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This PDF file contains the front matter associated with SPIE Proceedings Volume 12108 including the Title Page, Copyright information, Table of Contents, and Committee pages.
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In a recent work,1 chirp spread spectrum(CSS) was proposed as a low probability of intercept(LPI) waveform. CSS has been previously proposed for low power IoT applications and adopted in the LoRa standard. However, the LPI use of the waveform was new. The key in adopting CSS for LPI applications is the use of waveforms with a large time-bandwidth product. The pulse compression gain available to the intended receiver is not available to the intercept receiver. This report builds upon the previous work by testing the waveform in a 15 mile terrestrial link from atop Sandia Crest to points west. The transmit power level is swept from +27 dBm to -33 dBm. The intended receiver uses channelized matched processing whereas the intercept receiver deploys a wideband radiometer. The experiment measured the minimum transmit power level and maximum intercept range to keep the signal under the intercept receiver noise floor and yet detectable by the intended receiver.
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When an electromagnetically-nonlinear radar target is illuminated by a high-power stepped-frequency probe, a sequence of harmonics is unintentionally emitted by that target. Detection of the target is accomplished by receiving stimulated emissions somewhere in the sequence, while ranging is accomplished by processing amplitude and phase recorded at multiple harmonics across the sequence. The strength of the harmonics reflected from an electronic target depends greatly upon the orientation of that target (or equivalently, the orientation of the radar antennas). Data collected on handheld wireless devices reveals the harmonic angular-dependence of commercially-available electronics. Data collected on nonlinearly-terminated printed circuit boards implies the origin of this dependency. The results of this work suggest that electronic targets may be classified and ultimately identified by their unique harmonic-response-vs.-angle patterns.
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The US Army Combat Capabilities Development Command Army Research Laboratory (DEVCOM ARL) is currently developing unmanned aerial vehicle (UAV)-based radar imaging technology for counter-explosive hazard (CEH) applications. The explosive hazards under consideration include landmines, improvised explosive devices, and other closeto-ground-surface targets, which have long posed major detection challenges to any kind of sensors. Since many of these targets are buried underground, ground penetrating radar (GPR) imaging has emerged as one of the technologies holding great promise to solve this problem. In this paper, we consider UAV-based synthetic aperture radar (SAR) configurations capable of creating 2-D or 3-D images of underground targets, with both down-looking and side-looking sensing geometries. The clutter produced by rough ground surface and soil permittivity fluctuations is characterized via numerical simulations, with the purpose of evaluating the target-to-clutter ratio (TCR), which is the first indicator of detection performance in clutter-limited radar systems. For down-looking geometries, we compare the TCR performance of 2-D and 3-D imaging systems, as a function of target burial depth. For side-looking geometries, we compare the TCR in 2-D radar images created in the ground plane and underground vertical planes. The results of this analysis demonstrate that the 3-D down-looking GPR imaging system outperforms all the other configurations by a large margin.
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The real and imaginary components of the scattering matrix elements measured for each pixel in single look fully polarimetric SAR(POLSAR) are coherently combined from a large number of scatterers in each resolution bin. These components for the three independent Sinclair matrix scattering elements have normal distributions when collected over homogeneous regions. This is observed from the ocean surface, homogeneous desert regions, agricultural areas and more. These distributions are studied in this paper. Other distributions such as those for the amplitude ratios and the phase differences of the Sinclair matrix elements are addressed. This is done for single look fully polarimetric SIR-C data at L and C band and TerraSAR-X data. Distributions of observables from 4 look SIR-C data at L and C band are also addressed and compared to the single look distributions. All terrestial surfaces are considered where data is available.
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Based on the previous development of available radar simulators, this work further evaluates the detecting and estimating High-Ice-Water-Content (HIWC) conditions for airborne radar sensing. In hardware development, we developed a new prototype X-band, dual-polarized planar broadside array for the system upgrade. We used the previous flight campaigns data that combined radar and probe measurement to improve the physical models of the ice particles and their distributions. The usage of dual-polarized radar variables (such as ZDR and KDP) for forward-looking cases are then evaluated in parallel to the development of a new prototype of a low-cost airborne polarimetric radar sensor.
