In this paper, we explore the joint design of a transmit waveform and receive filter to enhance the detection performance of multiple-input multiple-output (MIMO) radar. Target echoes are assumed to be embedded in signal-dependent interference and colored Gaussian noise. As design metrics, we exploit two information-theoretic criteria, including mutual information (MI) and relative entropy. The joint design problems of MIMO radar associated with different information- theoretic criteria are established as a unified optimization framework within a constant-envelope (CE) constraint. We propose an efficient method based on the Riemannian optimization framework, which transforms the constraint optimization problems into unconstrained problems by leveraging the geometry of the feasible region. Several numerical examples are included to demonstrate the effectiveness of the proposed method.

To maximize the signal-to-interference-plus-noise ratio (SINR) under a constant-envelope constraint, an efficient joint design of the transmit waveform and the receive filter for multipleinput multiple-output (MIMO) radars is essential. In this paper, we propose a novel optimization framework to solve the resultant non-convex problem on a Riemannian product manifold. Based on the Riemannian structure of the formulated manifold, three Riemannian gradient-based methods are proposed to deal with the reformulated problem efficiently. The proposed algorithms provably converge to a local optimum from an arbitrary initialization point. Numerical experiments demonstrate the algorithmic advantages and performance gains of the proposed algorithms.

Dual-function radar-communication (DFRC) system is flexible to be applied in a variety of scenarios. However, it is challenging to implement a low-cost low-complexity DFRC system due to the dynamic cooperation between radar sensing and communication tasks. In this paper, we propose to implement a low-complexity multiple input multiple output DFRC (MIMO-DFRC) system relying on the generalized spatial modulation (GSM) and the low-resolution sampling. To deal with the induced quantization distortion and dynamic antenna allocation, we formulate the radar sensing problem as an atomic norm-based convex problem, which can be solved by off-the-shelf solvers. Simulation results demonstrate that the proposed MIMO-DFRC system can achieve delay and azimuth estimation with accuracy as low as about 10% of the resolution grids while employing 1-bit sampling.

Cognitive radar framework has recently been proposed in radar signal processing to develope algorithms for target detection, tracking, and waveform design in the presence of nonstationary environmental (clutter) characteristics. In this framework, there are the three main steps: sensing the environmental changes, learning the new environmental statistical characteristics, and adapting the radar algorithms to the new characteristics. Here, we focus on the second step of the framework to identify the new clutter characteristics after a change is detected in the environment. We form a dictionary of various clutter distributions and identify the distribution of the new clutter data through matching pursuit using probabilistic similarity and distance measures under sparsity constraints. Specifically, we use inner-product as a similarity measure, and we apply three different L 1 -norm type probabilistic distance measures. We both numerically and analytically analyze their clutter-distribution identification performances and show that Kulczynski is the best distance measure for distribution identification.

In this paper, we present a mathematical and computational framework for comparing and matching distributions in reproducing kernel Hilbert spaces (RKHS). This framework, called optimal transport in RKHS, is a generalization of the optimal transport problem in input spaces to (potentially) infinite-dimensional feature spaces. We provide a computable formulation of Kantorovich's optimal transport in RKHS. In particular, we explore the case in which data distributions in RKHS are Gaussian, obtaining closed-form expressions of both the estimated Wasserstein distance and optimal transport map via kernel matrices. Based on these expressions, we generalize the Bures metric on covariance matrices to infinite-dimensional settings, providing a new metric between covariance operators. Moreover, we extend the correlation alignment problem to Hilbert spaces, giving a new strategy for matching distributions in RKHS. Empirically, we apply the derived formulas under the Gaussianity assumption to image classification and domain adaptation. In both tasks, our algorithms yield state-of-the-art performances, demonstrating the effectiveness and potential of our framework.

In order to maximize the signal-to-interference-plus-noise ratio (SINR) under a constant-envelope (CE) constraint, a fast and efficient joint design of the transmit waveform and the receive filter for colocated multiple-input multiple-output (MIMO) radars is essential. Conventional joint optimization is performed using nonlinear optimization techniques such as the semidefinite relaxation (SDR) algorithm. In this letter, we propose a novel manifold-based alternating optimization (MAO) method, which reformulates the waveform optimization subproblem as an unconstrained optimization problem on a Riemannian manifold. We present the geometrical structure of the feasible region and derive the explicit expressions for the Riemannian gradient and the Riemannian Hessian, thus the reformulated optimization could be solved by using the Riemannian trust-region (RTR) algorithm. Numerical experiments demonstrate that the proposed method has faster convergence with reduced computational cost compared with conventional SDR-based algorithm in Euclidean space.

The low-rank approximation problem has recently attracted wide concern due to its excellent performance in real-world applications such as image restoration, traffic monitoring, and face recognition. Compared with the classic nuclear norm, the Schatten-p norm is stated to be a closer approximation to restrain the singular values for practical applications in the real world. However, Schatten-p norm minimization is a challenging non-convex, non-smooth, and non-Lipschitz problem. In this paper, inspired by the reweighted ℓ1 and ℓ2 norm for compressive sensing, the generalized iterative reweighted nuclear norm (GIRNN) and the generalized iterative reweighted Frobenius norm (GIRFN) algorithms are proposed to approximate Schatten-p norm minimization. By involving the proposed algorithms, the problem becomes more tractable and the closed solutions are derived from the iteratively reweighted subproblems. In addition, we prove that both proposed algorithms converge at a linear rate to a bounded optimum. Numerical experiments for the practical matrix completion (MC), robust principal component analysis (RPCA), and image decomposition problems are illustrated to validate the superior performance of both algorithms over some common state-of-the-art methods.

Graph matching plays a central role in such fields as computer vision, pattern recognition, and bioinformatics. Graph matching problems can be cast as two types of quadratic assignment problems (QAPs): Koopmans-Beckmann's QAP or Lawler's QAP. In our paper, we provide a unifying view for these two problems by introducing new rules for array operations in Hilbert spaces. Consequently, Lawler's QAP can be considered as the Koopmans-Beckmann's alignment between two arrays in reproducing kernel Hilbert spaces (RKHS), making it possible to efficiently solve the problem without computing a huge affinity matrix. Furthermore, we develop the entropy-regularized Frank-Wolfe (EnFW) algorithm for optimizing QAPs, which has the same convergence rate as the original FW algorithm while dramatically reducing the computational burden for each outer iteration. We conduct extensive experiments to evaluate our approach, and show that our algorithm significantly outperforms the state-of-the-art in both matching accuracy and scalability.

Sparse linear arrays, such as nested and co-prime arrays, are capable of resolving O(M2) sources using only O(M) sensors by exploiting their so-called difference coarray model. One popular approach to exploit the difference coarray model is to construct an augmented covariance matrix from the sample covariance matrix. By applying common direction-of-arrival (DOA) estimation algorithms to this augmented covariance matrix, more sources than the number of sensors can be identified. In this letter, inspired by the optimal transport theory, we develop a new approach to construct this augmented covariance matrix. We formulate a structured covariance estimation problem that minimizes the Bures-Wasserstein distance between the sample covariance matrix and the subsampled augmented covariance matrix, which can be either casted to a semi-definite programming problem, or directly solved using gradient-based methods. Our approach contributes to a new grid-less DOA estimation algorithm for sparse linear arrays. Numerical examples show that our approach achieves state-of-art estimation performance.

A synthetic aperture radar (SAR) system is severely affected by radio frequency systems, such as TV and cellular networks. Previous studies showed that narrowband radio frequency interference (RFI) is low rank and used the nuclear norm as a low-rank regularization to extract the RFI from the received signal. However, the nuclear norm is not an appropriate approximation of the true rank function. Hence, in this paper, the reweighted matrix-factorization (RMF) algorithm and the matrix-factorization decomposition (MFD) algorithm are proposed to suppress narrowband RFI for SAR systems, where the RMF algorithm uses the reweighted scheme to approximate the rank function, while the MFD algorithm restrains the upper bound of the rank as a prior condition. Moreover, the introduction of the MF scheme dramatically decreases the computational complexity and efficiently suppresses RFI. In addition, we further show that the sparse regularization of the useful signal (i.e., the useful SAR echo) not only protects the strong scatterers of the useful signal but also avoids low-rank overfitting. We employ the real SAR signals of both the sparse scene and the nonsparse scene with the measured RFI to verify the effectiveness of the proposed methods, and the proposed methods outperform the other methods for RFI suppression.

