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This work studies the field prediction and smoothing problems, where the spatio-temporal field in 2-D is described by a stochastic dynamical system and observed by a number of spatially deployed sensors. We adopt a finite-element technique to approximate the field dynamics with piece-wise Gaussian functions, leading to a high-dimensional linear stochastic system. By exploiting its sparsity, a local covariance intersection-based filter and smoother are developed in each sensor only for a moderate number of state variables via communications with nearby sensors. Such a cooperative scheme is both communication and computation efficient. We prove the uniform stability of the local filter and smoother under mild conditions, and validate their effectiveness on two application examples: the temperature prediction of a metal rod and the source localization of a PM $_{2.5}$ field with a real dataset in a city of China.

This paper investigates estimation of direction of arrivals (DOAs) and time of arrivals (TOAs) for a multi-user orthogonal frequency-division multiplexing (OFDM) system that is equipped with large-scale arrays and interfered by carrier frequency offsets (CFOs). We propose a novel scheme for joint TOA and DOA estimation with CFO compensation by taking advantages of large-scale receive antenna arrays. The pilot is designed to balance the pilot length and the estimation performance. The proposed CFO estimation scheme is with lower complexity. After analyzing the resolution of joint DOA and TOA estimation, we find a criterion to choose an appropriate smoothing window for the best resolution and provide insights in sub-carrier selection strategy. We also prove that the large-scale array can asymptotically achieve perfect resolution of both TOA and DOA estimation. We reveal the pseudo peak (PP) elimination property of large-scale arrays and exploit it to develop a novel path number estimation algorithm accordingly. Based on our numerical results, the proposed scheme can efficiently eliminate the CFO effect, the optimized smoothing window attains much better performance, and the path number estimation algorithm performs better than the traditional minimum description length (MDL) approach, especially in the low signal-to-noise ratio (SNR) regime.

In recent years, the sources localization has noticed an increase in research conducted on the problem of mixed far-field sources (FFSs) and near-field sources (NFSs). The main assumption of the existing researches is that the signals should be uncorrelated. Therefore, they cannot be used for multipath environments. The present paper provides a method called components separation algorithm (CSA) for the localization of multiple mixed FFSs and NFSs, including uncorrelated, lowly correlated and coherent signals. Firstly, by constructing one special cumulant matrix, and using a MUSIC-based technique, the noncoherent DOA vector (NDOAV) is extracted. By constructing another special cumulant matrix, and with respect to NDOAV, an estimate of the range, as well as a signal classification is obtained for noncoherent sources. Then, by estimating their kurtosis, the noncoherent component and consequently the coherent one of the second cumulant matrix is obtained. Finally, by introducing a novel approach based on squaring, projection, spatial smoothing, array interpolation transform and coherent component restoring, the parameters of coherent signals in each coherent group are estimated separately. The CSA prevents severe loss of the aperture. Furthermore, it does not require any pairing. The simulation results validate its satisfactory performance in terms of estimation accuracy, resolution, computational complexity, reasonable classification, and also its robustness against lowly correlated sources.

To ensure the proper functioning of active sensing systems in the presence of interferences from other electromagnetic equipment in a spectrally crowded environment, we devise four new solutions for spectrally compatible waveform design based on the min-max metric, namely, minimum modulus dynamic range, min-max spectral shape, minimum weighted peak sidelobe level, and minimum similarity. To address the resultant nonconvex and nonsmooth optimization problems, a unified algorithm framework is proposed. That is, we first approximate the min-max metric by using the “log-exponential smoothing” technique, then apply majorization-minimization to smooth and simplify the approximate optimization formulations, and finally use the Karush-Kuhn-Tucker theory to tackle the majorized problems. Besides, we develop an adaptive approximation parameter selection scheme, which monotonically decreases the approximation error at each iteration. The proposed algorithms are computationally efficient as they can be realized via fast Fourier transform. Finally, numerical examples are presented to demonstrate their excellent performance.