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In this paper, we present recent investigations by the U.S. Combat Capabilities Development Command (DEVCOM) Army Research Laboratory (ARL) into using low-frequency ultra-wideband (UWB) synthetic aperture radar (SAR) to detect obscured and buried targets. In particular, we investigate features that potentially discriminate between the target and clutter classes with the aim of classifying multiple target classes. In addition to the time- or spatial-domain complex data responses derived from the targets’ signatures, we consider the variations of the targets’ responses with changes across multiple polarization channels, viewing aspect angles, and frequency spectra. We apply deep neural networks to exploit these discrimination features extracted from SAR signatures of targets-of-interest and clutter.
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Polynomial chirplet representation of a frequency modulation radio frequency (FMRF) signal has many applications in radar and electronic support measurement (ESM). Fast and reliable estimation of polynomial chirplet parameters is valuable for FMRF signal processing. Traditionally, two types of techniques are used to estimate phase polynomial parameters, polynomial chirplet transform and multiple order phase difference approaches. The polynomial chirplet transform approach is robust to noises, however computationally expensive while the difference approach is computationally efficient, but sensitive noises. In this paper, a new multiple order difference approach is introduced to estimate parameters of a polynomial chirplet. In this new approach, we first compute the highest order coefficient of the polynomial chirplet, then remove the highest order monomial term by a monomial pursuit approach. Repeating these two steps, we develop a difference accumulation and monomial pursuit approach for estimating parameters of polynomial chirplet. Simulation tests show that the proposed method is robust to noises and has a low computational cost.
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Tracking with 2-D bistatic radar measurements is a challenging problem due to the nonlinear relationship between the sine-space radar measurements and the Cartesian coordinates, especially for long distances. For 2-D bistatic radar, this nonlinearity leads to a non-elliptical measurement uncertainty region in 2-D Cartesian coordinates, similar to a crescent, that causes consistency problems for a tracking filter. A solution is suggested by developing an unbiased and statistically consistent conversion of the position measurements to Cartesian coordinates, based on second order Taylor expansion. Such an approach was successfully used for monostatic radars but considered impractical for the bistatic case due to the difficulty to derive explicit conversion expressions. The implementation includes conversion of the bistatic range (rb) and sine-space angle measurement (u) to Cartesian position coordinates and tracking with a standard linear Kalman filter using the converted measurements, now linear in the state. This method is compared to the best-known existing filter, the converted measurement sigma point Kalman filter. Results show improved performance especially in terms of tracker consistency, keeping the state estimation error covariance statistically consistent with the actual estimation errors.
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Systems designed to detect the threat posed by drones should be able to both locate a drone and ideally determine its type in order to better estimate the level of threat. Previously, drone types have been discriminated using millimeter-wave Continuous Wave (CW) radar, which produces high quality micro-Doppler signatures of the drone propeller blades with fully sampled Doppler spectra. However, this method is unable to locate the target as it cannot measure range. By contrast, Frequency Modulated Continuous Wave (FMCW) data typically undersamples the micro-Doppler signatures of the blades but can be used to locate the target. In this paper we investigate FMCW features of four drones and if they can be used to discriminate the models using machine learning techniques, enabling both the location and classification of the drone. Millimeter-wave radar data are used for better Doppler sensitivity and shorter integration time. Experimentally collected data from Ttree quadcopters (DJI Phantom Standard 3, DJI Inspire 1, and Joyance JT5L-404) and a hexacopter (DJI S900) have been. For classification, feature extraction based machine learning was used. Several algorithms were developed for automated extraction of micro-Doppler strength, bulk Doppler to micro-Doppler ratio, and HERM line spacing from spectrograms. These feature values were fed to classifiers for training. The four models were classified with 85.1% accuracy. Higher accuracies greater than 95% were achieved for training using fewer drone models. The results are promising, establishing the potential for using FMCW radar to discriminate drone types.
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In this paper, we consider semi-supervised training of an attention-augmented convolutional autoencoder (AACAE) for human activity recognition using radar micro-Doppler signatures. The AA-CAE learns global information in addition to spatially localized features, thus enabling the classifier to overcome the limited receptive field of a conventional convolutional autoencoder (CAE). The design also permits the possibility of semi-supervised training of the AA-CAE using training data comprising unlabeled and labeled sets. More specifically, the semisupervised training regime is implemented by first pre-training the AA-CAE via unsupervised training of the attention-augmented autoencoder with the unlabeled portion of the training data. This is followed by fine-tuning of the AA-CAE for classification using the labeled portion. Using real-data measurements of six different human activities, we demonstrate that the semi-supervised AA-CAE yields higher classification accuracy with much less labeled data than a fully-supervised conventional CAE.
