Traditional ground moving target indicator (GMTI) processing attempts to separate moving objects in the scene from stationary clutter. Techniques such as space-time adaptive processing (STAP) require the use of an unknown covariance matrix of the interference (clutter, jamming, and thermal noise) that must be estimated from the remaining data not currently under test. Many problems exist with estimating the interference covariance including: heterogeneous, contaminated, and/or limited training data. There are many existing techniques for obtaining an interference covariance matrix estimate, most of which incorporate some kind of prior knowledge to improve the estimate. We propose a Bayesian framework that estimates both clutter and movers on a range-by- range basis without the explicit estimation of an interference covariance matrix. The approach incorporates the knowledge of an approximate digital elevation map (DEM), platform kinematics (platform velocity, crab angle, and antenna spacings), and the belief that movers are sparse in the scene. Computation using this Bayesian model is enabled by recent algorithm developments for fast inference on linear mixing models. The signal model and required processing steps are detailed. We test our approach using the KASSPER I dataset and compare the results to other current approaches.
Wide-area persistent radar video offers the ability to track moving targets. A shortcoming of the current technology is an inability to maintain track when Doppler shift places moving target returns co-located with strong clutter. Further, the high down-link data rate required for wide-area imaging presents a stringent system bottleneck. We present a multi-channel approach to augment the synthetic aperture radar (SAR) modality with space time adaptive processing (STAP) while constraining the down-link data rate to that of a single antenna SAR system. To this end, we adopt a multiple transmit, single receive (MISO) architecture. A frequency division design for orthogonal transmit waveforms is presented; the approach maintains coherence on clutter, achieves the maximal unaliased band of radial velocities, retains full resolution SAR images, and requires no increase in receiver data rate vis-a-vis the wide-area SAR modality. For Nt transmit antennas and N samples per pulse, the enhanced sensing provides a STAP capability with Nt times larger range bins than the SAR mode, at the
cost of O(log N) more computations per pulse. The proposed MISO system and the associated signal processing
are detailed, and the approach is numerically demonstrated via simulation of an airborne X-band system.
We propose a single-receive, multiple-transmit channel imaging radar system that limits received data rate while
also providing spatial processing for improved detection of moving targets. A multi-input, single-output (MISO)
system uses orthogonal waveforms to separate spatial channels at the single receiver. The use of orthogonal
waveforms necessitates several modications to both synthetic aperture radar imaging and adaptive space-time
beamforming. An orthogonal frequency-division transmit waveform scheme is proposed, and we derive the
attendant extensions to the standard backprojection and space-time beamforming algorithms.. We demonstrate
imaging and moving target detection results using data from an airborne X-band system. We conclude with a
discussion of the clutter covariance matrix of the resulting space-time beamformer and a suggested waveform
scheduling scheme to minimize the rank of the observed clutter subspace.
For large-scale linear inverse problems, a direct matrix-vector multiplication may not be computationally feasible,
rendering many gradient-based iterative algorithms impractical. For applications where data collection can be
modeled by Fourier encoding, the resulting Gram matrix possesses a block Toeplitz structure. This special
structure can be exploited to replace matrix-vector multiplication with FFTs. In this paper, we identify some
of the important applications which can benefit from the block Toeplitz structure of the Gram matrix. Also,
for illustration, we have applied this idea to reconstruct 2D simulated images from undersampled non-Cartesian
Fourier encoding data using three popular optimization routines, namely, FISTA, SpaRSA, and optimization
We utilize eight circular passes of measured airborne X-Band radar data to form a novel reflectivity surface
estimate. Our previous work demonstrated reflectivity surface estimation from narrow aperture multi-pass data
and this work extends those results to wide apertures. Narrow aperture surface estimates are co-registered in the
three spatial dimensions and combined non-coherently to form a wide-aperture data product. For the purpose
of visually conveying the scene reflectivity content a surface is formed from the wide angle data product. The
subject of this work is not on the optimality of the methods nor the global convexity of the cost functions.