Synthetic aperture radar (SAR), as a wideband radar system, is subject to interference by radio frequency systems, such as radio, TV, and cellular networks. Since the narrowband radio frequency interference (RFI) has a stable frequency in a snapshot sequence, it has a low-rank property that can be used to substract RFI from the received signal. The nuclear norm is a common convex relaxation to constrain the rank, but it is optimized by the singular value thresholding (SVT) algorithm, which uses a single threshold to treat all singular values and greatly over-punishes large singular values. Hence, in this paper, we propose two methods, the reweighted nuclear norm (RNN) algorithm and the reweighted Frobenius norm (RFN) algorithm, to separate the RFI and the useful signal. The RNN and RFN minimization problems are the approximations of the real rank function, which can protect large singular values and restrict the rank. As a result, the RFI is accurately extracted and the useful signal is successfully protected. Also, we strictly derive the closed-form solutions of the RNN and RFN minimization problems for complex radar signals, and we also employ downsampling to extract the mainband of the signal spectrum to speed up the convergence. Real SAR data is applied to demonstrate the effectiveness of the proposed methods for RFI suppression.

Radio-frequency systems, such as TV and cellular networks, severely interfere with synthetic aperture radar (SAR) systems. Narrowband radio-frequency interference (RFI) has a special low-rank property in the received signal matrix, because it performs like a sinusoid with nearly invariant frequency as the slow time proceeds. Exploiting this special property, in this paper, we divide the received signal matrix into several small matrices, in each of which the RFI is also low rank. Without losing the connection between these small matrices, we stack them into a three-mode tensor to separate the low-rank RFI tensor and recover the informative signal tensor. Previous studies employed the nuclear norm to regularize the low-rank RFI, which is not a good choice. Hence, we propose two reweighted algorithms, the reweighted tensor nuclear norm (RTNN) and the reweighted tensor Frobenius norm (RTFN) algorithms, to approximate the rank function in a tensor and accurately extract the low-rank RFI tensor from the received signal tensor. As a result, the introduction of the tensor structure dramatically decreases the computational cost. Furthermore, the reweighted scheme helps suppressing the RFI and recovering the useful signal with excellent performance. Finally, real SAR data with measured RFI is employed to demonstrate the effectiveness of the proposed methods for RFI mitigation.

Nowadays, in the electromagnetism environment, the complex interferences, including the narrowband interferences (NBIs) and wideband interferences (WBIs), may severely affect the imaging quality of synthetic aperture radar (SAR) systems. Most traditional methods can only tackle with one kind of isolated interferences, NBIs or WBIs, which are widely distributed in the 1-D range frequency domain or 2-D range time-frequency domain. In this paper, we propose a complex tensor robust principal component analysis (CT-RPCA) method based on a novel 3-D range-azimuth-space tensor model to mitigate continuously distributed NBIs and WBIs simultaneously. The main contributions of this paper are summarized in three aspects. First, we strictly prove the low-rank property of the isolated NBIs and WBIs in the range-azimuth domain. Second, we use multiple views of the signal to construct a novel 3-D range-azimuth-space tensor model, where both the NBI tensor and the WBI tensor have spatial low-rank property due to the approximately stable frequency bands along the spatial dimension. Third, the CT-RPCA method is employed to efficiently suppress NBIs and WBIs simultaneously by solving the tensor RPCA problem. Finally, the real SAR data with simulated complex interferences are employed to demonstrate the effectiveness of the proposed method.

Domain shift, which occurs when there is a mismatch between the distributions of training (source) and testing (target) datasets, usually results in poor performance of the trained model on the target domain. Existing algorithms typically solve this issue by reducing the distribution discrepancy in the input spaces. However, for kernel-based learning machines, performance highly depends on the statistical properties of data in reproducing kernel Hilbert spaces (RKHS). Motivated by these considerations, we propose a novel strategy for matching distributions in RKHS, which is done by aligning the RKHS covariance matrices (descriptors) across domains. This strategy is a generalization of the correlation alignment problem in Euclidean spaces to (potentially) infinite-dimensional feature spaces. In this paper, we provide two alignment approaches, for both of which we obtain closed-form expressions via kernel matrices. Furthermore, our approaches are scalable to large datasets since they can naturally handle out-of-sample instances. We conduct extensive experiments (248 domain adaptation tasks) to evaluate our approaches. Experiment results show that our approaches outperform other state-of-the-art methods in both accuracy and computationally efficiency.

Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph kernels, based on return probabilities of random walks. The advantages of our proposed kernels are that they can effectively exploit various node attributes, while being scalable to large datasets. We conduct extensive graph classification experiments to evaluate our graph kernels. The experimental results show that our graph kernels significantly outperform other state-of-the-art approaches in both accuracy and computational efficiency.

In recent years, many researchers have focused on the automatic target recognition problem for high-resolution synthetic aperture radar (SAR) systems. Most have directly employed the training data as the dictionary, which introduces error from speckle noise. In this letter, a joint low-rank and sparse multiview denoising (JLSMD) dictionary is generated, which combines multiview training samples for denoising. To extract the dictionary, we fully consider the low-rank property of multiview target images and the sparsity of speckle noise for SAR systems. The designed dictionary is more accurate than the training data in representing the target. With the help of the proposed JLSMD dictionary, we develop three algorithms based on the sparse representation classification and the support vector machine approach. We carry out experiments on the moving and stationary target acquisition and recognition public data set to evaluate the excellent performance of the proposed methods against several state-of-the-art methods, including deep learning methods.

Decision making and the social processes that influence it are of great importance to many problems. The ways people make decisions can determine whether a new technology is successful, whether resources are allocated optimality, or how society responds to a crisis. In this paper, we propose a model for how these decisions can be influenced using modern information technology and social networks. Specifically, we study the use of artificial social networks to make influential users that are desirable to society as a whole. In real life, this would be achieved by the publication of “best users” by the authority behind the artificial network. Graphically, this creates a set of temporary edges from those users to other users. We first develop a general model for an abstract, general case. We then apply it to a specific case study in a smart grid. Our results suggest that the proposed methodology has the potential to move the equilibrium of a system to a more desirable state and that the degree of the improvement, as well as other, graph-theoretic characteristics, depends on the mathematics of the decision being made.

Sparse linear arrays, such as co-prime and nested arrays, can identify up to O(M2) sources with only O(M) sensors by using co-array based MUSIC. We conduct analytical performance analysis of two coarray based MUSIC algorithms, namely the direct augmentation based MUSIC, and the spatial smoothing based MUSIC. In addition, we analyze the Cramér-Rao bound for sparse linear arrays, and show that for co-prime and nested arrays, it can decrease at a rate of O(M-5) as the number of sensors M goes to infinity, in contrast to O(M-3) in the ULA case. We use numerical examples to demonstrate our analytical results.

We investigate the problem of direction of arrival (DOA) estimation using sparse linear arrays, such as co-prime and nested arrays, in the case of missing data resulting from sensor failures. We introduce a signal model where sensor failures occur after taking certain number of snapshots. We formulate a structured covariance estimation problem by exploiting the special geometry of sparse linear arrays, which also provides enhanced degrees of freedom. Numerical examples show that, by utilizing the information in both complete measurements and incomplete measurements, our method achieves better estimation accuracy than the traditional method using only complete measurements.

In this paper, we provide a novel regression algorithm based on a Gaussian random field (GRF) indexed by a Riemannian manifold (M, g). We utilize both the labeled and unlabeled data sets to exploit the geometric structure of M. We use the recovered heat (H) kernel as the covariance function for the GRF (HGRF). We propose a Monte Carlo integral theorem on Riemannian manifolds and derive the corresponding convergence rate and approximation error. Based on this theorem, we correctly normalize the recovered eigenvector to make it compatible with Riemannian measure. More importantly, we prove that the HGRF is intrinsic to the original data manifold by comparing the pullback geometry and the original geoemtry of M. Essentially it is a semi-supervised learning method, which means the unlabeled data can be utilized to help identify the geometry structure of the unknown manifold M.