Grant-free random access is a promising protocol to support massive access in beyond fifth-generation (B5G) cellular Internet-of-Things (IoT) with sporadic traffic. Specifically, in each coherence interval, the base station (BS) performs joint activity detection and channel estimation (JADCE) before data transmission. Due to the deployment of a large-scale antennas array and the existence of a huge number of IoT devices, JADCE usually has high computational complexity and needs long pilot sequences. To solve these challenges, this paper proposes a dimension reduction method, which projects the original device state matrix to a low-dimensional space by exploiting its sparse and low-rank structure. Then, we develop an optimized design framework with a coupled full column rank constraint for JADCE to reduce the size of the search space. However, the resulting problem is non-convex and highly intractable, for which the conventional convex relaxation approaches are inapplicable. To this end, we propose a logarithmic smoothing method for the non-smoothed objective function and transform the interested matrix to a positive semidefinite matrix, followed by giving a Riemannian trust-region algorithm to solve the problem in complex field. Simulation results show that the proposed algorithm is efficient to a large-scale JADCE problem and requires shorter pilot sequences than the state-of-art algorithms which only exploit the sparsity of device state matrix., Comment: 16 pages, 11 figures

Frequency-resolved optical gating (FROG) is a popular technique for complete characterization of ultrashort laser pulses. The acquired data in FROG, called FROG trace, is the Fourier magnitude of the product of the unknown pulse with a time-shifted version of itself, for several different shifts. To estimate the pulse from the FROG trace, we propose an algorithm that minimizes a smoothed non-convex least-squares objective function. The method consists of two steps. First, we approximate the pulse by an iterative spectral algorithm. Then, the attained initialization is refined based upon a sequence of block stochastic gradient iterations. The algorithm is theoretically simple, numerically scalable, and easy-to-implement. Empirically, our approach outperforms the state-of-the-art when the FROG trace is incomplete, that is, when only few shifts are recorded. Simulations also suggest that the proposed algorithm exhibits similar computational cost compared to a state-of-the-art technique for both complete and incomplete data. In addition, we prove that in the vicinity of the true solution, the algorithm converges to a critical point. A Matlab implementation is publicly available at https://github.com/samuelpinilla/FROG., Simulations and comparisons are being added

We present a novel algorithm, an adaptive-lag smoother, approximating efficiently, in an online fashion, sequences of expectations under the marginal smoothing distributions in general state-space models. The algorithm evolves recursively a bank of estimators, one for each marginal, in resemblance with the so-called particle-based, rapid incremental smoother (PaRIS). Each estimator is propagated until a stopping criterion, measuring the fluctuations of the estimates, is met. The presented algorithm is furnished with theoretical results describing its asymptotic limit and memory usage., 12 pages, 8 figures

Recently, a novel method for developing filtering algorithms, based on the interconnection of two Bayesian filters and called double Bayesian filtering, has been proposed. In this manuscript we show that the same conceptual approach can be exploited to devise a new smoothing method, called double Bayesian smoothing. A double Bayesian smoother combines a double Bayesian filter, employed in its forward pass, with the interconnection of two backward information filters used in its backward pass. As a specific application of our general method, a detailed derivation of double Bayesian smoothing algorithms for conditionally linear Gaussian systems is illustrated. Numerical results for two specific dynamic systems evidence that these algorithms can achieve a better complexity-accuracy tradeoff and tracking capability than other smoothing techniques recently appeared in the literature., Comment: arXiv admin note: text overlap with arXiv:1902.05717 and arXiv:1907.01358

State space models in which the system state is a finite set--called the multi-object state--have generated considerable interest in recent years. Smoothing for state space models provides better estimation performance than filtering by using the full posterior rather than the filtering density. In multi-object state estimation, the Bayes multi-object filtering recursion admits an analytic solution known as the Generalized Labeled Multi-Bernoulli (GLMB) filter. In this work, we extend the analytic GLMB recursion to propagate the multi-object posterior. We also propose an implementation of this so-called multi-scan GLMB posterior recursion using a similar approach to the GLMB filter implementation.

A major drawback of subspace methods for direction-of-arrival estimation is their poor performance in the presence of coherent sources. Spatial smoothing is a common solution that can be used to restore the performance of these methods in such a case at the cost of increased array size requirement. In this paper, a Hadamard product perspective of the source resolvability problem of spatial-smoothing-based subspace methods is presented. The array size that ensures resolvability is derived as a function of the source number, the rank of the source covariance matrix, and the source coherency structure. This new result improves upon previous ones and recovers them in special cases. It is obtained by answering a long-standing question first asked explicitly in 1973 as to when the Hadamard product of two singular positive-semidefinite matrices is strictly positive definite. The problem of source identifiability is discussed as an extension. Numerical results are provided that corroborate our theoretical findings.