Instead, these results give us one of the first glimpses at measured wide angle three dimensional SAR image
products and provide a qualitative benchmark against which to measure future wide angle three dimensional
synthetic aperture radar autofocus and imaging algorithms.
We present a fast, scalable method to simultaneously register and classify vehicles in circular synthetic aperture
radar imagery. The method is robust to clutter, occlusions, and partial matches. Images are represented as a
set of attributed scattering centers that are mapped to local sets, which are invariant to rigid transformations.
Similarity between local sets is measured using a method called pyramid match hashing, which applies a pyramid
match kernel to compare sets and a Hamming distance to compare hash codes generated from those sets. By
preprocessing a database into a Hamming space, we are able to quickly find the nearest neighbor of a query
among a large number of records. To demonstrate the algorithm, we simulated X-band scattering from ten
civilian vehicles placed throughout a large scene, varying elevation angles in the 35 to 59 degree range. We
achieved better than 98 percent classification performance. We also classified seven vehicles in a 2006 public
release data collection with 100% success.
We present a set of simulated X-band scattering data for civilian vehicles. For ten facet models of civilian
vehicles, a high-frequency electromagnetic simulation produced fully polarized, far-field, monostatic scattering
for 360 degrees azimuth and elevation angles from 30 to 60 degrees. The 369 GB of phase history data is stored
in a MATLAB file format. This paper describes the CVDomes data set along with example imagery using 2D
backprojection, single pass 3D, and multi-pass 3D.
In this paper we consider classification of civilian vehicles using circular synthetic aperture radar. For wide-field
application in which the scene radius is a significant fraction of the flight path radius, vehicle signatures
are spatially variant due to layover. For a ten-class identification task using simulated X-band signatures, we
demonstrate 96% correct classification for single-pass 2D imagery with scene radius 0.4 times the flight radius.
Simulated scattering data include multi-path and material effects. Image signatures are represented by sets of
attributed scattering centers. Dissimilarity between attributed point sets is computed via a minimized partial
Hausdorff distance. Using multidimensional scaling, the distances are represented in a low-dimensional Euclidean
space for both visualization and improved classification. The minimized partial Hausdorff distance, while not
a true distance, empirically shows remarkable fidelity to the triangle inequality. Finally, in a limited two-class
study, we show that three-dimensional imaging of layover points using polarization cues provides improved class
We consider three dimensional target construction from SAR data collected on multiple complete circular apertures
at different elevation angle. The 3-D resolution of circular SAR systems is constrained by two factors: the
sparse sampling in elevation and the limited azimuthal persistence of the reflectors in the scene. Three dimensional
target reconstruction with multipass circular SAR data is further complicated by nonuniform elevation
spacing in real flight paths and non-constant elevation angle throughout the circular pass. In this paper we first
develop parametric spectral estimation methods that extend standard IFSAR method of height estimation to
apertures at more than two elevation angles. Next, we show that linear interpolation of the phase history data
leads to unsatisfactory performance in 3-D reconstruction from nonuniformly sampled elevation passes. We then
present a new sparsity regularized interpolation algorithm to preprocess nonuniform elevation samples to create
a virtual uniform linear array geometry. We illustrate the performance of the proposed method using simulated
At high frequencies, synthetic aperture radar (SAR) imagery can be represented as a set of points corresponding
to scattering centers. Using a collection of sequential azimuths with a fixed aperture we build a cube of points for
each of seven civilian vehicles in the Gotcha public release data set (GPRD). We present a baseline study of the
ability to discriminate between the vehicles using strictly 2D geometric information of the scattering centers. The
comparison algorithm is independent of pose and translation using a novel application of the partial Hausdorff
distance (PHD) minimized through a particle swarm optimization. Using the PHD has the added benefit of
reducing the effects of occlusions and clutter in comparing vehicles from pass to pass. We provide confusion
matrices for a variety of operating parameters including azimuth extent, various amplitude cutoffs, and various
parameters within PHD. Finally, we discuss extension of the approach to near-field imaging and to additional
point attributes, such as 3D location and polarimetric response.