Multiple scattering effects are commonly ignored in the detection and estimation of scatterers in signal processing research, because the energy of the first-order scattering is much larger than that of higher-order components. Although multiple scattering can significantly increase the estimation precision of point scatterers, it does not always lead to an improvement. Identifying conditions under which multiple scattering is beneficial or detrimental to estimation in a general setup is still an open problem. In this paper, we consider the effects of multiple scattering on the localization of two point scatterers. By comparing the Fisher information matrix on location parameters when multiple scattering exists and does not exist, we show analytically that information on ranges can benefit estimating directions of arrival via multiple scattering when the two scatterers are in far-field and well resolved.

Most existing radar algorithms are developed under the assumption that the environment (clutter) is stationary. However, in practice, the characteristics of the clutter can vary enormously depending on the radar-operational scenarios. If unaccounted for, these nonstationary variabilities may drastically hinder the radar performance. Therefore, to overcome such shortcomings, we develop a data-driven method for target detection in nonstationary environments. In this method, the radar dynamically detects changes in the environment and adapts to these changes by learning the new statistical characteristics of the environment and by intelligibly updating its statistical detection algorithm. Specifically, we employ drift detection algorithms to detect changes in the environment; incremental learning, particularly learning under concept drift algorithms, to learn the new statistical characteristics of the environment from the new radar data that become available in batches over a period of time. The newly learned environment characteristics are then integrated in the detection algorithm. We use Monte Carlo simulations to demonstrate that the developed method provides a significant improvement in the detection performance compared with detection techniques that are not aware of the environmental changes.

We consider the problem of using linear nested arrays to estimate the directions of arrival (DOAs) of distributed sources and to detect the source number, where we have more sources than actual physical sensors. Angular spread, caused by the multipath nature of the distributed sources, makes the commonly used point-source assumption challenging. We establish the signal model for distributed sources, using a nested array. Due to the characteristics of distributed sources, the regular spatial smoothing technique, which is used to exploit the increased degrees of freedom provided by the co-array, no longer works. We thus propose a novel spatial smoothing approach to circumvent this problem. Based on the analytical results, we construct the corresponding DOA estimation and source number detection methods. The effectiveness of the proposed methods is verified through numerical examples.

In this letter, we consider the problem of direction of arrival estimation using sparsity enforced reconstruction methods. Co-prime arrays with$M + N$sensors are utilized to increase the degrees of the freedom from$O(M + N)$to$O(MN)$. The key to the success of sparse-based direction of arrival estimation is that every target must fall on the predefined grid. Off-grid targets can highly jeopardize the reconstruction performance. In this letter, we use joint sparsity reconstruction methods to explore the underlying structure between the sparse signal and the gird mismatch. Two types of sparse reconstruction methods, the greedy method and the convex relaxation method, are considered. By implementing numerical experiments, we demonstrate that our proposed methods can fully utilize the virtual aperture created by co-prime arrays and also outperform the previously proposed MUSIC method with spatial smoothing.

Many practical applications require solving an optimization over large and high-dimensional data sets, which makes these problems hard to solve and prohibitively time consuming. In this paper, we propose a parallel distributed algorithm that uses an adaptive regularizer (PDAR) to solve a joint optimization problem with separable constraints. The regularizer is adaptive and depends on the step size between iterations and the iteration number. We show theoretical convergence of our algorithm to an optimal solution, and use a multi-agent three-bin resource allocation example to illustrate the effectiveness of the proposed algorithm. Numerical simulations show that our algorithm converges to the same optimal solution as other distributed methods, with significantly reduced computational time.

In this paper we propose a sparse model to accurately estimate target locations in a distributed multiple-input multiple-output (MIMO) radar system with phase mismatches at transmitters and receivers. We formulate the localization problem based on maximum a posteriori (MAP) estimation. To reduce the effect of phase mismatches we develop a novel alternating minimization approach based on sparse signal recovery and structured matrix perturbation. Using numerical simulations, we show that our algorithms significantly improve the performance of the distributed MIMO radar system.

Based on a recently proposed linear nested array, we consider the problem of source number detection and direction of arrival estimation for wideband Gaussian sources. This array provides O(N2) degrees of freedom with O(N) sensors, enabling us to estimate K sources with N <; K sensors. To employ the nested array for the wideband case, we propose effective strategies to apply nested-array processing to each frequency component, and combine all the spectral information of various frequencies to conduct the detection and estimation. In particular, for source detection, we propose a novel approach employing the idea of ensemble, used in machine learning and statistics. Numerical simulations demonstrate the advantages of our strategies.

We exploit the sparseness of induced currents on the surfaces of obscured perfectly conducting (PEC) scatterers in developing a single-frequency imaging algorithm in 2-D space. We model the induced currents on the targets by a set of unknown filament currents to which we apply the surface-equivalence theorem. We use$l_{1}$regularization to promote the solutions with a small number of equivalent sources placed in the vicinity of scatterer surfaces. The restored equivalent sources accurately determine the illuminated portions of the scatterer contours. We compare the performance of the algorithm with that of linear sampling (LSM) and MUSIC. We verify the proposed algorithm on the equivalent 3-D experimental model.

We propose a unified framework for jointly solving the problems of sensor selection (SS), resource allocation (RA) and data fusion (DF) in multi-modal sensor networks. Our framework is inspired by the trading behavior in commercial markets. We develop an iterative double-auction mechanism for computing the equilibrium of the market. The equilibrium point corresponds to the joint solution of SS, RA, DF problems. To illustrate the framework, we consider a scenario where the objective is to track an unknown variable number of moving targets of different categories, using a sensor network comprising of a multistatic radar, infrared camera, and a human scout. Numerical examples demonstrate the effectiveness of the proposed method.

Typical user demands of electricity vary throughout the day, which increases the cost to utility companies and decreases the stability of the power system. Time-of-use (TOU) pricing has been proposed as a demand-side management (DSM) method to influence user demands. In this paper, we describe a new approach of optimal TOU pricing strategy based on game theory (GT-TOU). We propose models for costs due to the fluctuating user demands to the utility companies, as well as the user satisfaction measurement because of the difference between the demand and actual load. We design utility functions for the company and the user, and obtain the Nash equilibrium using backward induction and iterative methods. Numerical example shows that our method is effective in leveling the user demand by setting optimal TOU prices, in potentially increasing the profit of the utility companies and ensuring overall user benefit.

We consider the problem of wide-band direction-of-arrival (DOA) estimation of hydroacoustic signals from marine vessels, which contain both random and sinusoidal components. We generalize the existing narrow-band maximum likelihood estimator to the wide-band case for DOA estimation of such signals. Our analytical comparison and numerical example show that the derived estimator provides better performance than the typical stochastic estimator.

The stability of low-rank matrix reconstruction with respect to noise is investigated in this paper. The$\ell _{\ast}$-constrained minimal singular value ($\ell _{\ast}$-CMSV) of the measurement operator is shown to determine the recovery performance of nuclear norm minimization-based algorithms. Compared with the stability results using the matrix restricted isometry constant, the performance bounds established using$\ell _{\ast}$-CMSV are more concise, and their derivations are less complex. Isotropic and subgaussian measurement operators are shown to have$\ell _{\ast}$-CMSVs bounded away from zero with high probability, as long as the number of measurements is relatively large. The$\ell _{\ast}$-CMSV for correlated Gaussian operators are also analyzed and used to illustrate the advantage of$\ell _{\ast}$-CMSV compared with the matrix restricted isometry constant. We also provide a fixed point characterization of$\ell _{\ast}$-CMSV that is potentially useful for its computation.

Passive sonar arrays are often used to find submerged vessels by measuring their radiated signal. Acoustic vector-sensor (AVS) arrays, which are normally towed by the ship at the ends of long cables, have been proven to be very effective for target direction of arrival (DOA) estimation. The flow noise, arising from the flow of water over the vector-sensor or its housing when the array is towed, is often a major source of interference to the towed array as it is usually directly coupled to the array sensing elements. In this paper, we obtain a closed-form expression for the spatial correlations of all the components of an AVS array in a flow-noise field. We apply the noise correlation model to DOA estimation using a uniform linear AVS array beamforming. The flow-noise impact on the beamforming capabilities is evaluated via numerical simulations.