Phase retrieval is an inverse problem which consists in recovering an unknown signal from a set of absolute squared projections. Recently, gradient descent algorithms have been developed to solve this problem. However, their optimization cost functions are non-convex and non-smooth. To address the non-smoothness of the cost function, some of these methods use truncation thresholds to calculate a truncated step gradient direction. But, the truncation requires designing parameters to obtain a desired performance in the phase recovery, which drastically modifies the search direction update, increasing the sampling complexity. Therefore, this paper develops the Phase Retrieval Smoothing Conjugate Gradient method (PR-SCG) which uses a smoothing function to retrieve the signal. PR-SCG is based on the smooth-ing projected gradient method which is useful for non-convex optimization problems. PR-SCG uses a nonlinear conjugate gradient of the smoothing function as the search direction to accelerate the convergence. Furthermore, the incremental Stochastic Smoothing Phase Retrieval algorithm (SSPR) is developed. SSPR involves a single equation per iteration which results in a simple, scalable, and fast approach useful when the size of the signal is large. Also, it is shown that SSPR converges linearly to the true signal, up to a global unimodular constant. Additionally, the proposed methods do not require truncation parameters. Simulation results are provided to validate the efficiency of PR-SCG and SSPR compared to existing phase retrieval algorithms. It is shown that PR-SCG and SSPR are able to reduce the number of measurements and iterations to recover the phase, compared with recently developed algorithms.

In this paper, the fixed-lag smoothing problem for conditionally linear Gaussian state-space models is investigated from a factor graph perspective. More specifically, after formulating Bayesian smoothing for an arbitrary state-space model as a forward–backward message passing over a factor graph, we focus on the above-mentioned class of models and derive two novel particle smoothers for it. Both the proposed techniques are based on the well-known two-filter smoothing approach and employ marginalized particle filtering in their forward pass. However, on the one hand, the first smoothing technique can only be employed to improve the accuracy of state estimates with respect to that achieved by forward filtering. On the other hand, the second method, that belongs to the class of Rao–Blackwellized particle smoothers, also provides a point mass approximation of the so-called joint smoothing distribution. Finally, our smoothing algorithms are compared, in terms of estimation accuracy and computational requirements, with a Rao–Blackwellized particle smoother recently proposed by Lindsten et al. (“Rao–Blackwellized particle smoothers for conditionally linear Gaussian models,” IEEE J. Sel. Topics Signal Process. , vol. 10, no. 2, pp. 353–365, 2016).

We present a novel Wiener smoothing filter procedure for pilot-symbol-assisted estimation of oscillator phase noise. The procedure consists of forward and backward first-order infinite impulse response filtering the pilot symbols and combining the filter outputs to generate an estimate of the phase noise. We analyze the mean-square-error performance of this pilot-symbol-assisted forward–backward Wiener smoothing filter (FBWSF) procedure and show its optimality under the assumption that the phase noise is modeled as a first-order autoregressive moving average process. We then apply the FBWSF as a code-aided phase noise compensation technique in an iterative receiver framework. The iterative receiver presented here first estimates phase noise roughly by using the pilot-symbol-assisted FBWSF; then, it refines the estimates with the code-aided version of FBWSF. The resulting receiver achieves excellent error performance at a feasible level of computational complexity.

Navigation, mapping, and tracking are state estimation problems relevant to a wide range of applications. These problems have traditionally been formulated using random vectors in stochastic filtering, smoothing, or optimization-based approaches. Alternatively, the problems can be formulated using random finite sets, which offer a more robust solution in poor detection conditions (i.e., low probabilities of detection, and high clutter intensity). This paper mathematically shows that the two estimation frameworks are related, and equivalences can be determined under a set of ideal detection conditions. The findings provide important insights into some of the limitations of each approach. These are validated using simulations with varying detection statistics, along with a real experimental dataset.

