We consider the problem of distributed detection in a large network of sensors under network communication constraints. Sensor nodes are randomly deployed and follow a random sleep/wake schedule. When awake, sensor nodes perform local detection tests and communicate detections over a multiple-access channel to a fusion center. The fusion center can detect both successful communications and communication collisions in the channel. We show that the optimum fusion rule is a weighted sum of the number of detections received and the number of collisions detected by the fusion node. We derive analytical expressions that characterize the performance of the system. Simulation examples compare theoretical predictions with numerical results.

Hyperspectral change detection (HSCD) provides an avenue for detecting subtle targets in complex backgrounds. Complicating the problem of change detection is the presence of shadow, illumination, and atmospheric differences, as well as misregistration and parallax error, which often produce the appearance of change. Recent development of a model-based (MB) approach to HSCD has demonstrated potential improvement for mitigating false alarms due specifically to shadow differences using calibrated data. Further development and application of the MB approach is provided here. The method is extended for use on both uncalibrated and relatively calibrated hyperspectral data and is applied to airborne hyperspectral imagery collected using the Hyperspectral Digital Imagery Collection Experiment visible to short-wave infrared sensor and uncalibrated tower imagery collected by the Air Force Research Laboratory.

We consider the problem of parameter estimation for signals characterized by sums of parameterized functions. We present a dynamic dictionary subset selection approach to parameter estimation where we iteratively select a small number of dictionary elements and then alter the parameters of these dictionary elements to achieve better signal model fit. The proposed approach avoids the use of highly oversampled (and highly correlated) dictionary elements, which are needed in fixed dictionary approaches to reduce parameter bias associated with dictionary quantization. We demonstrate estimation performance on a sinusoidal signal estimation example.

Within the hyperspectral community, change detection is a continued area of interest. Interesting changes in imagery typically correspond to changes in material reflectance associated with pixels in the scene. Using a physical model describing the sensor-reaching radiance, change detection can be formulated as a statistical hypothesis test. Complicating the problem of change detection is the presence of shadow, illumination, and atmospheric differences, as well as misregistration and parallax error, which often produce the appearance of change. The proposed physical model incorporates terms to account for both direct and diffuse shadow fractions to help mitigate false alarms associated with shadow differences between scenes. The resulting generalized likelihood ratio test (GLRT) provides an indicator of change at each pixel. The maximum likelihood estimates of the physical model parameters used for the GLRT are obtained from the entire joint data set to take advantage of coupled information existing between pixel measurements. Simulation results using synthetic and real imagery demonstrate the efficacy of the proposed approach.

We consider the problem of joint enhancement of multichannel images with pixel based constraints on the multichannel data. Previous work by Cetin and Karl introduced nonquadratic regularization methods for SAR image enhancement using sparsity enforcing penalty terms. We formulate an optimization problem that jointly enhances complex-valued multichannel images while preserving the cross-channel information, which we include as constraints tying the multichannel images together. We pose this problem as a joint optimization problem with constraints. We first reformulate it as an equivalent (unconstrained) dual problem and develop a numerically-efficient method for solving it. We develop the Dual Descent method, which has low complexity, for solving the joint optimization problem. The algorithm is applied to both an interferometric synthetic aperture radar (IFSAR) problem, in which the relative phase between two complex-valued images indicate height, and to a synthetic multimodal medical image example.

We consider characterization of building interior structure from two-pass interferometric circular synthetic aperture radar data. We model returns from complex building structures as the sum of the responses from scattering primitives-plates, dihedrals, and trihedrals-observed through transfer functions that characterize both the transmission through and reflection from dielectric surfaces. Maximum-likelihood estimates for the location of primitive features and wall propagation/reflection parameters are obtained through a two-stage detection-and-estimation algorithm. We employ a sparse reconstruction algorithm to detect primitive signatures in the presence of wall effects and refine our estimates using a nonlinear minimization of local cost functions. We show that using simplified wall and primitive models, we can extract geometrically relevant features which can be combined to reveal 3-D floorplan estimates of buildings. Examples illustrate the effectiveness of the feature extraction approach.

In sensor network self-localization, anchor nodes provide a convenient means to disambiguate scene translation and rotation, thereby affording estimates in an absolute coordinate system. However, localization performance depends on the positions of the anchor nodes relative to the unknown-location nodes. Conventional wisdom in the literature is that anchor nodes should be placed around the perimeter of the network. In this paper, we show analytically why this strategy works well universally. We demonstrate that perimeter placement forces the information provided by the anchor constraints to closely align with the subspace that cannot be estimated from inter-node measurements: the subspace of translations and rotations. Examples quantify the efficacy of perimeter placement of anchors.

