Publications

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The performance of a Ground Moving Target Indicator (GMTI) radar system depends on a variety of factors, many which are interdependent in some manner. It is often difficult to 'get your arms around' the problem of ascertaining achievable performance limits, and yet those limits exist and are dictated by physics. This report identifies and explores those limits, and how they depend on hardware system parameters and environmental conditions. Ultimately, this leads to a characterization of parameters that offer optimum performance for the overall GMTI radar system. While the information herein is not new to the literature, its collection into a single report hopes to offer some value in reducing the 'seek time'.

Doppler radars can distinguish targets from clutter if the target's velocity along the radar line of sight is beyond that of the clutter. Some targets of interest may have a Doppler shift similar to that of clutter. The nature of sea clutter is different in the clutter and exo-clutter regions. This behavior requires special consideration regarding where a radar can expect to find sea-clutter returns in Doppler space and what detection algorithms are most appropriate to help mitigate false alarms and increase probability of detection of a target. This paper studies the existing state-of-the-art in the understanding of Doppler characteristics of sea clutter and scattering from the ocean to better understand the design and performance choices of a radar in differentiating targets from clutter under prevailing sea conditions.

A Linear Frequency-Modulated (LFM) chirp is a function with unit amplitude and quadratic phase characteristic. In a focused Synthetic Aperture Radar (SAR) image, a residual chirp is undesired for targets of interest, as it coarsens the manifested resolution. However, for undesired spurious signals, a residual chirp is often advantageous because it spreads the energy and thereby diminishes its peak value. In either case, a good understanding of the effects of a residual LFM chirp on a SAR Impulse Response (IPR) is required to facilitate system analysis and design. This report presents an analysis of the effects of a residual chirp on the IPR. As reference, there is a rich body of publications on various aspects of LFM chirps. A quick search reveals a plethora of articles, going back to the early 1950s. We mention here purely as trivia one of the earlier analysis papers on this waveform by Klauder, et al.

Trihedral corner reflectors are the preferred canonical target for SAR performance evaluation for many radar development programs. The conventional trihedrals have problems with substantially reduced Radar Cross Section (RCS) at low grazing angles, unless they are tilted forward, but in which case other problems arise. Consequently there is a need for better low grazing angle performance for trihedrals. This is facilitated by extending the bottom plate. A relevant analysis of RCS for an infinite ground plate is presented. Practical aspects are also discussed.

Ground Moving Target Indicator (GMTI) radar maps echo data to range and range-rate, which is a function of a moving target's velocity and its position within the antenna beam footprint. Even stationary clutter will exhibit an apparent motion spectrum and can interfere with moving vehicle detections. Consequently it is very important for a radar to understand how stationary clutter maps into radar measurements of range and velocity. This mapping depends on a wide variety of factors, including details of the radar motion, orientation, and the 3-D topography of the clutter.

Angular orientation errors of the real antenna for Synthetic Aperture Radar (SAR) will manifest as undesired illumination gradients in SAR images. These gradients can be measured, and the pointing error can be calculated. This can be done for single images, but done more robustly using multi-image methods. Several methods are provided in this report. The pointing error can then be fed back to the navigation Kalman filter to correct for problematic heading (yaw) error drift. This can mitigate the need for uncomfortable and undesired IMU alignment maneuvers such as S-turns.

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Demand is increasing for imaging ships at sea. Conventional SAR fails because the ships are usually in motion, both with a forward velocity, and other linear and angular motions that accompany sea travel. Because the target itself is moving, this becomes an Inverse- SAR, or ISAR problem. Developing useful ISAR techniques and algorithms is considerably aided by first understanding the nature and characteristics of ship motion. Consequently, a brief study of some principles of naval architecture sheds useful light on this problem. We attempt to do so here. Ship motions are analyzed for their impact on range-Doppler imaging using Inverse Synthetic Aperture Radar (ISAR). A framework for analysis is developed, and limitations of simple ISAR systems are discussed.