International audience; Estimating means of data points lying on the Riemannian manifold of symmetric positive-definite (SPD) matrices has proved of great utility in applications requiring interpolation, extrapolation, smoothing, signal detection and classification. The power means of SPD matrices with exponent p in the interval [-1, 1] interpolate in between the Harmonic mean (p =-1) and the Arithmetic mean (p = 1), while the Geometric (Cartan/Karcher) mean, which is the one currently employed in most applications, corresponds to their limit evaluated at 0. In this article we treat the problem of estimating power means along the continuum p(-1, 1) given noisy observed measurement. We provide a general fixed point algorithm (MPM) and we show that its convergence rate for p = ±0.5 deteriorates very little with the number and dimension of points given as input. Along the whole continuum, MPM is also robust with respect to the dispersion of the points on the manifold (noise), much more so than the gradient descent algorithm usually employed to estimate the geometric mean. Thus, MPM is an efficient algorithm for the whole family of power means, including the geometric mean, which by MPM can be approximated with a desired precision by interpolating two solutions obtained with a small ±p value. We also present an approximated version of the MPM algorithm with very low computational complexity for the special case p=±½. Finally, we show the appeal of power means through the classification of brain-computer interface event-related potentials data.

This paper addresses the issue of robust sparse recovery in compressive sensing (CS) in the presence of impulsive measurement noise. Recently, robust data-fitting models, such as $\ell _1$ -norm, Lorentzian-norm, and Huber penalty function, have been employed to replace the popular $\ell _2$ -norm loss model to gain more robust performance. In this paper, we propose a robust formulation for sparse recovery using the generalized $\ell _p$ -norm with $0\leq p as the metric for the residual error. To solve this formulation efficiently, we develop an alternating direction method (ADM) via incorporating the proximity operator of $\ell _p$ -norm functions into the framework of augmented Lagrangian methods. Furthermore, to derive a convergent method for the nonconvex case of $p 1, a smoothing strategy has been employed. The convergence conditions of the proposed algorithm have been analyzed for both the convex and nonconvex cases. The new algorithm has been compared with some state-of-the-art robust algorithms via numerical simulations to show its improved performance in highly impulsive noise.

In this paper, we propose a strategy that is based on expectation maximization for tracking multiple point targets. The algorithm is similar to probabilistic multi-hypothesis tracking (PMHT) but does not relax the point target model assumptions. According to the point target models, a target can generate at most one measurement, and a measurement is generated by at most one target. With this model assumption, we show that the proposed algorithm can be implemented as iterations of Rauch-Tung-Striebel (RTS) smoothing for state estimation, and the loopy belief propagation method for marginal data association probabilities calculation. Using example illustrations with tracks, we compare the proposed algorithm with PMHT and joint probabilistic data association (JPDA) and show that PMHT and JPDA exhibit coalescence when there are closely moving targets whereas the proposed algorithm does not. Furthermore, extensive simulations c comparing the mean optimal subpattern assignment (MOSPA) performance of the algorithm for different scenarios averaged over several Monte Carlo iterations show that the proposed algorithm performs better than JPDA and PMHT. We also compare it to benchmarking algorithm: $N$ -scan pruning based track-oriented multiple hypothesis tracking (TOMHT). The proposed algorithm shows a good tradeoff between computational complexity and the MOSPA performance.

State estimation is studied for a special class of flag Hidden Markov Models (HMMs), which comprise 1) an arbitrary finite-state underlying Markov chain and 2) a structured observation process wherein a subset of states emit distinct flags with some probability while other states are unmeasured. For flag HMMs, an explicit computation of the probability of error for the maximum-likelihood filter and smoother is developed. Also, the form of the optimal filter is further characterized in terms of the time since the last flag, and this result is used to further simplify the error-probability computation. Some preliminary graph-theoretic insights into the error probability and its computation are discussed. Finally, these algebraic and structural results are leveraged to address sensor placement in two examples, including one on activity-monitoring in a home environment that is drawn from field data. These examples indicate that low error-probability filtering and smoothing can be achieved with relatively few sensors.

