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Detecting periodicity in a short sequence is an important problem, with many applications across science and engineering. Several efficient algorithms have been proposed for this over the years. There is a wide choice available today in terms of the tradeoff between algorithmic complexity and estimation accuracy. In spite of such a rich history, one particular aspect of period estimation has received very little attention from a fundamental perspective. Namely, given a discrete time periodic signal and a list of candidate integer periods, what is the absolute minimum datalength required to estimate its integer period? Notice that the answer we seek must be a fundamental bound, i.e., independent of any particular period estimation technique. Common intuition suggests the minimum datalength as twice the largest expected period. However, this is true only under some special contexts. This paper derives the exact necessary and sufficient bounds to this problem. The above-mentioned question is also extended to the case of mixtures of periodic signals. First, a careful mathematical formulation discussing the unique identifiability of the component periods (hidden integer periods) is presented. Once again, a rigorous theoretical framework in this regard is missing in the existing literature but is a necessary platform to derive precise bounds on the minimum necessary datalength. The bounds given here are generic, that is, independent of the algorithms used. Specific algorithm-dependent bounds are also presented in the end for the case of dictionary-based integer period estimation reported in recent years. [ABSTRACT FROM AUTHOR]

Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as many signal sources compared to the traditional methods for arbitrary signals. As a benchmark for these NC methods, we derive the closed-form deterministic $R$ -D NC Cramér-Rao bound (NC CRB) for the multi-dimensional parameter estimation of strictly non-circular (rectilinear) signal sources in this paper. Assuming a separable centro-symmetric $R$-D array, we show that in some special cases, the deterministic $R$-D NC CRB reduces to the existing deterministic $R$-D CRB for arbitrary signals. This suggests that no gain from strictly non-circular sources (NC gain) can be achieved under the deterministic data assumption in these cases. For more general scenarios, finding an analytical expression of the NC gain for an arbitrary number of sources is very challenging. Thus, in this paper, we simplify the derived NC CRB and the existing CRB for the special case of two closely-spaced strictly non-circular sources captured by a uniform linear array (ULA). Subsequently, we use these simplified CRB expressions to analytically compute the maximum achievable asymptotic NC gain for the considered two source case. The resulting expression only depends on the various physical parameters and we find the conditions that provide the largest NC gain. Our analysis is supported by extensive simulation results. [ABSTRACT FROM PUBLISHER]

The stability of sparse signal reconstruction with respect to measurement noise is investigated in this paper. We design efficient algorithms to verify the sufficient condition for unique \ell1 sparse recovery. One of our algorithms produces comparable results with the state-of-the-art technique and performs orders of magnitude faster. We show that the \ell1-constrained minimal singular value (\ell1-CMSV) of the measurement matrix determines, in a very concise manner, the recovery performance of \ell1-based algorithms such as the Basis Pursuit, the Dantzig selector, and the LASSO estimator. Compared to performance analysis involving the Restricted Isometry Constant, the arguments in this paper are much less complicated and provide more intuition on the stability of sparse signal recovery. We show also that, with high probability, the subgaussian ensemble generates measurement matrices with \ell1-CMSVs bounded away from zero, as long as the number of measurements is relatively large. To compute the \ell1-CMSV and its lower bound, we design two algorithms based on the interior point algorithm and the semidefinite relaxation. [ABSTRACT FROM AUTHOR]

Characterized by sudden structural changes, fault-prone systems are modeled using the framework of systems with switching parameters or hybrid systems. Since a closed-form mean-square optimal filtering algorithm for this class of systems does not exist, it is of particular interest to derive a lower bound on the state estimation error covariance. The well known Crameacuter-Rao bound is not applicable to fault-prone systems because of the discrete distribution of the fault indicators, which violates the regularity conditions associated with this bound. On the other hand, the Weiss-Weinstein lower bound is essentially free from regularity conditions. Moreover, a sequential version of the Weiss-Weinstein bound, suitable for Markovian dynamic systems, is presented by the authors in a companion paper. In the present paper, this sequential version is applied to several classes of fault-prone dynamic systems. The resulting bounds can be used to examine fault detectability and identifiability in these systems. Moreover, it is shown that several recently reported lower bounds for fault-prone systems are special cases of, or closely related to, the sequential version of the Weiss-Weinstein lower bound [ABSTRACT FROM PUBLISHER]