Modern day light emitting diodes (LEDs) are capable of producing high intensity light across a wide spread of frequencies. Hence, they are becoming a common ingredient in many lighting systems. In order to obtain desired lighting effects efficiently, it is important to sense the light received across different target locations and estimate the unknown properties (amplitudes, frequency offsets and phases) of the modulating signals. This facilitates the design of the driving waveforms for the LEDs. This procedure is known as illumination sensing and it enables efficient and effective usage of light energy to achieve the intended effects. We propose a novel two step approach to perform this estimation using sparse modeling which exploits the fact that the measurements at the sensors are sparse in the frequency offset space and the phase space. Further, we employ compressive sensing to reduce the dimensions of the measurement vector, thereby reducing the complexity of the estimation algorithm. This will enable quick estimation which is essential to avoid any lag in attaining the desired illumination effects. Also, we demonstrate the performance of the proposed approach in the presence of a modeling mismatch.

We consider the problem of target detection for coherent multi-input multi-output (MIMO) radar with widely separated antennas in the presence of phase synchronization mismatch between the transmitter and receiver pairs. First, we introduce a data model using von-Mises distribution to represent the phase error terms. Then we employ expectation-maximization algorithm to estimate the error distribution parameter and target returns as well as the noise variance. We develop a generalized likelihood ratio test (GLRT) target detector using these estimates and demonstrate the effect of phase uncertainties on the detection performance using Monte Carlo simulations.

We propose a method to detect a target in the presence of multipath reflections, employing sequential transmission of multiple frequencies in a slow-time (pulse-to-pulse) approach. First, we develop a parametric measurement model that accounts for the multipath components at multiple frequencies as well as Doppler shifts. Then, we develop a statistical detection test and analytically evaluate its performance characteristics. Based on the performance analysis, we propose an adaptive algorithm to select the best combination from a subset of frequencies that maximizes the detection performance. Our numerical examples show that the sequential approach requires more coherent pulses to match the performance of the simultaneous usage of multiple carriers in OFDM format. We also study the extent of performance degradation due to employing a subset of available frequencies.

We analyze the performance of a direction-of-arrival (DOA) estimation scheme based on overcomplete signal representation in this paper. We formulate the problem as a support recovery problem with joint sparsity constraints and analyze it in a hypothesis testing framework. We derive both upper and lower bounds on the probability of error by using Chernoff bound and Fano's inequality, respectively. The lower bound implies that the minimal number of samples necessary for accurate DOA estimation is proportional to the logarithm of the discretization level for arbitrary isotropic sensor arrays. We apply the upper bound to study the effect of noise. For uniform linear array (ULA) with only one source, the upper bound exponent indicates that the optimal overcomplete representation is achieved by uniform partition of the wave number space instead of the DOA space.

The performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space is analyzed. Support recovery is formulated as a multiple-hypothesis testing problem. Both upper and lower bounds on the probability of error are derived for general measurement matrices, by using the Chernoff bound and Fano's inequality, respectively. The upper bound shows that the performance is determined by a quantity measuring the measurement matrix incoherence, while the lower bound reveals the importance of the total measurement gain. The lower bound is applied to derive the minimal number of samples needed for accurate direction-of-arrival (DOA) estimation for a sparse representation based algorithm. When applied to Gaussian measurement ensembles, these bounds give necessary and sufficient conditions for a vanishing probability of error for majority realizations of the measurement matrix. Our results offer surprising insights into sparse signal recovery. For example, as far as support recovery is concerned, the well-known bound in Compressive Sensing with the Gaussian measurement matrix is generally not sufficient unless the noise level is low. Our study provides an alternative performance measure, one that is natural and important in practice, for signal recovery in Compressive Sensing and other application areas exploiting signal sparsity.

We address the problem of detecting a target moving in clutter environment using an orthogonal frequency division multiplexing (OFDM) radar. The broadband OFDM signal provides frequency diversity to improve the performance of the system. First, we develop a parametric model that accounts for the measurements at multiple frequencies including the Doppler shift. Then, we present a statistical detection test and evaluate its performance characteristics. Based on this, we propose an algorithm to adaptively design the parameters for the next transmitting waveform. Numerical examples illustrate our analytical results, demonstrating the achieved performance improvement due to the OFDM signaling method and adaptive waveform design.

We analyze the performance of a sensor system based on the head-related transfer function (HRTF) modeling of human hearing, in finding the direction of a source in 3-D space. Thus, this system has only two sensors with a few nearby reflectors. First, we present a parametric measurement model that incorporates the diffractions associated with the head shape and the multipath reflections related to the external ear (pinna). Then, we compute the asymptotic Cramer-Rao bound on the 3-D direction estimate for a stochastic source signal of unknown parametrized spectrum. We provide a few numerical examples to illustrate our analytical results.

Simulation, detection and estimation of the spread of a biochemical substance are key elements in environmental monitoring. Solving these problems are important for efficient decontamination purposes and prediction of the cloud evolution. We present a set of tools describing the measurements of an array of biochemical sensors through a physical dispersion model, which is amenable to statistical analysis. We first approximate the dispersion model of a contaminant in a realistic environment (for instance urban) through numerical simulations of reflected stochastic diffusions describing the microscopic transport phenomena due to wind and chemical diffusion using the Feynmann-Kac formula. Second, we propose a Bayesian framework based on a random field for localizing multiple dispersive sources with small amounts of measurements. Third, we present a sequential detector allowing on-line analysis and detecting whether a change has occurred, based on realistic numerical simulation. Numerical examples illustrate our results for a dispersion among buildings.

Controlling the polarization information in transmitted waveforms enables improving the performance of radar systems. We consider the design of optimal polarization for the estimation of target scattering embedded in heavy clutter. The goal is to minimize the mean squared error of the scattering estimation subject to an average radar pulse power constraint. We show that such a problem is equivalent to the optimal design of a radar sensing matrix that contains the polarization information. We formulate the optimal design as a nonlinear optimization problem which can be recast it in a convex form and is thus efficiently solvable by semi-definite programming (SDP). We compare the sensing performance of the optimally selected polarization over the conventional approaches. Our numerical results indicate that a significant amount of power gain is achieved in the target scattering estimation through such an optimal design.

In this paper we describe the optimization of an information theoretic criterion for radar waveform design. The method is used to design radar waveforms suitable for simultaneously estimating and tracking parameters of multiple targets. Our approach generalizes the information theoretic water-filling approach of Bell. The paper has two main contributions. First, a new information theoretic design criterion for designing multiple waveforms under a joint power constraint when beamforming is used both at transmitter and receiver. Then we provide a highly efficient algorithm for optimizing the transmitted waveforms, by approximating the information theoretic cost function. We show that using Lagrange relaxation the optimization problem can be decoupled into a parallel set of low-dimensional search problems at each frequency, with dimension defined by the number of targets instead of the number of frequency bands used.

We develop an adaptive waveform design method for target tracking. In our method, at each time step, we optimally select the parameters, including the polarization of the transmitted signal waveform to improve the tracking accuracy. An array of electromagnetic vector sensors is employed to fully recover the polarimetric information from the reflected signals. We derive our approach under a framework of sequential Bayesian filtering. We apply a sequential Monte Carlo method to manipulate the nonlinear and non-Gaussian state and measurement models. We design a criterion for the waveform optimization based on a posterior Cramer-Rao bound.