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Synthetic Aperture Radar (SAR) performance testing and estimation is facilitated by observing the system response to known target scene elements. Trihedral corner reflectors and other canonical targets play an important role because their Radar Cross Section (RCS) can be calculated analytically. However, reflector orientation and the proximity of the ground and mounting structures can significantly impact the accuracy and precision with which measurements can be made. These issues are examined in this report.

A principal measure of Synthetic Aperture Radar (SAR) image quality is the manifestation in the SAR image of a spatial impulse, that is, the SAR's Impulse Response (IPR). IPR requirements direct certain design decisions in a SAR. Anomalies in the IPR can point to specific anomalous behavior in the radar's hardware and/or software.

Computed Tomography (CT) is a well established technique, particularly in medical imaging, but also applied in Synthetic Aperture Radar (SAR) imaging. Basic CT imaging via back-projection is treated in many texts, but often with insufficient detail to appreciate subtleties such as the role of non-uniform sampling densities. Herein are given some details often neglected in many texts.

Coherent Change Detection (CCD) with Synthetic Aperture Radar (SAR) images is a technique whereby very subtle temporal changes can be discerned in a target scene. However, optimal performance requires carefully matching data collection geometries and adjusting the processing to compensate for imprecision in the collection geometries. Tolerances in the precision of the data collection are discussed, and anecdotal advice is presented for optimum CCD performance. Processing considerations are also discussed.

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Nonlinear FM (NLFM) waveforms offer a radar matched filter output with inherently low range sidelobes. This yields a 1-2 dB advantage in Signal-to-Noise Ratio over the output of a Linear FM (LFM) waveform with equivalent sidelobe filtering. This report presents details of processing NLFM waveforms in both range and Doppler dimensions, with special emphasis on compensating intra-pulse Doppler, often cited as a weakness of NLFM waveforms.

Pulsed Radar systems suffer range ambiguities, that is, echoes from pulses transmitted at different times arrive at the receiver simultaneously. Conventional mitigation techniques are not always adequate. However, pulse modulation schemes exist that allow separation of ambiguous ranges in Doppler space, allowing easy filtering of problematic ambiguous ranges.

Wideband radar signals are problematic for phased array antennas. Wideband radar signals can be generated from series or groups of narrow-band signals centered at different frequencies. An equivalent wideband LFM chirp can be assembled from lesser-bandwidth chirp segments in the data processing. The chirp segments can be transmitted as separate narrow-band pulses, each with their own steering phase operation. This overcomes the problematic dilemma of steering wideband chirps with phase shifters alone, that is, without true time-delay elements.

Nonlinear FM waveforms offer a radar matched filter output with inherently low range sidelobes. This yields a 1-2 dB advantage in Signal-to-Noise Ratio over the output of a Linear FM waveform with equivalent sidelobe filtering. This report presents design and implementation techniques for Nonlinear FM waveforms.

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The effects of a non-uniform antenna beam are sometimes visible in Synthetic Aperture Radar (SAR) images. This might be due to near-range operation, wide scenes, or inadequate antenna pointing accuracy. The effects can be mitigated in the SAR image by fitting very a simple model to the illumination profile and compensating the pixel brightness accordingly, in an automated fashion. This is accomplished without a detailed antenna pattern calibration, and allows for drift in the antenna beam alignments.

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The performance of a Synthetic Aperture Radar (SAR) system depends on a variety of factors, many which are interdependent in some manner. It is often difficult to ''get your arms around'' the problem of ascertaining achievable performance limits, and yet those limits exist and are dictated by physics, no matter how bright the engineer tasked to generate a system design. This report identifies and explores those limits, and how they depend on hardware system parameters and environmental conditions. Ultimately, this leads to a characterization of parameters that offer optimum performance for the overall SAR system. For example, there are definite optimum frequency bands that depend on weather conditions and range, and minimum radar PRF for a fixed real antenna aperture dimension is independent of frequency. While the information herein is not new to the literature, its collection into a single report hopes to offer some value in reducing the ''seek time''.