Imaging is not itself a system goal, but is rather a means to support inference tasks. For data processing with linearized signal models, we seek to report all high-probability
interpretations of the data and to report confidence labels in the form of posterior probabilities. A low-complexity recursive procedure is presented for Bayesian estimation in linear regression models. A Gaussian mixture is chosen as the prior on the unknown parameter vector. The algorithm returns both a set of high posterior probability mixing parameters
and an approximate minimum mean squared
error (MMSE) estimate of the parameter
vector. Emphasis is given to the case of a sparse parameter vector. Numerical simulations demonstrate estimation performance and illustrate
the distinctions between MMSE estimation and maximum a posteriori probability (MAP) model selection.
The proposed tree-search algorithm provides exact ratios of posterior probabilities for a set of high probability solutions to the sparse reconstruction problem. These relative probabilities serve to reveal potential ambiguity among multiple candidate solutions that are ambiguous due to low signal-to-noise ratio and/or significant correlation among columns in the super-resolving regressor matrix.
We study circular synthetic aperture radar (CSAR) systems collecting radar backscatter measurements over a
complete circular aperture of 360 degrees. This study is motivated by the GOTCHA CSAR data collection experiment
conducted by the Air Force Research Laboratory (AFRL). Circular SAR provides wide-angle information
about the anisotropic reflectivity of the scattering centers in the scene, and also provides three dimensional information
about the location of the scattering centers due to a non planar collection geometry. Three dimensional
imaging results with single pass circular SAR data reveals that the 3D resolution of the system is poor due to
the limited persistence of the reflectors in the scene. We present results on polarimetric processing of CSAR
data and illustrate reasoning of three dimensional shape from multi-view layover using prior information about
target scattering mechanisms. Next, we discuss processing of multipass (CSAR) data and present volumetric
imaging results with IFSAR and three dimensional backprojection techniques on the GOTCHA data set. We
observe that the volumetric imaging with GOTCHA data is degraded by aliasing and high sidelobes due to
nonlinear flightpaths and sparse and unequal sampling in elevation. We conclude with a model based technique
that resolves target features and enhances the volumetric imagery by extrapolating the phase history data using
the estimated model.
Radar resolution in three dimensions is considered for circular synthetic apertures at a constant elevation angle.
A closed-form expression is derived for the far-field 3-D point spread function for a circular aperture of 360 degrees
azimuth and is used to revisit the traditional measures of resolution along the x, y and z spatial axes. However,
the limited angular persistence of reflectors encountered in practice renders the traditional measures inadequate
for circular synthetic aperture radar imaging. Two alternative measures for 3-D resolution are presented: a
nonparametric measure based on level sets of a reflector's signature and a statistical measure using the Cramer-
Rao lower bound on location estimation error. Both proposed measures provide a quantitative evaluation of
3-D resolution as a function of scattering persistence and radar system parameters. The analysis shows that
3-D localization of a reflector requires a combination of large radar cross section and large angular persistence.
In addition, multiple elevations or a priori target scattering models, if available, may be used to significantly
enhance 3-D resolution.
Support Vector Regression is a well established robust method for function estimation. The Support Vector Machine uses inner-product kernels between support vectors and the input vectors to transform the nonlinear classification and regressions problem to a linear version.function where the surface is approximated with a linear
combination of the kernel function evaluated at the support vectors. In many applications, the number of these support vectors can be quite large which can increase the length of the prediction phase for large data sets. Here we study a technique for reducing the number of support vectors to achieve comparable function estimation accuracy. The method identifies support vectors that are close to the ε-tube and uses them to approximate the function estimate of the original algorithm.
We consider imaging strategies for synthetic aperture radar data
collections that span a wide angular aperture. Most traditional
radar imaging techniques are predicated on the assumption of
isotropic point scattering mechanisms, which does not hold for
wide apertures. We investigate point scattering center images for
narrowband, wide angle data, and consider the effect of limited
persistence on the resulting images. We investigate imaging
strategies that apply to wide angle apertures. We show that
coherent processing of the entire wide angle aperture may not be
the best image formation strategy for objects of practical
interest. Finally, we present initial results on resolution
enhancement techniques for wide angle apertures.