This paper addresses the problem of estimating the shape parameters of seismic wavefields in linear array for the separation of waves by exploiting the diversity of the polarization state and propagation velocity between wavefields. We propose a method based on the shift-invariance properties of multiple wavefields impinging on a uniform linear array of sensors to separate different waves, by jointly estimating the velocity and polarization parameters. Furthermore, the surface waves are removed using a spatial filter specifically designed to exploit velocity and polarization of different waves. We introduce a model for wideband polarized signals received by an array of three-components sensors used as a framework for implementing the proposed algorithms. Examples on simulated and experimental data illustrate the applicability of the proposed methods

We develop optimal design methods of polarimetric radar signals that improve the estimation accuracy of the target parameters. A weighted sum of the Cramer-Rao bound (CRB) of the parameters of interest is used as the cost function of the optimization. We employ an array of electromagnetic vector sensors to fully recover the polarization information from the target returns. Simulation examples illustrate the improved system performance

The resolution improvements of time reversal methods through exploiting nonhomogeneous media have attracted much interest recently with broad applications, including the destruction of kidney stones, underwater acoustics, radar, detection of defects in metals, communications, and mine detection. In this paper, we analyze the effect of inhomogeneity generated by multiple scattering among point scatterers under a multistatic sensing setup. We derive the Cramér-Rao bounds (CRBs) on parameters of the scatterers and compare the CRBs for multiple scattering using the Foldy-Lax model with the reference case without multiple scattering using the Born approximation. We find that multiple scattering could significantly improve the estimation performance of the system. For the case where multiple scattering is not possible, e.g., where only a single target scatterer exists in the illuminated scenario, we propose the use of artificial scatterers, which could effectively improve the estimation performance of the target despite a decrease in the degrees of freedom of the estimation problem due to the introduced unknown parameters of the artificial scatterers. Numerical examples demonstrate the advantage of the artificial scatterer.

We develop an efficient distributed sequential Bayesian estimation method to localize a diffusive source in wireless sensor networks. Potential applications include security, environmental monitoring, pollution control, and explosives detection. We first derive the physical model of the substance dispersion by solving the diffusion equations under different environmental scenarios. We then integrate the derived dispersion models into the distributed processing technologies, and propose a distributed sequential Bayesian localization technique, in which the state belief is transmitted in the wireless sensor networks and updated using the measurements from the new sensor node. In order to decrease the required communication burden we propose two parameterizable belief approximations: a Gaussian approximation and a new linear combination of polynomial Gaussian approximation. We also apply the idea of information-driven sensor scheduling and select the next sensor node according to certain criterions to reduce the response time and save energy consumption of the sensor network.

We treat the problem of beamforming for signal estimation in the presence of steering vector uncertainties, where the goal is to estimate a signal amplitude from a set of array observations. Conventional beamforming methods typically aim at maximizing the signal-to-interference-plus-noise ratio (SINR). Recently, a maximum likelihood (ML) approach was introduced that leads to an iterative beamformer. Here we suggest an expected least-squares (LS) strategy that results in a simple linear beamformer. We then demonstrate through simulations that the LS beamformer often performs similarly to the ML method in terms of mean-squared error and outperforms conventional SINR-based approaches.

Burst-mode receivers are key components of optical transmission systems, including passive optical networks, and have received much attention in recent years. We present new, efficient methods for burst optical signal detection in burst-mode data transmission using a modified K-means clustering technique. We also develop a data-aided feedforward symbol-timing recovery method based on a polynomial interpolation and maximum-likelihood estimation theory. A performance criterion considering the error caused by the interpolation approximation is derived for this method. The proposed detection and timing recovery approaches can be implemented effectively and rapidly; therefore, they are very suitable for burst-mode receivers. We also provide some numerical examples to demonstrate the performance of the proposed methods.

We develop a semi-deterministic semi-stochastic channel model for the multiple-input multiple-output (MIMO) system under the macrocell environment with local-to-mobile and local-to-base scatterers. We show that employing closely-spaced antennas (e.g., phased array) at the base station is capable of achieving diversity via the local-to-base scatterers, which avoids impractical large aperture requirement for the spatial diversity at the base station. We evaluate the system performance in terms of ergodic capacity, average pairwise error probability (PEP), and signal-to-noise ratio (SNR); derive closed-form expressions for lower and upper bounds on the capacity and PEP; and show that the capacity, multiplexing and diversity gains are limited by the number of multipaths around the base station. The base-station array affects the lower bound on the capacity and the upper bound on the error probability through the same metric; thus, optimal design of the base station array based on this metric will optimize the two different information theoretic measures simultaneously. The fading correlation matrix also appears in the two bounds in the same form. To improve the performance of the macrocell MIMO system, we propose using artificial scatterers and discuss optimal design issues. Numerical examples demonstrate the accuracy of our analytical results and tightness of performance bounds.

We develop algorithms for biochemical detection and estimation in arbitrary two-dimensional (2D) environments using integrated sensor arrays. The development of biochemical sensor techniques has been a subject of considerable research interest in recent years. We propose statistical algorithms for automatic monitoring of biochemical agents in realistically shaped 2D environments using multi-sensor measurements. We derive models for the concentration distribution using the diffusion equation and finite element approximations. Using these results, we develop parametric statistical models and a maximum likelihood estimation algorithm to find the parameters of the biochemical agent. To detect the presence of a source, we develop a generalized likelihood ratio test. We demonstrate the applicability of our techniques through numerical examples. Our results are potentially useful for national security, environmental engineering, food industry, oil industry, etc.

We compute Crame/spl acute/r-Rao bounds (CRBs) for the target and compound-Gaussian clutter parameters using radar array measurements. In particular, we compute CRBs for (i) complex target amplitudes, (ii) the spatial covariance matrix of the speckle component, (iii) texture distribution parameters. We first derive general CRB expressions under an arbitrary texture model and simplify them for gamma and inverse gamma texture distributions. We use the generalized Gauss-Laguerre quadrature to compute the CRBs for gamma texture, whereas the CRBs for inverse-gamma texture do not require numerical integration. We use numerical simulations to validate our results.

Although a vast number of publications have appeared on image registration, performance analysis is usually performed visually and little attention has been given to statistical performance bounds. Such bounds can be useful in evaluating image registration techniques, determining parameter regions where more successful registration is possible, and choosing features to be used for the registration. We derive Cramer-Rao bounds for a wide variety of geometric deformation models including translation, rotation, shearing, rigid, more general affine and non-linear transformations, and for intensity distortion and geometric deformation simultaneously. Numerical examples for illustrating the analytical performance bounds are presented.

The paper proposes several improvements on the Direction of Gradient (DOG) algorithm proposed in [1] for detecting and localizing a biochemical source with moving sensors. In particular, we show that the DOG algorithm can be turned into a distributed control scheme for a mobile sensing network, and that the maximum likelihood estimation proposed in the original algorithm can be replaced with more computationally efficient numerical procedures. Simulations on a single sensor and on a group of mobile sensors are provided that show that the proposed modifications simplify the original algorithm and improve its performance.

We develop a semi-deterministic semi-stochastic channel model for a multiple-input multiple-output (MIMO) system under the macrocell environment with local-to-mobile and local-to-base scatterers, and show that the channel capacity, multiplexing gain and diversity gain are multipath limited in the sense that they are limited by the number of multipaths around the base station. We derive a lower bound on the ergodic capacity and an upper bound on the average pairwise error detection probability. It is shown that the base-station array affects the two different information theoretic measures through the same metric, and the fading correlation matrix also appears in the two bounds with the same form. Numerical examples show the tightness of the two bounds.

Burst mode receivers are key components of optical transmission systems and have received much attention in recent years. We present new efficient methods for burst optical signal detection and blind channel estimation in burst-mode data transmission based on a modified K-means clustering technique. A data-aided feedforward symbol timing recovery method is also developed, based on polynomial interpolation and maximum likelihood estimation theory. It can be implemented rapidly and efficiently; therefore, it is suitable for burst mode receivers. A performance criterion of this method has also been derived. We also give some numerical examples to demonstrate the performance of the proposed methods.

We have recently proposed a frequency-domain channel estimation algorithm for a single-user orthogonal frequency division multiplexing (OFDM) wireless system in the presence of synchronous interference. However, the interference cyclic prefix does not usually align with the desired user's cyclic prefix (i.e., the interferer is asynchronous) and thus a different approach is required. For an asynchronous interferer in a rich multipath environment, the received frequency-domain measurement is correlated in space with a full-rank covariance matrix on each subcarrier. Therefore, the synchronous algorithms may give poor detection performance since they assume reduced rank interference and use a smaller number of parameters. We overcome these problems by employing an appropriately structured model with a properly defined number of covariance parameters. We estimate the interference covariance parameters using a residual method of moments (RMM) estimator and the mean (i.e., the desired user's channel) parameters by maximum likelihood (ML) estimation. Since the RMM estimates are invariant to the mean, we obtain simple non-iterative estimates of the covariance parameters while having optimal statistical efficiency. Numerical results illustrate the applicability of the proposed algorithm.