Limitations on focused scene size for the Polar Format Algorithm (PFA) for Synthetic Aperture Radar (SAR) image formation are derived. A post processing filtering technique for compensating the spatially variant blurring in the image is examined. Modifications to this technique to enhance its robustness are proposed.

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Traditional polar format image formation for Synthetic Aperture Radar (SAR) requires a large amount of processing power and memory in order to accomplish in real-time. These requirements can thus eliminate the possible usage of interpreted language environments such as MATLAB. However, with trapezoidal aperture phase history collection and changes to the traditional polar format algorithm, certain optimizations make MATLAB a possible tool for image formation. Thus, this document's purpose is two-fold. The first outlines a change to the existing Polar Format MATLAB implementation utilizing the Chirp Z-Transform that improves performance and memory usage achieving near realtime results for smaller apertures. The second is the addition of two new possible image formation options that perform a more traditional interpolation style image formation. These options allow the continued exploration of possible interpolation methods for image formation and some preliminary results comparing image quality are given.

Sandia National Laboratories designs and builds Synthetic Aperture Radar (SAR) systems capable of forming high-quality exceptionally fine resolution images. During the spring of 2004 a series of test flights were completed with a Ka-band testbed SAR on Sandia's DeHavilland DHC-6 Twin Otter aircraft. A large data set was collected including real-time fine-resolution images of a variety of target scenes. This paper offers a sampling of high quality images representative of the output of Sandia's Ka-band testbed radar with resolutions as fine as 4 inches. Images will be annotated with descriptions of collection geometries and other relevant image parameters.

Airborne synthetic aperture radar (SAR) imaging systems have reached a degree of accuracy and sophistication that requires the validity of the free-space approximation for radio-wave propagation to be questioned. Based on the thin-lens approximation, a closed-form model for the focal length of a gravity wave-modulated refractive-index interface in the lower troposphere is developed. The model corroborates the suggestion that mesoscale, quasi-deterministic variations of the clear-air radio refractive-index field can cause diffraction patterns on the ground that are consistent with reflectivity artifacts occasionally seen in SAR images, particularly in those collected at long ranges, short wavelengths, and small grazing angles.

SAR phase history data represents a polar array in the Fourier space of a scene being imaged. Polar Format processing is about reformatting the collected SAR data to a Cartesian data location array for efficient processing and image formation. In a real-time system, this reformatting or ''re-gridding'' operation is the most processing intensive, consuming the majority of the processing time; it also is a source of error in the final image. Therefore, any effort to reduce processing time while not degrading image quality is valued. What is proposed in this document is a new way of implementing real-time polar-format processing through a variation on the traditional interpolation/2-D Fast Fourier Transform (FFT) algorithm. The proposed change is based upon the frequency scaling property of the Fourier Transform, which allows a post azimuth FFT interpolation. A post azimuth processing interpolation provides overall benefits to image quality and potentially more efficient implementation of the polar format image formation process.

Relatively small motion measurement errors manifest themselves principally as a phase error in Synthetic Aperture Radar (SAR) complex data samples, and if large enough become observable as a smearing, blurring, or other degradation in the image. The phase error function can be measured and then deconvolved from the original data to compensate for the presumed motion error, ultimately resulting in a well-focused image. Techniques that do this are termed 'autofocus' algorithms. A very popular autofocus algorithm is the Phase Gradient Autofocus (PGA) algorithm. The nearly universal, and typically reasonable, assumption is that the motion errors are less than the range resolution of the radar, allowing solely a phase correction to suffice. Very large relative motion measurement errors manifest themselves as an unexpected additional shifting or migration of target locations beyond any deterministic migration during the course of the synthetic aperture. Degradation in images from data exhibiting errors of this magnitude are substantial, often rendering the image completely useless. When residual range migration due to either real or apparent motion errors exceeds the range resolution, conventional autofocus algorithms fail. Excessive residual migration is increasingly encountered as resolutions become finer, less expensive inertial sensors are used, and operating ranges become longer (due to atmospheric phenomena). A new migration-correction autofocus algorithm has been developed that estimates the excessive residual migration and applies phase and frequency corrections to properly focus the image. This overcomes the conventional constraint that motion errors not exceed the SAR range resolution.