We consider mean squared estimation with lookahead of a continuous-time signal corrupted by additive white Gaussian noise. We show that the mutual information rate function, i.e., the mutual information rate as function of the signal-to-noise ratio (SNR), does not, in general, determine the minimum mean squared error (MMSE) with fixed finite lookahead, in contrast to the special cases with 0 and infinite lookahead (filtering and smoothing errors), respectively, which were previously established in the literature. We also establish a new expectation identity under a generalized observation model where the Gaussian channel has an SNR jump at $t=0$, capturing the tradeoff between lookahead and SNR. Further, we study the class of continuous-time stationary Gauss-Markov processes (Ornstein-Uhlenbeck processes) as channel inputs, and explicitly characterize the behavior of the minimum mean squared error (MMSE) with finite lookahead and signal-to-noise ratio (SNR). The MMSE with lookahead is shown to converge exponentially rapidly to the non-causal error, with the exponent being the reciprocal of the non-causal error. We extend our results to mixtures of Ornstein-Uhlenbeck processes, and use the insight gained to present lower and upper bounds on the MMSE with lookahead for a class of stationary Gaussian input processes, whose spectrum can be expressed as a mixture of Ornstein-Uhlenbeck spectra., Comment: 30 pages, 10 figures, submitted to IEEE Transactions on Information Theory

Two-dimensional (2D) phase unwrapping is an estimation problem of a continuous phase function, over a 2D domain, from its wrapped samples. In this paper, we propose a novel approach for high-resolution 2D phase unwrapping. In the first step—SPline Smoothing (SPS), we construct a pair of the smoothest spline functions which minimize the energies of their local changes while interpolating, respectively, the cosine and the sine of given wrapped samples. If these functions have no common zero over the domain, the proposed estimate of the continuous phase function can be obtained by algebraic phase unwrapping in the second step—Algebraic Phase Unwrapping (APU). To avoid the occurrence of common zeros in SPS due to phase noise in the observed wrapped samples, we also propose a denoising step—Denoising by Selective Smoothing (DSS)—as preprocessing, which selectively smooths unreliable wrapped samples by using convex optimization. The smoothness of the proposed unwrapped phase function is guaranteed globally over the domain without losing any desired consistency with all reliable wrapped samples. Numerical experiments for terrain height estimation demonstrate the effectiveness of the proposed 2D phase unwrapping scheme.

This article considers the filtering problem for linear and Gaussian state-space models with large dimensions, a setup in which the optimal Kalman Filter (KF) might not be applicable owing to the excessive cost of manipulating huge covariance matrices. Among the most popular alternatives that enable cheaper and reasonable computation is the Ensemble KF (EnKF), a Monte Carlo-based approximation. In this article, we consider a class of a posteriori distributions with diagonal covariance matrices and propose fast approximate deterministic-based algorithms based on the Variational Bayesian (VB) approach. More specifically, we derive two iterative KF-like algorithms that differ in the way they operate between two successive filtering estimates; one involves a smoothing estimate and the other involves a prediction estimate. Despite its iterative nature, the prediction-based algorithm provides a computational cost that is, on the one hand, independent of the number of iterations in the limit of very large state dimensions, and on the other hand, always much smaller than the cost of the EnKF. The cost of the smoothing-based algorithm depends on the number of iterations that may, in some situations, make this algorithm slower than the EnKF. The performances of the proposed filters are studied and compared to those of the KF and EnKF through a numerical example.

The impulse response of wireless channels between the N-t transmit and N-r receive antennas of a MIMO-OFDM system are group approximately sparse (ga-sparse), i.e., NtNt the channels have a small number of significant paths relative to the channel delay spread and the time-lags of the significant paths between transmit and receive antenna pairs coincide. Often, wireless channels are also group approximately cluster-sparse (gac-sparse), i.e., every ga-sparse channel consists of clusters, where a few clusters have all strong components while most clusters have all weak components. In this paper, we cast the problem of estimating the ga-sparse and gac-sparse block-fading and time-varying channels in the sparse Bayesian learning (SBL) framework and propose a bouquet of novel algorithms for pilot-based channel estimation, and joint channel estimation and data detection, in MIMO-OFDM systems. The proposed algorithms are capable of estimating the sparse wireless channels even when the measurement matrix is only partially known. Further, we employ a first-order autoregressive modeling of the temporal variation of the ga-sparse and gac-sparse channels and propose a recursive Kalman filtering and smoothing (KFS) technique for joint channel estimation, tracking, and data detection. We also propose novel, parallel-implementation based, low-complexity techniques for estimating gac-sparse channels. Monte Carlo simulations illustrate the benefit of exploiting the gac-sparse structure in the wireless channel in terms of the mean square error (MSE) and coded bit error rate (BER) performance.