We consider a method for estimating classification performance of a model-based synthetic aperture radar (SAR) automatic target recognition system. Target classification is performed by comparing an unordered feature set extracted from a measured SAR image chip with an unordered feature set predicted from a hypothesized target class and pose. A Bayes likelihood metric that incorporates uncertainty in both the predicted and extracted feature vectors is used to compute the match score. Evaluation of the match likelihoods requires a correspondence between the unordered predicted and extracted feature sets. This is a bipartite graph matching problem with insertions and deletions; we show that the optimal match can be found in polynomial time. We extend the results in 1 to estimate classification performance for a ten-class SAR ATR problem. We consider a synthetic classification problem to validate the classifier and to address resolution and robustness questions in the likelihood scoring method. Specifically, we consider performance versus SAR resolution, performance degradation due to mismatch between the assumed and actual feature statistics, and performance impact of correlated feature attributes.
In this paper, the phase of a radar range profile is shown to contain valuable information for inverse scattering problems. A physics-based high-frequency parametric model is adopted for the radar backscatter, and information is quantified using the variance of parameters estimated from noisy radar range profiles. Through analysis of the Fisher information matrix, phase is observed to yield up to a factor of ten increase in achievable resolution; moreover, phase is shown to allow reliable discrimination of frequency-dependent scattering behaviors. Results are confirmed using measured radar imagery from a 2-inch resolution X-band system.
Ultra wideband (UWB) radar is an emerging technology with potential for all-weather, remote sensing of objects obscured by foliage or buried underground. Multiple octaves of frequency coverage and 90 degrees or more of viewing angles across a synthesized aperture are used to obtain high spatial resolution mapping of scattering behavior. Additionally, fully polarimetric responses can be measured, providing a multichannel characterization of objects in a scene. However, the diversity in wavelength and viewing angle presents significant challenges for system engineering and data interpretation. In particular, the multichannel UWB system poses unique imaging challenges arising from the variation of the UWB antenna response. We present an overview of calibration techniques for polarimetric wideband imagery, and introduce an image domain calibration technique using calibration targets.
In this paper we introduce multi-channel techniques to compensate for effects of antenna shading and crosstalk in wideband, wide-angle full polarization radar imaging. We model the systems as a 2D integral operator that includes the transmit pulse function, receive and transmit antenna transfer functions, and response from scattering objects. Existing imaging algorithms provide an approximate inversion of this integral operator, without compensation for the effect of antenna transfer functions. Thus, standard processing results in image quality diminished by the inherent variation of the antenna response--in magnitude, phase and polarization--across a large band of frequencies and wide range of aspect angles. We propose three inversion techniques for this integral operator, to improve polarization purity and to achieve localized point spread functions. The first technique uses a local approximation to the system model, and propose a conceptually simple method for the inversion. The other two techniques propose inversion methods for the exact system model in different transform domains. The result is imagery with improved polarization purity and a more localized point spread function.
In this paper we present the results of an empirical study investigating subband prescreener detection. The prescreener is used with ultra-wideband foliage penetrating synthetic aperture radar imagery. Our results demonstrate that, for the selected set of computationally simple features, lower resolution imagery can be used at the early detection stages. We also present initial multiband detection results. These results indicate that a combination of lower resolution subbands can be used in a fast prescreening algorithm without appreciable performance loss when compared to the fullband detector.
We consider the problem of detecting anisotropic scattering of targets from wideband SAR measurements. We first develop a scattering model for the response of an ideal dihedral when interrogated by a wideband radar. We formulate a stochastic detection problem based on this model and Gaussian clutter models. We investigate the performance of three detectors, the conventional imaging detector, a generalized likelihood ratio test (GLRT) detector based on the dihedral anisotropic scattering model, and a sum-of- squares detector motivated as a computationally attractive alternative to the GLRT test. We also investigate the performance degradation of the GLRT detector when using truncated angle response filters, and analyze detector sensitivity to changes in target length. Finally, we present initial results of angular matched filter detection applied to UWB radar measurements collected by the Army Research Laboratory at Aberdeen Proving Grounds.