We consider characterization of building interior structure from two-pass interferometric circular SAR data. We extract dihedral and trihedral scattering primitives that dominate mono-static returns from buildings. The 3D location of each scattering primitive is estimated using the phase information in two-pass data. Using simplified wall and primitive models, we match model signatures to the extracted features using a hypothesis selection and refinement loop. Examples illustrate the effectiveness of the feature extraction approach.

In this paper, we outline two parameter estimation schemes for discerning canonical shape parameters from bistatic and monostatic radar data collected over a non-linear flight path. We present initial results characterizing both optimal and sub-optimal estimation performance for location and size estimation of plates, dihedrals, and trihedrals.

Summary form only given. Despite significant recent progress in automatic target exploitation (ATE) and recognition (ATR), current ATE systems do not meet the requirements of modern battlefield environments. Next generation ATE systems must actively manage sensor resources, aggregate sensed information across multiple platforms and diverse signaling modalities, and adapt to increasingly agile adversaries and operating conditions. Thus, the fundamental research challenge is to develop an integrated systems theory that jointly treats information fusion, control, and adaptation using multiple, dynamic multimodal sensor platforms in resource constrained environments.

This paper considers the accuracy of sensor node location estimates from self-calibration in sensor networks. The location parameters are shown to have a natural decomposition into relative configuration and centroid transformation components based on the influence of measurements and prior information in the problem. A linear representation of the transformation parameter space, which includes rotations and translations, is shown to coincide with the nullspace of the unconstrained Fisher information matrix (FIM). To regularize the absolute localization problem, we consider constraints on the coordinate locations and the impact of these constraints on relative and absolute location error. A geometric interpretation of the constrained Cramer-Rao bound (CRB) is provided based on the principal angles between the measurement subspace and the constraint subspace. Examples illustrate the utility of this error decomposition.

This paper discusses the effect of motion measurement errors (MMEs) on measured bistatic synthetic aperture radar (SAR) phase history data that has been motion compensated to the scene origin. We characterize the effect of low-frequency MMEs on bistatic SAR images, and, based on this characterization, we derive limits on the allowable MMEs to be used as system specifications. Finally, we demonstrate that proper orientation of a bistatic SAR image during the image formation process allows application of monostatic SAR autofocus algorithms in postprocessing to mitigate image defocus.

Self-localization is an important component of distributed sensor systems. The presence of a few highly erroneous measurements, or outliers, results in erroneous sensor location estimates. In this paper, we employ the EM algorithm to iteratively detect outlier measurements and provide robust position estimates of the sensors. The derivation of the algorithm is given, and Monte-Carlo simulations are presented to compare this estimator to others. The performance of the EM-based algorithm is also shown to be close to the Cramer-Rao lower bound for position estimation when perfect knowledge of the outlier process is known.

Automatic self-localization is a critical need for the effective use of ad hoc sensor networks in military or civilian applications. In general, self-localization involves the combination of absolute location information (e.g., from a global positioning system) with relative calibration information (e.g., distance measurements between sensors) over regions of the network. Furthermore, it is generally desirable to distribute the computational burden across the network and minimize the amount of intersensor communication. We demonstrate that the information used for sensor localization is fundamentally local with regard to the network topology and use this observation to reformulate the problem within a graphical model framework. We then present and demonstrate the utility of nonparametric belief propagation (NBP), a recent generalization of particle filtering, for both estimating sensor locations and representing location uncertainties. NBP has the advantage that it is easily implemented in a distributed fashion, admits a wide variety of statistical models, and can represent multimodal uncertainty. Using simulations of small to moderately sized sensor networks, we show that NBP may be made robust to outlier measurement errors by a simple model augmentation, and that judicious message construction can result in better estimates. Furthermore, we provide an analysis of NBP's communications requirements, showing that typically only a few messages per sensor are required, and that even low bit-rate approximations of these messages can be used with little or no performance impact.

This paper discusses reconstruction of three-dimensional surfaces from multiple bistatic synthetic aperture radar (SAR) images. Techniques for surface reconstruction from multiple monostatic SAR images already exist, including interferometric processing and stereo SAR. We generalize these methods to obtain algorithms for bistatic interferometric SAR and bistatic stereo SAR. We also propose a framework for predicting the performance of our multistatic stereo SAR algorithm, and, from this framework, we suggest a metric for use in planning strategic deployment of multistatic assets.