This paper proposes an iterative equalizer based on Kalman filtering and smoothing (IEKFS) for multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels. A state-space model with a priori information and the corresponding Kalman filtering (KF) and Kalman smoothing (KS) operations are developed. The KF operations perform a linear minimum mean-square error (MMSE) equalization procedure with soft interference cancellation. In addition, the KF and KS operations produce and exchange the updated extrinsic information. During this IEKFS process, the soft estimate of a desired symbol does not participate in the equalization procedures for the desired symbol; only the feedback information of the other transmit symbols is used. Therefore, the proposed IEKFS performs iterative linear MMSE equalization based on the Kalman framework and turbo principle. The complexity of the IEKFS is linear with respect to the number of transmit signal vectors in a transmission block, and simulation results show that the IEKFS can achieve near-optimum bit error rate performances approaching the matched filter bound (MFB) of the channel in various environments.

We consider the problem of direction of arrival (DOA) estimation using a newly proposed structure of non-uniform linear arrays, referred to as co-prime arrays, in this paper. By exploiting the second order statistical information of the received signals, co-prime arrays exhibit O(MN) degrees of freedom with only M + N sensors. A sparsity based recovery method is proposed to fully utilize these degrees of freedom. Unlike traditional sparse recovery methods, the proposed method is based on the developing theory of super resolution, which considers a continuous range of possible sources instead of discretizing this range into a discrete grid. With this approach, off-grid effects inherited in traditional sparse recovery can be neglected, thus improving the accuracy of DOA estimation. In this paper we show that in the noiseless case one can theoretically detect up to M N sources with only 2M + N sensors. The noise 2 statistics of co-prime arrays are also analyzed to demonstrate the robustness of the proposed optimization scheme. A source number detection method is presented based on the spectrum reconstructed from the sparse method. By extensive numerical examples, we show the superiority of the proposed method in terms of DOA estimation accuracy, degrees of freedom, and resolution ability compared with previous methods, such as MUSIC with spatial smoothing and the discrete sparse recovery method., Comment: Submitted on December 17th, 2013

We present a novel motion smoothing algorithm for hand-held cameras with application to video stabilization. Video stabilization seeks to remove unwanted frame-to-frame jitter due to camera shake. For video stabilization, we use a pure 3D rotation motion model with known camera projection parameters. The 3D camera rotation can be reliably tracked by a gyroscope as commonly found on a smart phone or tablet. In this paper, we directly smooth the sequence of camera rotation matrices for the video frames by exploiting the Riemannian geometry on a manifold. Our contributions are 1) formulation of motion smoothing as a geodesic-convex constrained regression problem on a nonlinear manifold based on geodesic distance, 2) computation of gradient and Hessian of the objective function using Riemannian geometry for gradient-related manifold optimization, and 3) generalization of the two-metric projection algorithm in Euclidean space to manifolds to solve the proposed manifold optimization problem efficiently. The geodesic-distance-based smoothness metric better exploits the manifold structure of sequences of rotation matrices. The geodesic-convex constraints effectively guarantee that no black borders intrude into the stabilized frames. The proposed manifold optimization algorithm can find the global optimal solution in only a few iterations. Experimental results show that video stabilization based on our motion smoothing algorithm outperforms state-of-the-art methods by generating videos with less jitter and without black borders.

In this work, we are interested in the improvements attainable when multiscan processing of external knowledge is performed over a moving time window. We propose a novel algorithm that enforces the state constraints by using a Fixed-Lag Smoothing procedure within the prediction step of the Bayesian recursion. For proving the improvements, we utilize differential entropy as a measure of uncertainty and show that the approach guarantees a lower or equal posterior differential entropy than classical single-step constrained filtering. Simulation results using examples for single-target tracking are presented to verify that a Sequential Monte Carlo implementation of the proposed algorithm guarantees an improved tracking accuracy.