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This paper introduces the radar text data set (RadarTD) for technical language modeling. This data set is comprised of sentences containing radar parameters, values, and units determined from real-world values. This data set is created based on values determined from published academic research. Additionally, each statement is assigned a sentiment label and goal priority label. Preliminary investigations into the applicability of this data set are explored using the BERT model and several bi-directional LSTM models. These models are evaluated on text classification and named entity recognition tasks. This study evaluates the applicability of technical language modeling using neural networks to analyze input statements for cognitive radar applications. These findings suggest that this data set can be used to achieve reasonable performance for both text classification and named entity recognition for autonomous radar applications.
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We studied the technique and solutions of applying anti-jamming beamforming processing to the measured three-dimensional (3D) radiation patterns of GNSS antennas. We developed a small-scale, 2X3 custom array for demonstrating the GPS-L1 band operation. The process of measuring the 3D patterns is described. The visualization of individual and combined element pattern measurements serves as the basis for algorithm selections. The performance of anti-jamming post-processed beamforming and 3D pattern generation is evaluated using the measured pattern data. The technique and measurement process will be beneficial for the analysis of both civilian and military GNSS-based landing and navigational flight systems.
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We report the integration of an open-source software-defined radio (SDR) receiver to detect and track in realtime harmonic radar echoes produced by a non-linear device (transponder) mounted on a very small target. We describe a series of experimental measurements that were conducted to validate the sensitivity of the receiver system. In addition, we describe the implementation of a high-speed digital signal processing and a target detection algorithm. Finally, the experimental data and the results after the signal processing for detection are presented. In particular, it is demonstrated that the platform is a cost-effective receiver solution for the detection of transponders in Harmonic radar applications, relatively simple to program and implement.
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The US Army Combat Capabilities Development Command Army Research Laboratory is developing a dualband, full-polarization, side-looking synthetic aperture radar using an RF system-on-a-chip for the detection of landmines. The system employs two separate front-ends to operate in the bands from 0.5 to 1.8 GHz and from 2.1 to 3.8 GHz. An antenna array is set up with two transmitters (one vertical and one horizontal) and two receivers (one vertical and one horizontal) to enable fully-polarimetric operation. A continuous wave stepped-frequency waveform is employed, and each combination of polarizations is simultaneously transmitted and received. This system was tested at a desert site. The targets that were tested were remote anti-armor mine system landmines, M20 metal landmines, and VS2.2 plastic landmines. The targets are imaged under a number of emplacement scenarios so that imaging results address targets made of various materials at different orientations and ranges. Furthermore, obscured targets and buried targets are also investigated. The effect of antenna coupling and techniques for reducing this effect are discussed. Then, the imaging results for each target scenario is shown and analyzed. Imaging results between data from the two frequency bands are compared and the success of detection for different emplacements is analyzed.
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Within the field of target recognition, significant attention is given to data fusion techniques to optimize decision making in systems of multiple sensors. The challenge of fusing synthetic aperture radar (SAR) and electrooptical (EO) imagery is of particular interest to the defense community due to those sensors’ prevalence in target recognition systems. In this paper, the performances of two network architectures (a simple CNN and a ResNet) are compared, each implemented with multiple fusion methods to classify SAR and EO imagery of military targets. The Synthetic and Measured Paired Labeled Experiment (SAMPLE) dataset is used, an expansion of the MSTAR dataset, using both original measured SAR data and synthetic EO data. The classification performance of both networks is compared using the data modalities individually, using feature level fusion, using decision level fusion, and using a novel fusion method based on the three RGB-input channels of the ResNet (or other CNN for color image processing). In the input channel fusion method proposed, SAR imagery is fed to one of the three input channels, and the grayscale EO data is passed to a second of the three input channels. Despite its simplicity and off-the-shelf implementation, the input channel fusion method provides strong results, indicating it is worthy of further study.