We develop parametric modeling and estimation methods for STAP data based on the results of the 2-D Wold-like decomposition. It is shown that the same parametric model that results from the 2-D Wold-like orthogonal decomposition naturally arises as the physical model in the problem of space-time processing of airborne radar data. This correspondence is exploited to derive a computationally efficient parametric partially adaptive detection algorithm. We prove that it is sufficient to estimate only the spectral support parameters of each interference component in order to obtain a projection matrix onto the subspace orthogonal to the interference subspace. The proposed partially adaptive parametric processing algorithm employs this property. The proposed parametric interference mitigation procedure can be applied when only the information in a single range gate is available, thus achieving high performance gain when the data in the different range gates cannot be assumed stationary.

We propose finite-length multi-input multi-output adaptive equalization methods for "smart" antenna arrays using the statistical theory of canonical correlations. We show that the proposed methods are related to maximum likelihood reduced-rank channel and noise estimation algorithms in unknown spatially correlated noise, and to several recently proposed adaptive equalization schemes.

The performance breakdown of subspace-based parameter estimation methods can be naturally related to a switch of vectors between the estimated signal and noise subspaces (a "subspace swap"). We derive a lower bound for the probability of such an occurrence and use it to obtain a simple data-based indicator of whether or not the probability of a performance breakdown is significant. We also present a conceptually simple technique to determine from the data whether or not a subspace swap has actually occurred, and to extend the range of SNR values or data samples in which a given subspace method produces accurate estimates.

We present an algorithm for estimating active and passive mechanical properties of the heart using magnetic resonance imaging (MRI) tissue-tagging and blood pressure measurements. We combine physical modeling with a finite-element formulation and dynamic analysis, and apply non-linear optimization to estimate the unknown parameters. We assume that the myocardium's stiffness tensor is anisotropic and non-homogeneous.

We derive Cramer-Rao bounds (CRBs) on the errors of estimating the parameters (location and moment) of a current dipole source using data from electro-encephalography (EEG), magneto-encephalography (MEG), or the combined EEG/MEG modality. We use a realistic head model based on knowledge of surfaces separating tissues of different conductivities, obtained from magnetic resonance (MR) or computer tomography (CT) imaging systems. The electric potentials and magnetic field components at the respective sensors are functions of the source parameters through integral equations. These potentials and field are computed using the boundary or the finite element method (BEM or FEM), with a weighted residuals technique. We present a unified framework for the measurements computed by these methods that enables the derivation of the bounds. The resulting bounds may be used, for instance, to choose the best configuration of the sensors for a given patient and region of expected source location. Numerical results are used to demonstrate an application for shelving expected accuracies in estimating the source parameters as a function of its position in the brain, based on real EEG/MEG system and MR or CT images. The results include contours of equal precision in the estimation and surfaces showing the size of the 90% confidence volume for a dipole on a sphere inside the brain.

Wakes induced by the motion of vessels may extend for tens of kilometers and exist for hours under certain conditions in the open sea. This provides a useful feature for long-range ship detection. The authors present a method for passively detecting a ship wake using measurements obtained by an airborne SQUID magnetic transducer that measures the first order gradients of the magnetic signature induced by the wake. Analytical formulas for wake magnetic gradients are derived to provide guidelines for using the airborne detector. They also derive bounds on the probability of wake detection for cross correlation and square-law detectors, which can be used to predict the expected performance. Numerical examples are used to demonstrate the applicability of their results.

A robust, flexible system for tracking the point to point nonrigid motion of the left ventricular (LV) endocardial wall in image sequences has been developed. This system is unique in its ability to model motion trajectories across multiple frames. The foundation of this system is an adaptive transversal filter based on the recursive least-squares algorithm. This filter facilitates the integration of models for periodicity and proximal smoothness as appropriate using a contour-based description of the object's boundaries. A set of correspondences between contours and an associated set of correspondence quality measures comprise the input to the system. Frame-to-frame relationships from two different frames of reference are derived and analyzed using synthetic and actual images. Two multiframe temporal models, both based on a sum of sinusoids, are derived. Illustrative examples of the system's output are presented for quantitative analysis. Validation of the system is performed by comparing computed trajectory estimates with the trajectories of physical markers implanted in the LV wall. Sample case studies of marker trajectory comparisons are presented. Ensemble statistics from comparisons with 15 marker trajectories are acquired and analyzed. A multiframe temporal model without spatial periodicity constraints was determined to provide excellent performance with the least computational cost. A multiframe spatiotemporal model provided the best performance based on statistical standard deviation, although at significant computational expense.

We present maximum likelihood (ML) methods for active estimation of range (time delay), velocity (Doppler shift), and direction of a point target with a radar array in spatially correlated noise with unknown covariance. We consider structured and unstructured array response models and compute the Cramer-Rao bound (CRB) for the time delay, Doppler shift, and direction of arrival. We derive ambiguity functions for the above models and discuss the relationship between identifiability, ambiguity, and the Fisher information matrix.

We propose a framework of performance measures for analyzing estimators of geometrical vectors that have intuitive physical interpretations, are independent of the coordinate frame and parameterization, and have no artificial singularities. We obtain finite-sample and asymptotic lower bounds on them for large classes of estimators and show how they may be used as system design criteria. We determine a simple asymptotic relationship that is applicable to both the measures and their bounds.

We present two adaptive cross-product algorithms for tracking the direction to a moving source using an electromagnetic vector sensor. The first is a cross-product algorithm with a forgetting factor, for which we analyze the performance and derive an asymptotic expression of the variance of angular estimation error. We find the optimal forgetting factor that minimizes this variance. The second is a Kalman filter combined with the cross-product algorithm, which is applicable when the angular acceleration of the source is approximately constant.

We develop vector-sensor array processing to estimate the angles-of-arrival (AOAs) and time delays of multipath channels in the space-time-polarization domain. A MUSIC-type algorithm for joint angle and delay estimation with a vector-sensor array is derived. Potential applications include multipath channel estimation and mobile localization. Simulation results show that the space-time-polarization parameterization of the multipath channels results in improved accuracy and resolution performance.

We develop detection methods for automatic environmental monitoring of disposal sites on the deep ocean floor using chemical sensor arrays. Such sites have been proposed for the relocation of dredge materials from harbors and shipping channels; the monitoring is used to detect possible release of pollutants at the site. We model the underwater transport of the pollutants as a diffusion process, and obtain a measurement model by exploiting the spatial and temporal evolution of the associated concentration distribution. The detection problem is defined by a one side hypothesis test for the case of multiple sources. We derive two detectors, the generalized likelihood ratio (GLR) test and the mean detector, and determine their performance in terms of the probabilities of false alarm and detection. The results are applied to the design of chemical sensor arrays satisfying criteria specified in terms of these probabilities, and to optimally select numbers of sensors and time samples. Numerical examples are used to demonstrate the applicability of our results.

We develop a minimum-noise-variance beamformer employing one electromagnetic vector sensor, capable of measuring the complete electric and magnetic fields induced by electromagnetic signals at one point. Two types of signals are considered: one carries a single message, and the other carries two independent messages simultaneously. The state of polarization of the interference under consideration ranges from completely polarized to unpolarized. To analyze the performance, we first obtain explicit expressions for the signal to interference-plus-noise ratio (SINR) in terms of the parameters of the desired signal, interference and noise. Then we discuss some physical implications associated with the SINR expressions. Our SINR expressions provide a basis for effective interference suppression, as well as generation of dual-message signals of which the two message signals have minimum interference effect on one another.

We consider the passive direction-of-arrival (DOA) estimation problem using arrays of acoustic vector-sensors located in a fluid, at or near a plane boundary. We formulate a general measurement model applicable to most surfaces, and derive an expression for the Cramer-Rao bound (CRB) of a single source. The CRB is used to analyze the practically important cases of ideal rigid and pressure-release surfaces in detail. An important quantitative comparison is made between a stand-off array of pressure sensors and a surface-mounted array of velocity sensors for the latter surface. In particular, we define and find an expression for the critical distance, at which the arrays have an equivalent performance.