An attributed scattering center model exploits scattering phenomenology that is not accessed through traditional SAR image formation. Frequency, aspect, and polarization dependent scattering behaviors are jointly processed to provide a concise, descriptive, high resolution analysis of regions of interest. Used in conjunction with other features such as shadows, context, and image texture, attributed scattering center features hold promise for both feature- based and model-based automatic target recognition systems. In this conference paper, we present a parametric model for radar scattering as a function of frequency and aspect angle; the model is suggested by high-frequency monostatic far-field scattering solutions provided by the geometrical theory of diffraction and physical optics. The scattering model is used for analysis of synthetic aperture radar data. The estimated parameters provide a concise, physically relevant description of measured scattering for use in target recognition, data compression and scattering studies.The scattering model may be fit to either complex- valued imagery or to radar phase history data using a nonlinear least-squares estimator. Statistical analysis of the scattering model serves to characterize uncertainty to estimated scattering parameters. Feature estimation performance bounds are evaluated for X-band, K-band, and ultra wideband synthetic aperture radar scenarios.
Polarimetric diversity can be exploited in synthetic aperture radar (SAR) for enhanced target detection and target description. Detection statistics and target features can be computed from either polarimetric imagery or parametric processing of SAR phase histories. We adopt an M- ary Bayes classification approach and derive Bayes-optimal decision rules for detection and description of scattering centers. Scattering centers are modeled as one of M canonical geometric types with unknown amplitude, phase and orientation angle; clutter is modeled as one of M canonical geometric types with unknown amplitude, phase and orientation angel; clutter is modeled as a spherically invariant random vector. For the Bayes optimal decision rules, we provide a simple geometric interpretation and an efficient computational implementation. Moreover, we characterize the certainty of decisions by deriving an approximate posteriori probability.
Using a point scatterer assumption, high-frequency SAR phase histories can be modeled as a sum of 2D complex exponentials in additive noise. This paper summarizes our SAR signal modeling experience using the XPatch simulated scattering data. We apply several 2D parametric estimation techniques including 2D TLS-Prony, MEMP, 2D IQML, and 2D CLEAN to estimate the complex exponential model parameters. From the estimation results, we discuss the engineering trade-offs among memory requirement, computation requirement, and estimation accuracy.
We present an algorithm for the removal of narrow-band interference from wideband signals. We apply the algorithm to suppress radio frequency interference encountered by ultra- wideband synthetic aperture radar systems used for foliage- and ground-penetrating imaging. For this application, we seek maximal reduction of interference energy, minimal loss and distortion of wideband target responses, and real-time implementation. To balance these competing objectives, we exploit prior information concerning the interference environment in designing an estimate-and-subtract-estimation algorithm. The use of prior knowledge allows fast, near-least-squares estimation of the interference and permits iterative target signature excision in the interference estimation procedure to decrease estimation bias. The results is greater interference suppression, less target signature loss and distortion, and faster computation than is provided by existing techniques.
A new approach to scattering center extraction is developed based on a model derived from the geometric theory of diffraction (GTD). For stepped frequency measurements at high frequencies, this model is better matched to the physical scattering process than the Prony or discrete Fourier transform modeling methods. In addition, the GTD-based model extracts more information about the scattering centers, allowing partial identification of scattering center geometry in addition to determining energy and downrange distance. We derive expressions for the Cramer-Rao bound of this model; using these expressions we analyze the behavior of the new model as a function of scatterer separation, bandwidth, number of data points, and noise level. We compare these results with those for the Prony model. Additionally, a maximum likelihood algorithm for the model is developed. Estimation results using data measured on a compact range are presented to validate the proposed modeling procedure.