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Certain engineering fluids are useful to dissipate heat emitted from high power silicon dies. In jet impingement cooling, whereby a jet of fluid is directly sprayed on the device being cooled, the electrical characteristics of the cooling fluids are an important consideration for the cooling design of radio frequency amplifiers. To prevent abnormal behavior and to ensure that modeling and simulation accurately predict the amplifier’s performance, the fluid must have the proper dielectric properties to guarantee sufficient insulation under various temperatures and conditions. This study focuses on determining the relative permittivity and the electric loss tangent of four types of engineering fluids: NovecTM 7300, NovecTM 7500, FluorinertTM FC-40, and FluorinertTM FC-3283 from 500 MHz to 20 GHz across 0℃ (more accurately 1°C) to 50°C at 10°C intervals. The findings of this study indicate that both FC fluids had a lower relative permittivity and loss tangent values than the Novec fluids. These results suggest that the FC fluids would be better suited for amplifier cooling since they are less conductive than the Novec fluids.
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In this study, we intended to verify simulations and measured data to support the development of an ultra-small and low power, handheld, or drone-carried ultra-wideband impulse radar (IR). Such a radar can remotely detect layers in snow or ice that tend to crack or break under certain conditions. First, we introduce the basic hardware design and configuration as a background, then we developed a series of electromagnetics sensing models, which can support training and testing of an algorithm based on machine-learning (ML), since the time-domain radar signatures of those hazardous structures are not widely available. We compared the principles and performance of these computational models and validated them with lab measurements and some initial snow measurements.
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Lightweight antennas with accompanying transceivers can be mounted to the gear of a soldier to act as a radar system, both active and passive. In common squad configurations, nine (9) soldiers form a variety of positional shapes in their patrols, most commonly triangles, squares, and straight lines. The culmination of the receivers for the entire squad creates complex antenna arrays. In this paper, we investigate the antenna array patterns for these squad configurations. This radar system as a whole can act as an active system, with one node acting as the transmitter, or as a purely passive system, exploiting transmitters of opportunity depending on the RF infrastructure of the current environment. The array patterns can also be manipulated to meet other situational needs, including vehicular or ship mounted systems for a wide variety of purposes.
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This paper investigates the use of micro-Doppler signatures of drones and birds for their detection and classification. Assessments made from simulated results are verified by data collected using a 10-GHz continuous wave (CW) radar system. Time/Velocity spectrograms generated for micro-Doppler analysis of multiple drones and birds are used for target identification and movement classification within TensorFlow. Results using Support Vector Machine (SVM) indicate 96% accuracy for drones vs. birds and 85% accuracy among individual drone and bird distinction between 5 classes.
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Over recent years, drone identification and detection has become an increasing concern for public safety and security. In this paper, we explore the use of convolutional neural networks (CNNs) applied to the continuous and discrete wavelet transform (CWT/DWT) scalogram of reflected radar signals from drones. In particular, we use the Martin-Mulgrew model to simulate the radar signals reflected off of five different types of drones from an X-band and W-band radar. The drones have different blade lengths and blade rotation rates, and these parameters will affect their respective scalograms, allowing for the use of CNNs in this classification problem. Results with real radar data sets collected in the laboratory are also presented.
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The increased usage of unmanned aerial devices for commercial usage, such as drones, has presented a new challenge in aircraft security and overall public safety. Therefore, there is an urgent need to accurately detect and track drones. The objective of this paper is to classify rotary drones and fixed wing drones based on their trajectories. In order to develop classification models, Stone Soup open-source software framework is used to generate simulated track data using the location information of the drones available through Global Position System (GPS) telemetry data. Stone Soup can be used to study the quality of the tracks when classifying drones. To study the performance of the various classification methods in a realistic environment, false alarms were generated along with the tracker outputs. Tracker output is segmented into sub-trajectories and were used as inputs to the different classification models. Traditional machine learning algorithms namely Support Vector Machines (SVM), K-Nearest Neighbour (KNN), Decision Trees (DT) and a deep learning algorithm namely Convolutional Neural Networks (CNN) were considered for developing classification models. Kinematic features derived from the sub-trajectories were used as features for machine learning algorithms while images obtained from the sub-trajectories were used as input to the CNN. In order to handle class imbalances, data augmentation was used. The performance of the various classification models validated the objective of this paper.