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When residual range migration due to either real or apparent motion errors exceeds the range resolution, conventional autofocus algorithms fail. A new migration-correction autofocus algorithm has been developed that estimates the migration and applies phase and frequency corrections to properly focus the image.

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Brief disclosures may often be sufficient for the filing of a Technical Advance with Sandia's Intellectual Property Center, but still be inadequate to facilitate an optimum patent application where more detail and explanation are required. Consequently, the crafting of a patent application may require considerably more additional interaction between the application preparer and the inventors. This inefficiency can be considerably mitigated if the inventors address some critical aspects of a patent application when they write a technical report.

Modern high-performance Synthetic Aperture Radar (SAR) systems have evolved into highly versatile, robust, and reliable tactical sensors, offering images and information not available from other sensor systems. For example, real-time images are routinely formed by the Sandia-designed General Atomics (AN/APY-8) Lynx SAR yielding 4-inch resolution at 25 km range (representing better than arc-second resolutions) in clouds, smoke, and rain. Sandia's Real-Time Visualization (RTV) program operates an Interferometric SAR (IFSAR) system that forms three dimensional (3-D) topographic maps in near real-time with National Imagery and Mapping Agency (MIMA) Digital Terrain Elevation Data (DTED) level 4 performance (3 meter post spacing with 0.8-meter height accuracy) or better. When exported to 3-D rendering software, this data allows remarkable interactive fly-through experiences. Coherent Change Detection (CCD) allows detecting tire tracks on dirt roads, foot-prints, and other minor, otherwise indiscernible ground disturbances long after their originators have left the scene. Ground Moving Target Indicator (GMTI) radar modes allow detecting and tracking moving vehicles. A Sandia program known as "MiniSAR" is developing technologies that are expected to culminate in a fully functioning, high-performance, real-time SAR that weighs less than 20 Ibs. The purpose of this paper is to provide an overview of recent technology developments, as well as current on-going research and development efforts at Sandia National Laboratories.

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The state-of-the-art of inertial micro-sensors (gyroscopes and accelerometers) has advanced to the point where they are displacing the more traditional sensors in many size, power, and/or cost-sensitive applications. A factor limiting the range of application of inertial micro-sensors has been their relatively poor bias stability. The incorporation of an integral sensitive axis rotation capability would enable bias mitigation through proven techniques such as indexing, and foster the use of inertial micro-sensors in more accuracy-sensitive applications. Fabricating the integral rotation mechanism in MEMS technology would minimize the penalties associated with incorporation of this capability, and preserve the inherent advantages of inertial micro-sensors.

Data collection for interferometric synthetic aperture radar (IFSAR) mapping systems currently utilize two operation modes. A single-antenna, dual-pass IFSAR operation mode is the first mode in which a platform carrying a single antenna traverses a flight path by the scene of interest twice collecting data. A dual-antenna, single-pass IFSAR operation mode is the second mode where a platform possessing two antennas flies past the scene of interest collecting data. There are advantages and disadvantages associated with both of these data collection modes. The single-antenna, dual-pass IFSAR operation mode possesses an imprecise knowledge of the antenna baseline length but allows for large antenna baseline lengths. This imprecise antenna baseline length knowledge lends itself to inaccurate target height scaling. The dual-antenna, one-pass IFSAR operation mode allows for a precise knowledge of the limited antenna baseline length but this limited baseline length leads to increased target height noise. This paper presents a new, innovative dual-antenna, dual-pass IFSAR operation mode which overcomes the disadvantages of the two current IFSAR operation modes. Improved target height information is now obtained with this new mode by accurately estimating the antenna baseline length between the dual flight passes using the data itself. Consequently, this new IFSAR operation mode possesses the target height scaling accuracies of the dual-antenna, one-pass operation mode and the height-noise performance of the one-antenna, dual-pass operation mode.