This paper presents a game theory approach to the constrained state estimation of linear discrete time dynamic systems. In the application of state estimators, there is often known model or signal information that is either ignored or dealt with heuristically. For example, constraints on the state values (which may be based on physical considerations) are often neglected because they do not easily fit into the structure of the state estimator. This paper develops a method for incorporating state equality constraints into a minimax state estimator. The algorithm is demonstrated on a simple vehicle tracking simulation. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of unsupervised Bayesian hidden Markov chain restoration. When the hidden chain is stationary, the classical "Hidden Markov Chain" (HMC) model is quite efficient, and associated unsupervised Bayesian restoration methods using the "Expectation-Maximization" (EM) algorithm work well. When the hidden chain is non stationary, on the other hand, the unsupervised restoration results using the HMC model can be poor, due to a bad match between the real and estimated models. The novelty of this paper is to offer a more appropriate model for hidden nonstationary Markov chains, via the theory of evidence. Using recent results relating to Triplet Markov Chains (TMCs), we show, via simulations, that the classical restoration results can be improved by the use of the theory of evidence and Dempster-Shafer fusion. The latter improvement is performed in an entirely unsupervised way using an original parameter estimation method. Some application examples to unsupervised image segmentation are also provided. [ABSTRACT FROM AUTHOR]

Performance evaluation of multi-target tracking algorithms is of great practical importance in the design, parameter optimization and comparison of tracking systems. The goal of performance evaluation is to measure the distance between two sets of tracks: the ground truth tracks and the set of estimated tracks. This paper proposes a mathematically rigorous metric for this purpose. The basis of the proposed distance measure is the recently formulated consistent metric for performance evaluation of multi-target filters, referred to as the OSPA metric. Multi-target filters sequentially estimate the number of targets and their position in the state space. The OSPA metric is therefore defined on the space of finite sets of vectors. The distinction between filtering and tracking is that tracking algorithms output tracks and a track represents a labeled temporal sequence of state estimates, associated with the same target. The metric proposed in this paper is therefore defined on the space of finite sets of tracks and incorporates the labeling error. Numerical examples demonstrate that the proposed metric behaves in a manner consistent with our expectations. [ABSTRACT FROM PUBLISHER]

This paper considers the statistical performance of the MUSIC method under the condition that two closely spaced sources impinging on an array of sensors are effectively resolved, i.e., the spectrum exhibits two peaks in the neighborhood of the true directions-of-arrival (DOA). The MUSIC algorithm is known to have an infinite resolution power in theory. However, in the presence of modeling errors, sources can not be resolved with certainty, even if the array correlation matrix is perfectly known. The focus of this paper is to predict the bias and variance of the DOA estimates taking into account the possible resolution failure of MUSIC. This performance prediction, based on our recent mathematical investigation, is new to the best of our knowledge. A general mathematical framework to derive closed form expressions of the bias and variance versus the model mismatch, conditioned on a general statistical resolution test is proposed. In order to illustrate our mathematical approach, statistical tests with one and two conditions, respectively, are investigated. The accuracy of the performance prediction is illustrated in a simulation study. It is found that the proposed approach outperforms the "classical" technique, which ignores the possible resolution failure of the MUSIC algorithm. Therefore, our results provide better tools for determining the necessary antenna calibration accuracy to achieve some targeted specifications on the estimator performance. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of blind identification of a convolutive multiple-input-multiple-output (MIMO) system with No outputs and Ni inputs. While many methods have been proposed to blindly identify convolutive MIMO systems with No ≥ Ni (overdetermined), very scarce results exist for the case of No < Ni (underdetermined), all of which refer to systems that either have some special structure or special No and Ni values. In this paper, we show that, as long as min(No, Ni) ≥ 2, independent of whether the system is overdetermined or underdetermined, we can always find the appropriate order of statistics that guarantees identifiability of the system response within trivial ambiguities. We also propose an algorithm to reach the solution, that consists of parallel factorization (PARAFAC) of a K-way tensor containing K th-order statistics of the system outputs, followed by an iterative scheme. For a certain order of statistics K, we provide the description of the class of identifiable MIMO systems. We also show that this class can be expanded by applying PARAFAC decomposition to a pair of tensors instead of one tensor. The proposed approach constitutes a novel scheme for estimation of underdetermined systems, and improves over existing approaches for overdetermined systems. [ABSTRACT FROM AUTHOR]

In this paper, we present a new parametric modeling of three-dimensional homogeneous volumes of textured images (3-D texture) based on 3-D Wold decomposition for discrete processes. This decomposition additively separates any 3-D discrete homogeneous process into three mutually orthogonal components: a purely indeterministic, a "remote past"—type deterministic and an evanescent component. The evanescent component can be further decomposed into two orthogonal components called type 1 evanescent and type 2 evanescent. Assuming that the 3-D image volume is a finite realization of a discrete homogeneous stochastic process, the 3-D texture field can be uniquely represented as a sum of four mutually orthogonal components with different spectral properties. The aim of this paper is to present new parametric models able to describe both the spectral support and spatial characteristics of each component. A spectral decomposition algorithm to separate a 3-D texture into structured and unstructured parts is also proposed. [ABSTRACT FROM AUTHOR]