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The all-weather and light condition operability of synthetic aperture radar (SAR) imaging systems makes them the optimal choice for several civilian and military remote sensing applications. Deep learning methods have demonstrated state-ofthe-art classification performance on standard SAR datasets such as the Moving and Stationary Target Acquisition and Recognition (MSTAR) Standard Operating Conditions (SOC) 10-target dataset. However, high acquisition costs limit the availability SAR domain data, both in number and diversity for use in training neural networks. This in turn limits the performance of these networks when used to classify SAR images acquired using radar system specifications and imaging environments that differ from the specifications used to create the images used for training. In this work, Siamese Networks, made up of twin AlexNet-based CNNs, were trained using subsets of the Military Ground Target Dataset (MGTD) and MSTAR datasets to learn radar specification and imaging environment invariant features thereby increasing the classification performance on the MGTD test set by 4.17%.
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Mobile Ad-hoc Networks are a growing field of interest. They have many real-world applications, such as enabling internet connected sensors to operate in environments without pre-existing infrastructure. In past work, we have demonstrated that the Long Range (LoRa) radio frequency (RF) modulation technique, in conjunction with a mesh network can meet these needs in static networks. To extend this to applications with mobile nodes, several adaptations have been implemented to extend the original B.A.T.M.A.N (Better Approach to Mobile Ad-hoc Networking) mesh network algorithm. Node movement models were developed and tested to improve simulation accuracy. We also implemented situationally aware, machine learning (ML) based, route discovery techniques to ensure adequate network information is available in dynamic environments, without adding excessive overhead in static situations. To optimize these changes, a Black Box Optimizer was used in conjunction with an event-based simulation tool to train the ML model.
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In this paper, we explore the properties of various mathematical structures for use in radar applications, namely Orthogonal Sudoku arrays and Costas Cubes. The overarching theme is for the paper to serve as a foray into further explorations of these structures in more radar specific areas (e.g. noise radar). We, therefore, provide a brief description of each of these structures using mathematical theory before pivoting into computational results and a Radar specific application in antenna array patterns. Afterwards, the key points of this exploration and further application of these structures in radar is then discussed.
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There is growing research interest to merge the idea of a metacognitive radar with that of a tracking radar. The concept of metacognition can be broadly summarized as the process of learning about learning. In a metacognitive tracking radar, the system uses cognitive processes to detect and track a target in a dynamic environment. The radar then applies metacognitive techniques to select the cognitive process that yields the most accurate target track. In the context of target tracking, cognitive processes are various tracking algorithms. Currently, metacognitive tracking radar systems have only been demonstrated on targets of known trajectories. Their performance in the case of a randomly maneuvering target has not been explored. This paper presents an initial approach to this problem. First, an algorithm to generate random target trajectories is presented. Then, these trajectories are estimated using two estimation algorithms: the Extended Kalman Filter (EKF) and the Interacting Multiple Model (IMM) estimator. Finally, the performances of these two algorithms are compared.
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The information about intrapulse modulation is commonly used to augment data in electronic intelligence systems. However, increasingly popular nonlinear frequency modulated (NLFM) waveform is hardly ever distinguished as a separate waveform class by electronic support systems. In this paper a method of recognizing NLFM radar signal is presented. The algorithm is based on two novel features extracted from fractional Fourier transform (FrFT) and instantaneous frequency estimated via quasi-maximum-likelihood (QML) method. Moreover, the algorithm is designed to be resistant to the multipath effects, which are inherent to land-based intercept systems.
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Millimeter Wave Radar: Joint Session with Conferences 12108 and 12111
The micro-Doppler signature of a small unmanned aerial vehicle (UAV), resulting from the rotation of propeller blades, can be used to differentiate UAVs from other common confusing elements such as birds. Moreover, the micro-Doppler signature varies depending on the shape of individual UAV components such that these signatures can be used to differentiate between different UAV models. In order to investigate how different UAV components affect the signature, a high-fidelity micro-Doppler simulation has been developed previously, capable of generating micro-Doppler returns from 3D CAD models. This simulation requires experimental validation and so a 94 GHz radar has been designed and built for lab-based micro-Doppler measurements of UAV components in CW or FMCW Doppler modes. This allows for controlled experimental recreations of simulated scenarios in which the experimental micro-Doppler signatures of different UAV components can be measured and used for robust simulation validation. In this paper, the radar design will be explained in detail and the radar performance will be reviewed. Chirps are generated around 1 GHz using an Analog Devices AD9914 DDS board and upconverted onto a low phase noise STALO at 6.833 GHz. The upper sideband is filtered and frequency multiplied by 12 to 94 GHz. In FMCW mode the maximum chirp bandwidth is 3 GHz. The receiver is homodyne using a 94 GHz I-Q mixer to de-chirp to baseband. Feedhorn antennas are used for close range lab measurements, but larger antennas could be fitted for longer range outdoor data collection.