Ad hoc localization of wireless sensor nodes is a fundamental problem in wireless sensor networks. Despite the recent proposals for the development of ad hoc localization algorithms, the fundamental behavior in systems using measurements has not been characterized. In this paper, we take a first step toward such a characterization by examining the behavior of error inducing parameters in multihop localization systems in an algorithm independent manner. We first derive the Crame Rao Bound for Gaussian measurement error for multihop localization systems using distance and angular measurements. Later on, we use these bounds on a carefully controlled set of scenarios to study the trends in the error induced by the measurement technology accuracy, network density, beacon node concentration, and beacon uncertainty. By exposing these trends, the goal of this paper is to develop a fundamental understanding of the error behavior that can provide a set of guidelines to be considered during the design and deployment of multihop localization systems.

Distributed sensing systems fuse information from various local measurements to form joint estimates of physical phenomena. We study Bayesian parameter estimation with measurement failures, where the probability of failing to make an observation depends on the unknown parameters. Both the absence and the existence of the measurements provide information about the parameters. We present lower bounds for minimum mean square error estimation. The bounds are applied to the analysis of sensor arrays for source localization and the distributed estimation problem with binary detectors.

Automatic self-calibration of ad-hoc sensor networks is a critical need for their use in military or civilian applications. In general, self-calibration involves the combination of absolute location information (e.g. GPS) with relative calibration information (e.g. estimated distance between sensors) over regions of the network. We formulate the self-calibration problem as a graphical model, enabling the application of nonparametric belief propagation (NBP), a recent generalization of particle filtering, for both estimating sensor locations and representing location uncertainties. NBP has the advantage that it is easily implemented in a distributed fashion, can represent multi-modal uncertainty, and admits a wide variety of statistical models. This last point is particularly appealing in that it can be used to provide robustness against occasional high-variance (outlier) noise. We illustrate the performance of NBP using Monte Carlo analysis on an example network.

Automatic self-calibration of ad-hoc sensor networks is a critical need for their use in military or civilian applications. In general, self-calibration involves the combination of absolute location information (e.g. GPS) with relative calibration information (e.g. time delay or received signal strength between sensors) over regions of the network. Furthermore, it is generally desirable to distribute the computational burden across the network and minimize the amount of inter-sensor communication. We demonstrate that the information used for sensor calibration is fundamentally local with regard to the network topology and use this observation to reformulate the problem within a graphical model framework. We then demonstrate the utility of nonparametric belief propagation (NBP), a recent generalization of particle filtering, for both estimating sensor locations and representing location uncertainties. NBP has the advantage that it is easily implemented in a distributed fashion, admits a wide variety of statistical models, and can represent multi-modal uncertainty. We illustrate the performance of NBP on several example networks while comparing to a previously published nonlinear least squares method.

We consider the effect of unknown signal propagation velocity on direction-of-arrival (DOA) estimation performance using an array of sensors. For general arrays, the DOA estimation variance, as measured by the Crame/spl acute/r-Rao bound (CRB), degrades when the propagation velocity is unknown. In this letter, we show that for both two- and three-dimensional arrays, the CRB on the DOA angle is independent of whether or not the propagation velocity is known if and only if the sensor locations satisfy the isotropy conditions given in earlier work. The results hold for both narrowband and wideband signals.

We consider the role of array geometry on the Direction of Arrival (DOA) estimating performance of the array where the impinging signal is wideband. We define the criteria under which the planar and volume arrays are isotropic, and derive the necessary and sufficient conditions on the location of array elements so that the array has isotropic performance. We also present several designs of isotropic planar and volume arrays and give example geometries.

We present an algorithm for locating and orienting a set of sensor arrays that have been deployed in a scene at unknown locations and orientation angles. This self-calibration problem is solved using a number of source signals also deployed in the scene. We assume each array can estimate the time-of-arrival and direction-of-arrival of every source. From this information we compute the array locations and orientations. We consider four subproblems, in which the source signals or emission times are either known or unknown. We develop necessary conditions for solving the self-calibration problem and provide a maximum likelihood solution and corresponding location error estimate.