Noise reduction and signal decomposition are among important and practical issues in time-domain signal analysis. This paper presents an adaptive notch filter (ANF) to achieve both these objectives. For noise reduction purpose, the proposed adaptive filter successfully extracts a single sinusoid of a possibly time-varying nature from a noise-corrupted signal. The paper proceeds with introducing a chain of filters which is capable of estimating the fundamental frequency of a signal composed of harmonically related sinusoids, and of decomposing it into its constituent components. The order of differential equations governing this algorithm is 2n + 1, where n is the number of constituent sinusoids that should be extracted. Stability analysis of the proposed algorithm is carried out based on the application of the local averaging theory under the assumption of slow adaptation. When compared with the conventional Fourier analysis, the proposed method provides instantaneous values of the constituting components. Moreover, it is adaptive with respect to the fundamental frequency of the signal. Simulation results verify the validity of the presented algorithm and confirm its desirable transient and steady-state performances as well as its desirable noise characteristics. [ABSTRACT FROM AUTHOR]

This paper examines the asymptotic performance of MUSIC-like algorithms for estimating directions of arrival (DOA) of narrowband complex noncircular sources. Using closed-form expressions of the covariance of the asymptotic distribution of different projection matrices, it provides a unifying framework for investigating the asymptotic performance of arbitrary subspace- based algorithms valid for Gaussian or non-Gaussian and complex circular or noncircular sources. We also derive different robustness properties from the asymptotic covariance of the estimated DOA given by such algorithms. These results are successively applied to four algorithms: to two attractive MUSIC-like algorithms previously introduced in the literature, to an extension of these algorithms, and to an optimally weighted MUSIC algorithm proposed in this paper. Numerical examples illustrate the performance of the studied algorithms compared to the asymptotically minimum variance (AMY) algorithms introduced as benchmarks. [ABSTRACT FROM AUTHOR]

This paper discusses underdetermined (i.e., with more sources than sensors) blind source separation (BSS) using a two-stage sparse representation approach. The first challenging task of this approach is to estimate precisely the unknown mixing matrix. In this paper, an algorithm for estimating the mixing matrix that can be viewed as an extension of the DUET and the TIFROM methods is first developed. Standard clustering algorithms (e.g., K-means method) also can be used for estimating the mixing matrix if the sources are sufficiently sparse. Compared with the DUET, the TIFROM methods, and standard clustering algorithms, with the authors' proposed method, a broader class of problems can be solved, because the required key condition on sparsity of the sources can be considerably relaxed. The second task of the two-stage approach is to estimate the source matrix using a standard linear programming algorithm. Another main contribution of the work described in this paper is the development of a recoverability analysis. After extending the results in [7], a necessary and sufficient condition for recoverability of a source vector is obtained. Based on this condition and various types of source sparsity, several probability inequalities and probability estimates for the recoverability issue are established. Finally, simulation results that illustrate the effectiveness of the theoretical results are presented. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating the direction of arrival (DOA) of an extended target in radar array processing. Two algorithms are proposed that do not assume that the power azimuthal distribution of the scatterers is symmetric with respect to the mass center of the target. The first one is based on spectral moments which are easily related to the target's DOA. The second method stems from a previous paper by the present authors and consists of a least-squares fit on the elements of the covartance matrix. Both methods are simple and are shown to provide accurate estimates. Furthermore, they extend the range of unambiguous DOAs that can be estimated, compared with the same previous paper. [ABSTRACT FROM AUTHOR]

The development of high-resolution two-dimensional spectral estimation techniques is of notable interest in synthetic aperture radar (SAR) imaging. Typically, data-independent techniques are exploited to form the SAR images, although such approaches will suffer from limited resolution and high sidelobe levels. Recent work on data-adaptive approaches have shown that both the iterative adaptive approach (IAA) and the sparse learning via iterative minimization (SLIM) algorithm offer excellent performance with high-resolution and low side lobe levels for both complete and incomplete data sets. Regrettably, both algorithms are computationally intensive if applied directly to the phase history data to form the SAR images. To help alleviate this, efficient implementations have also been proposed. In this paper, we further this work, proposing yet further improved implementation strategies, including approaches using the segmented IAA approach and the approximative quasi-Newton technique. Furthermore, we introduce a combined IAA-MAP algorithm as well as a hybrid IAA- and SLIM-based estimation scheme for SAR imaging. The effectiveness of the SAR imaging algorithms and the computational complexities of their fast implementations are demonstrated using the simulated Slicy data set and the experimentally measured GOTCHA data set. [ABSTRACT FROM PUBLISHER]