We propose a new class of nested vector-sensor arrays which is capable of significantly increasing the degrees of freedom (DOF). This is not a simple extension of the nested scalar-sensor array, but a novel signal model. The structure is obtained by systematically nesting two or more uniform linear arrays with vector sensors. By using one component's information of the interspectral tensor, which is equivalent to the higher-dimensional second-order statistics of the received data, the proposed nested vector-sensor array can provide O(N2) DOF with only N physical sensors. To utilize the increased DOF, a novel spatial smoothing approach is proposed, which needs multilinear algebra in order to preserve the data structure and avoid reorganization. Thus, the data is stored in a higher-order tensor. Both the signal model of the nested vector-sensor array and the signal processing strategies, which include spatial smoothing, source number detection, and direction of arrival (DOA) estimation, are developed in the multidimensional sense. Based on the analytical results, we consider two main applications: electromagnetic (EM) vector sensors and acoustic vector sensors. The effectiveness of the proposed methods is verified through numerical examples.

We consider algorithms and recovery guarantees for the analysis sparse model in which the signal is sparse with respect to a highly coherent frame. We consider the use of a monotone version of the fast iterative shrinkage- thresholding algorithm (MFISTA) to solve the analysis sparse recovery problem. Since the proximal operator in MFISTA does not have a closed-form solution for the analysis model, it cannot be applied directly. Instead, we examine two alternatives based on smoothing and decomposition transformations that relax the original sparse recovery problem, and then implement MFISTA on the relaxed formulation. We refer to these two methods as smoothing-based and decomposition-based MFISTA. We analyze the convergence of both algorithms, and establish that smoothing- based MFISTA converges more rapidly when applied to general nonsmooth optimization problems. We then derive a performance bound on the reconstruction error using these techniques. The bound proves that our methods can recover a signal sparse in a redundant tight frame when the measurement matrix satisfies a properly adapted restricted isometry property. Numerical examples demonstrate the performance of our methods and show that smoothing-based MFISTA converges faster than the decomposition-based alternative in real applications, such as MRI image reconstruction., Submitted on Aug 22th, 2013; Updated on Dec 1st, 2013

A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities. This probabilistic approach can naturally accommodate general models for the data distribution, lending itself to various fitting criteria that yield optimum estimates in the maximum-a-posteriori sense. In particular, two algorithms are devised for Gaussian- and Poisson-distributed data, that minimize the rank-regularized least-squares error and Kullback-Leibler divergence, respectively. The proposed technique is able to recover the "ground-truth'' tensor rank when tested on synthetic data, and to complete brain imaging and yeast gene expression datasets with 50% and 15% of missing entries respectively, resulting in recovery errors at -10dB and -15dB., 12 pages, submitted to IEEE Transactions on Signal Processing

This paper presents a fixed interval smoothing multi-scan algorithm for target tracking in clutter. Both the probability of target existence and the target trajectory probability density function are calculated using all available measurements. This improves both the false track discrimination and the target trajectory estimate. The fixed interval smoothing fuses the forward and the backward multi-scan predictions, to obtain the smoothing predictions and smoothing innovations. Both trajectory estimates and the data association probabilities are calculated using the smoothing innovations. An overlapping batch procedure is described which limits the smoothing delay.

Bernoulli filters are a class of exact Bayesian filters for non-linear/non-Gaussian recursive estimation of dynamic systems, recently emerged from the random set theoretical framework. The common feature of Bernoulli filters is that they are designed for stochastic dynamic systems which randomly switch on and off. The applications are primarily in target tracking, where the switching process models target appearance or disappearance from the surveillance volume. The concept, however, is applicable to a range of dynamic phenomena, such as epidemics, pollution, social trends, etc. Bernoulli filters in general have no analytic solution and are implemented as particle filters or Gaussian sum filters. This tutorial paper reviews the theory of Bernoulli filters as well as their implementation for different measurement models. The theory is backed up by applications in sensor networks, bearings-only tracking, passive radar/sonar surveillance, visual tracking, monitoring/prediction of an epidemic and tracking using natural language statements. More advanced topics of smoothing, multi-target detection/tracking, parameter estimation and sensor control are briefly reviewed with pointers for further reading.