Minimum-mean squared error (MMSE) receivers are designed and analyzed for multiple data rate direct-sequence code-division multiple-access (DS-CDMA) systems. The inherent cyclostationarity of the DS-CDMA signal is exploited to construct receivers for asynchronous multipath channels. Multiple- and single-bandwidth access are treated for both single and multicarrier scenarios. In general, the optimal receiver is periodically time-varying. When the period of the optimal receiver is large, suboptimal receivers are proposed to achieve a lower complexity implementation; the receivers are designed as a function of the cyclic statistics of the signals. In multiple chipping rate systems, the complexity of receivers for smaller bandwidth users can also be controlled by changing their front-end filter bandwidth. The effect of front-end filter bandwidth on receiver performance and system capacity is quantified for a variable chipping rate system. Analysis and simulation show that significant performance gains are realized by the periodically time-varying MMSE receivers over their time-invariant counterparts.

High-frequency models for radar backscatter can include components with different structures that correspond to different physical scattering mechanisms on an object. We consider the problem of structure selection for an attributed scattering center model that includes both localized and distributed scattering terms. We propose three structure classification algorithms, and compare their performance. We show that a threshold test on the estimated length parameter performs as well as a GLRT test, but is computationally more efficient. A computationally fast image-based test is shown to perform as well as the GLRT and length-based tests for scattering center lengths greater than twice the crossrange resolution of the measurements.

A Bayesian approach is presented for model-based classification of images with application to synthetic-aperture radar. Posterior probabilities are computed for candidate hypotheses using physical features estimated from sensor data along with features predicted from these hypotheses. The likelihood scoring allows propagation of uncertainty arising in both the sensor data and object models. The Bayesian classification, including the determination of a correspondence between unordered random features, is shown to be tractable, yielding a classification algorithm, a method for estimating error rates, and a tool for evaluating the performance sensitivity. The radar image features used for classification are point locations with an associated vector of physical attributes; the attributed features are adopted from a parametric model of high-frequency radar scattering. With the emergence of wideband sensor technology, these physical features expand interpretation of radar imagery to access the frequency- and aspect-dependent scattering information carried in the image phase.

We consider the problem of estimating a parametric model that describes radar backscattering from synthetic aperture radar imagery. We adopt a scattering center model that incorporates both frequency and aspect dependence of scattering. We develop an approximate maximum likelihood algorithm for parameter estimation directly on regions of the SAR image. The algorithm autonomously selects model order and structure. Results are presented for both synthetic and measured SAR imagery, and algorithm accuracy is compared with the Cramer-Rao bound.

Detection methods for multiple rate direct sequence code division multiple access (DS-CDMA) signalling are addressed. Attention is focused on the development of receivers based on the minimum mean squared error (MMSE). Due to the cyclostationarity of the multirate signal, a representation of the multirate signal in terms of the Fourier basis is possible. This expansion facilitates construction of the MMSE receivers. Both variable spreading gain as well as variable chipping rate DS-CDMA access schemes are considered. For the multiple chipping rate system, the effect of the front-end filter bandwidth on the receiver performance is studied. Simulation results are provided to compare the performance of the proposed receivers.

As multimedia applications proliferate, there is a desire to provide wireless transport to information streams with inherently different data rates. Direct-sequence code division multiple access (DS-CDMA) is a natural multiple-access strategy for multiple data-rate systems. Previous work on multirate DS-CDMA receivers has focused on signal-processing techniques, which detect all users of all rates simultaneously. In the current work, multirate users have multiple bandwidths. Thus, it is proposed to exploit bandwidth differences to achieve frequency-based rate separation followed by single-rate detection schemes. Such a methodology enables a tradeoff between receiver complexity and performance. The performance of the proposed filters and receivers are derived for both a modified matched filter and modified decorrelator employing rate separation. The performance of a multirate CDMA overlay system is evaluated. In addition, chip pulse shaping for wide-band users is developed to improve performance for narrow-band users for the overlay system.

High-frequency radar measurements of man-made targets are dominated by returns from isolated scattering centers, such as corners and flat plates. Characterizing the features of these scattering centers provides a parsimonious, physically relevant signal representation for use in automatic target recognition (ATR). In this paper, we present a framework for feature extraction predicated on parametric models for the radar returns. The models are motivated by the scattering behaviour predicted by the geometrical theory of diffraction. For each scattering center, statistically robust estimation of model parameters provides high-resolution attributes including location, geometry, and polarization response. We present statistical analysis of the scattering model to describe feature uncertainty, and we provide a least-squares algorithm for feature estimation. We survey existing algorithms for simplified models, and derive bounds for the error incurred in adopting the simplified models. A model order selection algorithm is given, and an M-ary generalized likelihood ratio test is given for classifying polarimetric responses in spherically invariant random clutter.