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Marine autonomy is a field receiving a high degree of interest for its many potential applications in terms of commerce, crew safety, and the military. A successful autonomous vessel depends on a sophisticated degree of situational awareness facilitated by sensors. We are investigating sub-THz radar sensors for this purpose, with the primary goal being the characterization of sea clutter and targets in terms of both amplitude and Doppler statistics at frequencies spanning 24 to 350 GHz, where presently there is a lack of data. Sub-THz frequencies are of particular interest due to improved range and Doppler resolutions, and reduced sensor size, factors expected to be critical in enabling anomaly detection in the dynamic marine environment. As part of this work, a new 207 GHz frequency modulated continuous wave (FMCW) radar is being developed for the collection of clutter and target phenomenology data. The architecture uses a direct digital synthesis (DDS) generated chirp which is upconverted onto a low phase noise microwave LO then frequency multiplied by 24 to the carrier frequency. Twin Gaussian optics lens antennas (GOLAs) are used for transmit and receive with beamwidths of 2° , with adjustable linear polarization. The radar head is gimbal mounted for raster scanning RCS maps or for use in staring mode Doppler measurements. A chirp bandwidth of 4 GHz enables range bins of a few centimeters and high speed chirps enable a maximum unambiguous velocity of ±5 m/s.
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This work addresses the design considerations, simulations, and fundamental framework of a novel Relative Navigation (RN) radar sensor operating at millimeter-wave bands, aiming at operating in ocean environments. A “multi-loop” system structure is suggested, which is believed to be the method to achieve the accuracy and reliability of a non-traditional tracking radar sensor. Simulation studies and data collection verification for preliminary hardware and software elements are presented.
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Synthetic Aperture Radar (SAR) projects a 3-D scene’s reflectivity into a 2-D image. In doing so, it generally focuses the image to a surface, usually a ground plane. Consequently, scatterers above or below the focal/ground plane typically exhibit some degree of distortion manifesting as a geometric distortion and misfocusing or smearing. Limits to acceptable misfocusing define a Height of Focus (HOF), analogous to Depth of Field in optical systems. This may be exacerbated by the radar’s flightpath during the synthetic aperture data collection. HOF is very radar flightpath dependent. Some flightpaths like straight and level flightpaths will have very large HOF limits. Other flightpaths, especially those that exhibit large out-of-plane motion will have very small HOF limits, perhaps even small fractions of a meter. This paper explores the impact of various flightpaths on HOF, and discusses the conditions for increasing or decreasing HOF. We note also that HOF might be exploited for target height estimation and offer insight to other height estimation techniques.
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This paper presents a new 3D time-space detector for small ships in single look complex (SLC) synthetic aperture radar (SAR) imagery, optimized for small targets around 5-15 m long that are unfocused due to target motion induced by ocean surface waves. Imagery is decomposed into subapertures to form a time sequence of images and the 3D power spectral density (PSD) is evaluated. Within the PSD, the response due to wave clutter is concentrated near low frequency and wavenumber relative to the target response. The clutter spectrum is estimated from collected training data and used to whiten data for cells under test (CUT). The time-space extent of the target PSD is estimated using a generic small target point-scattering model obtained from simulated data using a computer-aided design (CAD) model of a 10 m target under moderate surface conditions that is noncoherently averaged over target heading and speed. The target PSD estimate is used as a template and applied to the whitened, magnitude-detected CUT, forming a test statistic. Experiments on RADARSAT2 data demonstrate improvement over a simple power detector of 2-6 dB that is robust to both clutter and target conditions.
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Various applications of the delay line discriminator (DLD) have been described in the open literature – primarily for use as part of a waveform classifier. In this work, we document the performance of the DLD when employed as a radar waveform estimator, assuming that a preliminary algorithm has detected the rising and falling pulse edges. We examine some of the issues associated with the waveform estimation problem, in particular the effects of signal-to-noise ratio (SNR) and DLD parameter settings on the waveform estimation. In the process, we outline analytic techniques used for classification of linear FM, constant frequency, and phase modulated waveforms.
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