We consider beamforming and Capon direction of arrival (DOA) estimation using arrays of acoustic vector sensors. We derive an expression for the Cramer-Rao bound (CRB) on the DOA parameters of a single source. Using this, we give conditions that minimize the lower bound on the asymptotic mean-square angular error, and conditions that ensure it is isotropic. The asymptotic performance of the Capon (1969, 1971) and beamforming estimators is analyzed and compared with a scalar-sensor array. The vector-sensor array is seen to have improved performance due to its elements' directional sensitivity. Large sample approximations for the mean-square error (MSE) matrices of the estimators are derived. Throughout, we compare vector-sensor arrays with their scalar-sensor counterparts.

We investigate the linear dependence of the steering vectors of one electromagnetic vector sensor. We show that every 3 steering vectors with distinct DOAs are linearly independent. We also show that 4 steering vectors with distinct DOAs are linearly independent if the ellipticity angles of the signals associated with any 2 of the 4 steering vectors are distinct. We then establish that 5 steering vectors are linearly independent if exactly 2 or 3 of them correspond to circularly polarized signals with the same spin direction. Finally, we demonstrate that given any 5 steering vectors, then for any DOA there exists a steering vector which is linearly dependent on the 5 steering vectors.

A framework for tracking pointwise periodic non-rigid motion of the heart's left ventricular (LV) wall is presented which incorporates information from two different magnetic resonance imaging (MRI) techniques. New developments in phase-contrast cine MR imaging have produced spatial maps of instantaneous velocity that heave proven accuracy within the myocardium, or wall, of the heart. This information is combined with shape-based matching techniques to provide improved estimates of trajectories, especially in regions where shape information is limited. These raw trajectories act as input to a recursive least squares (RLS) filter which applies the constraints of temporal periodicity and spatial smoothness for the final estimate. The results of the RLS filter are compared with the motion of actual implanted markers. Comparisons are also made between exclusively shape-based filtered and phase-contrast enhanced trajectory estimates using both phantom and actual canine heart MR images.>

A framework for temporal analysis of left ventricular (LV) endocardial wall motion is presented. This approach uses harmonic estimation to model the periodic nature of cardiac motion. A method for flow vector computation is presented which defines a relationship between image-derived, shape-based correspondences and a more desirable, smoothly varying, set of correspondences. A recursive filter is then constructed which takes into consideration this relationship as well as knowledge of temporal trends. The trajectories of magnetic resonance (MR) contrast markers implanted in the LV wall are compared with trajectories estimated by the filter. The results of this comparison confirm that although cardiac motion is a 3-D problem, 2-D analysis provides a rich testing ground for algorithm development.

Sensor array processing algorithms for source localization often require precise knowledge of the sensor locations, which is often not available in practice. Errors in the sensor locations are known to degrade severely the performance of these algorithms. This paper proposes iterative damped Gauss-Newton maximum likelihood array sensor localization algorithms using known calibration source signals. Cramér-Rao bound (CRB) expressions for the sensor location parameters are found for this problem. Two calibration source signal models are considered. One assumes that each signal waveform is known up to a scaling constant and phase, while the other requires complete knowledge of the signal waveform. For uncorrelated, completely known calibration signals, a necessary and sufficient condition for the optimal choice of the source bearings that minimizes the sensor position CRB variances is presented. Numerical results illustrate that the maximum likelihood calibration algorithms attain the CRB asymptotically. Sensor-Array-Processing Algorithmen zur Lokalisierung von Quellen setzen oft eine präzise Kenntnis der Sensorpositionen voraus, die in der Praxis oft nicht verfügbar ist. Es ist bekannt, daβ Fehler in den Sensorpositionen die Leistungsfähigkeit dieser Algorithmen stark reduzieren. Die vorliegende Arbeit schlägt iterative gedämpfte Gauβ-Newton Maximum-Likelihood Algorithmen zur Array-Sensor-Lokalisierung vor, die bekannte Kalibrierungs-Quellen-Signale verwenden. Für dieses Problem werden Ausdrücke für die Cramer-Rao-Schranke (CRB) der Sensor-positions-Parameter gefunden. Es werden zwei Modelle für die Kalibrierungs-Quellen-Signale betrachtet. Das eine Modell setzt voraus, daβ jedes Signal bis auf eine Skalierungskonstante und eine phase bekannt ist, während das andere die vollständige Kenntnis der Signale erfordert. Für unkorrelierte, vollständig bekannte Kalibrierungssignale wird eine notwendige und hinreichende Bedingung für die optimale Wahl der Quellenpositionen angegeben, die die CRB-Varianzen der Sensorpositionen minimiert. Numerische Ergebnisse zeigen, daβ die Maximum-Likelihood Kalibrierungsalgorithmen die CRB asymptotisch erreichen. Les algorithmes de traitement des réseaux de senseurs pour la localisation de source nécessitent souvent une connaissance précise de l'emplacement des senseurs, qui n'est souvent pas disponible en pratique. Les erreurs dans la localisation des senseurs sont connues pour dégrader sévèrement les performances de ces algorithmes. Cet article propose des algorithmes de localisation de source de Gauss-Newton au maximum de vraisemblance amortis itératifs utilisant des signaux de calibration de source. Des expressions de la limite de Cramer-Rao (LCR) pour les paramètres d'emplacement de senseur sont trouvées pour ce problème. Deux modèles de signal de calibration de source sont considérés. Le premier suppose que chaque forme d'onde du signal est connue à une constante d'échelle et de phase près, alors que le second réclame une connaissance parfaite de la forme d'onde du signal. Pour des signaux de calibration non correlés et complètement connus, une condition nécessaire et suffisante pour le choix optimal des orientations de source, qui minimise les variances LCR de la position du senseur, est présentée. Les résultats numériques illustrent le fait que les algorithmes de calibration selon le maximum de vraisemblance atteignent assymptotiquement le LCR.

We present a method to simplify the analytical computation of the Cramer-Rao bound. The method circumvents bound calculations for so-called nuisance parameters. Under mild regularity conditions the technique, which replaces expectations with almost sure limits, can significantly lower the analytical complexity as compared to traditional methods. The dimension of a matrix that requires computation and inversion is reduced to the length of the parameter vector of interest. We give applications to random variables having densities in the exponential family. For normal distributions the resulting expressions take on particularly simple closed forms.>

A new, efficient algorithm for tracking the roots of time-varying polynomials with complex coefficients is presented. The algorithm updates a vector of polynomial roots in response to a perturbation in polynomial coefficients. The update requires only the solution of a single set of linear equations. The algorithm has been used successfully to track the roots of high-order polynomials. The accuracy of the algorithm can be improved by iteration. When operated iteratively, it converges rapidly, and usually requires less than ten iterations to reach the maximum accuracy achievable using sixteen significant digital arithmetic.>

The asymptotic tracking properties of an adaptive notch filter with pole-zeros constraints for the cancellation or retrieval of multiple time-varying sine waves in additive noise are analyzed. The methods of Ljung and Gunnarsson (see Automatica, vol.26, no.1, p.7-21, Jan. 1990) are used in order to analyze the asymptotic mean-square parameter error, when the variations in the underlying frequencies and the gain of the algorithm are assumed to be sufficiently small. A closed-form expression for the mean square error (MSE) is derived as a function of the tuning variables of the algorithm. The results give insight into the operational properties of the algorithm and are used in order to minimize the MSE with respect to the tuning variables.>

By imposing mild restrictions on the analytic form of the probability density functions (PDFs) characterizing the model, the family of filtering problems for which exact recursive solutions are known is extended. It is shown that the recursive computation can be done with bounded complexity per iteration on the new family. This family has the potential to model many filtering problems.>

An analysis is made of the consistency of two direction-of-arrival estimation algorithms used in the presence of multipath propagation and with very few snapshots. The conditional maximum-likelihood (CML) algorithm and the method of direction estimation (MODE) are discussed. The cost functions of these algorithms are shown to coincide for a very large number of snapshots or very large signal-to-noise ratio. Necessary and sufficient conditions are derived for the algorithms to yield unique estimates. It is shown that their uniqueness conditions coincide with fundamental uniqueness conditions for the array that are independent of the algorithm used.>