The focus of this paper is a convergence study of the frequency sensitive competitive learning (FSCL) algorithm. We approximate the final phase of FSCL learning by a diffusion process described by the Fokker-Plank equation. Sufficient and necessary conditions are presented for the convergence of the diffusion process to a local equilibrium. The analysis parallels that by Ritter-Schulten (1988) for Kohonen's self-organizing map. We show that the convergence conditions involve only the learning rate and that they are the same as the conditions for weak convergence described previously. Our analysis thus broadens the class of algorithms that have been shown to have these types of convergence characteristics.

The paper considers linear correlation filters used for image pattern recognition. First, the authors develop a statistical theory to predict the classification performance of a general class of correlation filters for wide sense stationary (WSS) clutter. This analysis includes as special cases the synthetic discriminant function (SDF), the minimum variance SDF (MVSDF), and the minimum average correlation energy (MACE) filters. Second, the authors develop a modified filter design applicable to nonzero mean noise; this latter case occurs in many applications where the magnitude image is used for classification. They compare the performance of several filters on synthetic radar imagery.

A new method for estimating two-dimensional (2-D) poles and amplitude coefficients in a Prony model is presented. This method involves two parts, each utilizing a 1-D singular-value-decomposition-based technique, and is capable of locating frequencies anywhere in the 2-D frequency plane. Simulations are shown which demonstrate the performance of the algorithm.>

Features extracted from the bispectrum of radar signals are used for classification of unknown radar targets. The classification performance compared with the performance of other classifiers that are not based on higher-order spectral processing of the measured radar data. The radar signals used are experimental measurements that correspond to scattering from real radar targets. The data is corrupted with different types of disturbances that are likely to occur in a typical radar system. Although the number of data samples is relatively small and may be insufficient to produce very accurate bispectral estimates, it is concluded that the bispectrum classifier may outperform other known classifiers under conditions of colored noise and non-Gaussian noise.>

Expressions are derived for the Cramer-Rao bounds (CRBs) of the parameters of an exponential model with one set of poles and multiple sets of amplitude coefficients. The poles of this model may lie anywhere in the complex plane. The CRB for pole angle is log-symmetric about the unit circle with minimum on the unit circle, while the CRB for pole magnitude has its minimum inside the unit circle for finite-length datasets and is not symmetric. Simulation results show that error-standard-deviation ellipses about poles turn out to be circular. The CRBs for estimates of the amplitude coefficients of real and imaginary parts are also available.>

The following problem is considered: given a polynomial with zeros that do not lie on or inside the unit circle, find the closest polynomial with zeros that are all on or inside the unit circle. The measure of closeness used is the Euclidean distance in coefficient space. The direct formulation of this problem leads to a minimization problem with nonlinear constraints, and direct solution is difficult. The problem is approached by considering a related minimization problem with linear constraints. It is then hypothesized that only a finite number of solutions to the linear problem are candidate solutions to the given nonlinear problem. While a general proof of the hypothesis has not been found, numerical examples indicate that it may hold for a large number of cases.>

The authors consider the following problem: given a normalized (finite-duration) covariance sequence which is not nonnegative definite (NND), find the closest NND sequence to it. Here, closeness is measured by the Euclidean distance in coefficient space. They provide a solution to this problem by considering a set of constrained minimization problems. The solution to the constrained minimization problem does not in general give NND solutions. Properties of NND solutions are established and used to find the minimizing NND sequence.>

A three step method for obtaining nearly maximum likelihood ARMA spectral estimates is presented. The computational complexity of the algorithm is comparable to Yule-Walker methods, but the method gives asymptotically efficient estimates. The implementation of the algorithm is discussed, and numerical examples are presented to illustrate its performance.

This paper presents a fast recursive least squares algorithm for estimating the AR coefficients in an AR or ARMA model. The algorithm is based on solving an overdetermined system of "t" Extended Yule Walker equations for the "p" AR coefficients. Experimental results indicate that the proposed algorithm is able to provide improved estimates over those of similar recursive algorithms, at a computational cost of an additional 2t multiplies and 2t adds.(1)

Recently, a method for generating an ARMA spectral estimator model which possessed super-resolution performance was developed [2]. This method entailed minimizing a weighted quadratic functional of a set of "basic error terms." An issue which remained to be resolved at that time was the selection of the weighting matrix that characterized the functional being minimized. A weighting matrix selection procedure has recently been developed and is herein reported [8]. This procedure has typically yielded an improvement in spectral estimation performance.