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An Interferometric Moving Target Indicator radar can be used to measure the tangential velocity component of a moving target. Multiple baselines, along with the conventional radial velocity measurement, allow estimating the true 3-D velocity vector of a target.

Imaging systems such as Synthetic Aperture Radar collect band-limited data from which an image of a target scene is rendered. The band-limited nature of the data generates sidelobes, or ''spilled energy'' most evident in the neighborhood of bright point-like objects. It is generally considered desirable to minimize these sidelobes, even at the expense of some generally small increase in system bandwidth. This is accomplished by shaping the spectrum with window functions prior to inversion or transformation into an image. A window function that minimizes sidelobe energy can be constructed based on prolate spheroidal wave functions. A parametric design procedure allows doing so even with constraints on allowable increases in system bandwidth. This approach is extended to accommodate spectral notches or holes, although the guaranteed minimum sidelobe energy can be quite high in this case. Interestingly, for a fixed bandwidth, the minimum-mean-squared-error image rendering of a target scene is achieved with no windowing at all (rectangular or boxcar window).

A Synthetic Aperture Radar (SAR) image is a two-dimensional projection of the radar reflectivity from a 3-dimensional object or scene. Stereoscopic SAR employs two SAR images from distinct flight paths that can be processed together to extract information of the third collapsed dimension (typically height) with some degree of accuracy. However, more than two SAR images of the same scene can similarly be processed to further improve height accuracy, and hence 3-dimensional position accuracy. This report shows how.

Superresolution concepts offer the potential of resolution beyond the classical limit. This great promise has not generally been realized. In this study we investigate the potential application of superresolution concepts to synthetic aperture radar. The analytical basis for superresolution theory is discussed. The application of the concept to synthetic aperture radar is investigated as an operator inversion problem. Generally, the operator inversion problem is ill posed. A criterion for judging superresolution processing of an image is presented.

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Interferometric SAR (IFSAR) can be shown to be a special case of 3-D SAR image formation. In fact, traditional IFSAR processing results in the equivalent of merely a super-resolved, under-sampled, 3-D SAR image. However, when approached as a 3-D SAR problem, a number of IFSAR properties and anomalies are easily explained. For example, IFSAR decorrelation with height is merely ordinary migration in 3-D SAR. Consequently, treating IFSAR as a 3-D SAR problem allows insight and development of proper motion compensation techniques and image formation operations to facilitate optimal height estimation. Furthermore, multiple antenna phase centers and baselines are easily incorporated into this formulation, providing essentially a sparse array in the elevation dimension. This paper shows the Polar Format image formation algorithm extended to 3 dimensions, and then proceeds to apply it to the IFSAR collection geometry. This suggests a more optimal reordering of the traditional IFSAR processing steps.

The requirement to efficiently form images over a large range of geometries has a profound impact on the design of a Synthetic Aperture Radar (SAR) system. This article shows how a data set conducive to efficient processing might increase the total RF bandwidth. It also presents examples of how a fixed RF bandwidth might then limit SAR geometries.

SAR range-Doppler images are inherently 2-dimensional. Targets with a height offset lay over onto offset range and azimuth locations. Just which image locations are laid upon depends on the imaging geometry, including depression angle, squint angle, and target bearing. This is the well known layover phenomenon. Images formed with different aperture geometries will exhibit different layover characteristics. These differences can be exploited to ascertain target height information, in a stereoscopic manner. Depending on the imaging geometries, height accuracy can be on the order of horizontal position accuracies, thereby rivaling the best IFSAR capabilities in fine resolution SAR images. All that is required for this to work are two distinct passes with suitably different geometries from any plain old SAR.