Two different types of data model used in estimating the direction-of-arrival (DOA) of narrowband signals using sensor arrays are considered: the conditional model (CM), which assumes the signals to be nonrandom, and the unconditional model (UM), which assumes the signals to be random. These models leased to different maximum-likelihood (ML) methods (termed CML and UML, respectively) and different Cramer-Rao bounds (CRB) on DOA estimation accuracy (B/sub c/ and B/sub u/, respectively). An explicit expression is derived for the covariance matrix of the UML and for B/sub u/. It is shown that CML, UML, and a recently introduced method of direction estimation (MODE), as well as many other DOA estimation methods, have the same asymptotic statistical properties under CM as under UM. It is proven that: CML is statistically less efficient then UNL; MODE is asymptotically equivalent to UML; UML and MODE achieve the unconditional CRB, B/sub u/; and B/sub u/ is a lower bound on the asymptotic statistical accuracy of any (consistent) DOA estimate based on the data sample covariance matrix; B/sub c/ cannot be attained. It is also proven that B/sub u/ and B/sub c/ decrease monotonically as the number of sensors or snapshots increases and increase monotonically as the number of sources increases.>

The authors present two new polynomial factorization algorithms suitable for use in adaptive signal processing applications where it is required to track the movements of roots. Their distinguishing feature is that they provide methods for updating the roots optimally (and efficiently) in response to coefficient perturbations. This is useful, for example, for online estimation and tracking of time-varying roots. A Gauss-Newton type algorithm that requires approximately 2n/sup 2/ floating-point operations to update all roots of an nth-order polynomial is presented. An eigenvalue-based method that requires approximately 6n floating-point operations per individual root update is also proposed. Close to the true root vector, the rate of convergence of both algorithms is quadratic or faster. Unlike available direct pole estimation algorithms, the methods proposed here are not restricted to estimation of the roots of ARMA (autoregressive moving average)-like processes, but can be used in any situation where online estimates of polynomial coefficients are available.>

A number of results have been presented recently on the statistical performance of the multiple signal characterization (MUSIC) and the maximum-likelihood (ML) estimators for determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements. It is shown that in the class of weighted MUSIC estimators, the unweighted MUSIC achieves the best performance (i.e. the minimum variance of estimation errors) in large samples. The covariance matrix of the ML estimator is derived, and detailed analytic studies of the statistical efficiency of MUSIC and ML estimators are presented. These studies include performance comparisons of MUSIC and MLE with each other as well as with the ultimate performance corresponding to the Cramer-Rao bound (CRB).>

A method is presented for underwater acoustic source parameter estimation when many multipaths exist. The method is based on an asymptotic maximum likelihood (ML) estimator in the frequency domain and an acoustic image model for the ocean. Cramer-Rao bounds are calculated and compared with Monte Carlo simulation results.>

The authors analyze the convergence of several adaptive notch filter algorithms for sine waves in colored noise, which were recently proposed in the literature. After pointing out the previous algorithms' potential convergence problems, an algorithm is proposed for this problem that does not have convergence problems and provides accurate estimation results.>

The authors consider methods for solving the problem of finding the directions of multiple plane waves with linear arrays of sensors and the related one of estimating the parameters of multiple superimposed exponential signals in noise. Specifically, the MUSIC and maximum-likelihood (ML) methods have been proposed for solving these problems. The authors study the performance of the MUSIC and ML methods, and analyze their statistical efficiency. They also derive the Cramer-Rao bound (CRB) for the estimation problems mentioned above, and establish some useful properties of the CRB covariance matrix. The relationship between the MUSIC and ML estimators is investigated as well.>

The authors establish the large-sample accuracy properties of two nonlinear least-squares estimators (NLSEs) of sine waves parameters: the basic NLSE, which ignores the possible correlation of the noise; and the optimal NLSE, which, besides the sine-wave parameters, also estimates the noise correlation (appropriately parameterized). It is shown that these two NLSEs have the same accuracy in large samples. This result provides complete justification for preferring the computationally less-expensive basic NLSE over the optimal NLSE. Both estimators are shown to achieve the Cramer-Rao bound (CRB) as the sample size increases. A simple explicit expression for the CRB matrix is provided which should be useful in studying the performance of sine-wave parameter estimators designed to work in the colored noise case.>

The problem of calibrating dynamic sensor locations in a two-dimensional array with the aid of far-field sources is considered. The authors do not know the exact sensor locations, but postulate a known, nominal array geometry in which the location of one sensor and the direction to a second sensor are known. The time-varying sensor displacements from the nominal locations are assumed to be small relative to the intersensor spacing. The auxiliary sources have unknown, time-invariant bearings. They measure the time delays from the sources to the sensors, corrupted by additive noise, and apply an extended Kalman filter. Results of simulations show that calibration can be achieved provided there is enough a priori knowledge of the source bearings.>

A new family of algorithms is developed for adaptive parameter estimation of constrained autoregressive moving-average (ARMA) signals in the presence of noise. These algorithms utilize a priori known information concerning the signal's properties, such as its spectral shape or a spatial domain characteristic. Special cases include autoregressive (AR) and band-pass spectrum signals in the presence of noise, signal deconvolution and image deblurring.

This paper presents a new algorithm for the identification of the carrier and fundamental frequencies of harmonic signals transmitted over single-sideband channels. The method uses a Recursive Prediction Error (RPE) algorithm which produces fast convergence and accurate estimates. Simulation results demonstrate the performance of the algorithm.

Adaptive notch filters are used to eliminate narrow-band or sine wave components with unknown or slowly time varying frequencies from observed time series. This paper derives the asymptotic bias and variance of the sine wave frequency estimate obtained by the adaptive notch filter recently proposed in [4].

A new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow-band or sine wave signals in an additive broadband process. The algorithm is of recursive prediction error (RPE) form and uses a special constrained model of proper infinite impulse response (IIR) with a minimal number of parameters. The convergent filter is characterized by highly narrow bandwidth and uniform notches of desired shape. For sufficiently large data sets, the algorithm approaches the Cramer-Rao bound in estimating the frequencies of the sine wave signals.

A new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise. The algorithm is composed of two cascaded parts. The first estimates the fundamental frequency and enhances the harmonic component in the input. The second estimates the harmonic amplitudes and phases. Performance analysis provides new results for the asymptotic Cramer-Rao bound (CRB) on the parameters of harmonic signals with additive white noise.

This paper provides a new derivation and interpretation for the fast recursive least squares (RLS) algorithm of [1-3] and for the (block) Levinson algorithm as specialized conjugate direction methods (CDMs). The fast RLS time update is shown to be equivalent to a particular combination of two last steps in CDM recursions, giving a novel geometric description for this method. The results for the Levinson algorithm extend the ones of [9] on its relationship to the CDM.

The extraction of sinusoids in white noise, using least-squares predictors, has attracted a lot of attention in the past, mainly in the context of the adaptive line enhancer (ALE). However, very few results exist for the colored noise case, or for the whitening performance of the predictors. We use a matrix formulation to derive the optimal least-squares coefficients and frequency response of the ALE or the D-step predictor, for sinusoids (real or complex) in additive colored noise. Several cases are considered; in low-pass background noise the amplitude gain of the sinusoids becomes essentially a monotonically increasing function of their frequency, and a decreasing function for high-pass noise. For the whitening application, signal to noise ratio (SNR) bounds of the output are derived when the input is a white signal plus a sinusoidal interference. This performance is achievable using (possibly complex) exact least-squares recursions, such as our ladder form implementations.

In this presentation the stable and optimal operation of the adaptive line enhancer (ALE) is considered. By improving the estimate of the steady-state mean square error (MSE), a tighter stability constraint is obtained, as well as more accurate expressions for the SNR gain attained by the ALE when filtering sinusoidal signals in white noise. Since the LMS algorithm used for adapting the ALE weights aims at minimizing the MSE, and not at maximizing the output SNR, the proper choice of the algorithm's parameters for maximizing the SNR gain is considered. In particular, it is shown that for a given step-size parameter µ (which satisfies the stability constraint) there exists an optimal number of weights which maximizes the SNR gain. Computer simulations verify the analytical results.