |
where p refers to platform and h to platform altitude, it is possible to formulate the distance between platform and target as
q
R(t) = γ2 (vpt − Xo)2 + Yo2 (22)
where γ is the normalized relative speed (NRS), and Xo and Yo the azimuth
and slant range image coordinates of the target.
As presented in paper I, γ is found to be
(23)
The most basic time-domain SAR algorithm is GBP, described by (5). The algorithm consist of a coherent summation of radar echoes along the synthetic aperture for each image pixel. In the summation, the distance for each azimuth position to the image pixel is calculated. Since there is a moving target, the range-history will not be the same as for a stationary image pixel. Instead we can consider that the image pixel grid moves with the same NRS as that of the moving target. This will make the moving target focused in the SAR image. This simple principle of considering that the image grid moves according to a certain NRS generalizes to all SAR algorithms, and allows for the focusing of moving targets.
However, if instead we want to focus a moving target based on a SAR image only, not having the radar echo data, we have to modify the focusing method. Such a method is presented in part I.
5.5 Estimation of Moving Target Dynamics Parameters
Estimation and detection are very closely linked together. With correct target dynamics parameters in STAP and SAR processing, the target becomes focused and best chance for detection is obtained. In contrary, when trying to estimate target parameters we have detected a moving target, but we do not know its speed or moving direction, also we do not know the position of the target. What we want is to determine are these parameters. In order to accurately estimate the position, we need to focus the target as much as possible, i.e. we have to find the speed and moving direction of the target first.
As mentioned a moving target can be detected by for instance trying to detect a chirp in the SAR image. This chirp also contains information about the NRS allowing it to be estimated. This information can be extracted by for instance phase unwrapping or by using time-frequency techniques such as the Wigner-Ville transform combined with the Hough transform [21]. Another way to find NRS is by attempting to refocus the target locally in the SAR image by varying the NRS as the focusing parameter and using the peak magnitude value of the moving target in the SAR image as the objective function. This method is presented in part I of this thesis. NRS represents the magnitude of the difference vector between the target and platform velocity vectors. In order to also find the direction of the difference vector and thus determining the target speed parameters the steering vector in STAP is used. Further, it is also possible, if the moving target is very strong in its surrounding, to calculate a 2D FFT and from the SAR spectrum determine both NRS and target bearing.
The position where the target appears in the image, and the velocity vector is enough to determine the azimuth shift in the SAR image, and to reposition the target. Thus, when the moving target velocity vector has been estimated and the target is focused in the SAR image, the target position can be estimated.
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