Lynx is a high resolution, synthetic aperture radar (SAR) that has been designed and built by Sandia National Laboratories in collaboration with General Atomics (GA). Although Lynx may be operated on a wide variety of manned and unmanned platforms, it is primarily intended to be fielded on unmanned aerial vehicles. In particular, it may be operated on the Predator, I-GNAT, or Prowler II platforms manufactured by GA Aeronautical Systems, Inc. The Lynx production weight is less than 120 lb. and has a slant range of 30 km (in 4 mm/hr rain). It has operator selectable resolution and is capable of 0.1 m resolution in spotlight mode and 0.3 m resolution in stripmap mode. In ground moving target indicator mode, the minimum detectable velocity is 6 knots with a minimum target cross-section of 10 dBsm. In coherent change detection mode, Lynx makes registered, complex image comparisons either of 0.1 m resolution (minimum) spotlight images or of 0.3 m resolution (minimum) strip images. The Lynx user interface features a view manager that allows it to pan and zoom like a video camera. Lynx was developed under corporate finding from GA and will be manufactured by GA for both military and commercial applications. The Lynx system architecture will be presented and some of its unique features will be described. Imagery at the finest resolutions in both spotlight and strip modes have been obtained and will also be presented.

This paper addresses theoretical aspects of forming images from an airborne Synthetic Aperture Radar (SAR) of targets buried below the earth's surface. Soil is generally a lossy, dispersive medium, with wide ranging variability in these attributes depending on soil type, moisture content, and a host of other physical properties. Focussing a SAR subsurface image presents new dimensions of complexity relative to its surface-image counterpart, even when the soil's properties are known. This paper treats the soil as a lossy, dispersive half space, and presents a practical model for the radar echo-delay time to point scatterers within it. This model is then used to illustrate effects of refraction, dispersion, and attenuation on a SAR's phase histories, and the resulting image. Various data collection geometries and processing strategies are examined for both 2-Dimensional and 3-Dimensional SAR images. The conclusions from this work are that 1) focussing a SAR image must generally take into account both refraction and dispersion, 2) resolving targets at different depths in lossy soils requires perhaps unprecedented sidelobe attenuation, that for some soils may only be achievable with specialized window functions, 3) the impulse response of the soil itself places a practical limit on the usable bandwidth of the radar, and 4) dynamic ranges and sensitivities will need to be orders of magnitude greater than typical surface-imaging SARs, leading to significant impact on SAR parameters, for example compressing the usable range of pulse repetition frequencies (PRFs).

Synthetic Aperture Radar (SAR) is used to form images that are maps of radar reflectivity of some scene of interest, from range soundings taken over some spatial aperture. Additionally, the range soundings are typically synthesized from a sampled frequency aperture. Efficient processing of the collected data necessitates using efficient digital signal processing techniques such as vector multiplies and fast implementations of the Discrete Fourier Transform. Inherent in image formation algorithms that use these is a trade-off between the size of the scene that can be acceptably imaged, and the resolution with which the image can be made. These limits arise from migration errors and spatially variant phase errors, and different algorithms mitigate these to varying degrees. Two fairly successful algorithms for airborne SARs are Polar Format processing, and Overlapped Subaperture (OSA) processing. This report introduces and summarizes the analysis of generalized Tiered Subaperture (TSA) techniques that are a superset of both Polar Format processing and OSA processing. It is shown how tiers of subapertures in both azimuth and range can effectively mitigate both migration errors and spatially variant phase errors to allow virtually arbitrary scene sizes, even in a dynamic motion environment.

Synthetic Aperture Radar (SAR) from an airborne platform has been proposed for imaging targets beneath the earth`s surface. The propagation of the radar`s energy within the ground, however, is much different than in the earth`s atmosphere. The result is signal refraction, echo delay, propagation losses, dispersion, and volumetric scattering. These all combine to make SAR image formation from an airborne platform much more challenging than a surface imaging counterpart. This report treats the ground as a lossy dispersive half-space, and presents a model for the radar echo based on measurable parameters. The model is then used to explore various imaging schemes, and image properties. Dynamic range is discussed, as is the impact of loss on dynamic range. Modified window functions are proposed to mitigate effects of sidelobes of shallow targets overwhelming deeper targets.