This paper presents a novel jointly sparse signal reconstruction algorithm for the DOA estimation problem, aiming to achieve faster convergence rate and better estimation accuracy compared to existing \ell 2,1-norm minimization approaches. The proposed greedy block coordinate descent (GBCD) algorithm shares similarity with the standard block coordinate descent method for \ell 2,1-norm minimization, but adopts a greedy block selection rule which gives preference to sparsity. Although greedy, the proposed algorithm is proved to also have global convergence in this paper. Through theoretical analysis we demonstrate its stability in the sense that all nonzero supports found by the proposed algorithm are the actual ones under certain conditions. Last, we move forward to propose a weighted form of the block selection rule based on the MUSIC prior. The refinement greatly improves the estimation accuracy especially when two point sources are closely spaced. Numerical experiments show that the proposed GBCD algorithm has several notable advantages over the existing DOA estimation methods, such as fast convergence rate, accurate reconstruction, and noise resistance. [ABSTRACT FROM PUBLISHER]

As an active branch of network tomography, delay tomography has received considerable attentions in recent years. However, most methods in the literature assume that the delays of different links are independent of each other, and pursuit sub-optimal estimate instead of the maximum likelihood estimate (MLE) due to computational challenges. In this paper, we propose a novel method to implement the EM algorithm widely used in delay tomography analysis for multicast networks. The proposed method makes use of a “delay pattern database” to avoid all redundant computations in the E-step, and is much faster than the traditional implementation. With the help of this new implementation, finding MLE for large networks, which was considered impractical previously, becomes an easy task. Taking advantage of this computational breakthrough, we further consider models for potential spatial dependence of links, and propose a novel adaptive spatially dependent model (ASDM) for delay tomography. In ASDM, Markov dependence among nearby links is allowed, and spatially dependent links (SDLs) can be automatically recognized via model selection. The superiority of the new methods is confirmed by simulation studies. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a channel estimation scheme for a two-hop nonregenerative MIMO relay system without the direct link between source and destination. This scheme has two phases. In the first phase, the source does not transmit while the relay transmits and the destination receives. In the second phase, the source transmits, the relay amplifies and forwards, and the destination receives. At the destination, the data received in the first phase are used to estimate the relay-to-destination channel, and the data received in the second phase are used to estimate the source-to-relay channel. The linear minimum mean-square error estimation (LMMSE) is used for channel estimation, which allows the use of prior knowledge of channel correlations. For phase 1, an algorithm is developed to compute the optimal source pilot matrix for use at the relay. For phase 2, an algorithm is developed to compute the optimal source pilot matrix for use at the source and the optimal relay pilot matrix for use at the relay. [ABSTRACT FROM AUTHOR]

This paper addresses a transmission energy problem for distributed (or decentralized) estimation in multihop wireless sensor networks (WSN). A primary advantage of distributed estimation is its energy efficiency when compared to centralized estimation. Two distributed estimation schemes are considered in this paper: progressive estimation and consensus estimation. We develop a generalized energy planning algorithm for a progressive estimation method which exploits routing tree and channel state information. We also analyze the energy cost for a consensus estimation method used in broadcast multihop WSN. We demonstrate by analysis and simulation that, subject to an equivalent performance, the total energy cost for consensus estimation is typically much higher than that for progressive estimation, but the peak energy for the former can be less than that for the latter. [ABSTRACT FROM PUBLISHER]

Sparse signal representation (SSR) is considered to be an appealing alternative to classical beamforming for direction-of-arrival (DOA) estimation. For wideband signals, the SSR-based approach constructs steering matrices, referred to as dictionaries in this paper, corresponding to different frequency components of the target signal. However, the SSR-based approach is subject to ambiguity resulting from not only spatial aliasing, just like in classical beamforming, but also from the over-completeness of the dictionary, which is typical to SSR. We show that the ambiguity caused by the over-completeness of the dictionary can be alleviated by using multiple measurement vectors. In addition, by considering the uniform linear array (ULA) structure, we argue that if the target signal contains at least two frequencies, whose absolute difference phrased in wavelengths is larger than twice the array spacing, the spatial aliasing corresponding to these frequencies will be completely distinct. These properties enable us to adapt the existing \ell1 algorithms to extract the target DOAs without ambiguity. [ABSTRACT FROM PUBLISHER]

Detection of the number of sinusoids embedded in noise is a fundamental problem in statistical signal processing. Most parametric methods minimize the sum of a data fit (likelihood) term and a complexity penalty term. The latter is often derived via information theoretic criteria, such as minimum description length (MDL), or via Bayesian approaches including Bayesian information criterion (BIC) or maximum a posteriori (MAP). While the resulting estimators are asymptotically consistent, empirically their finite sample performance is strongly dependent on the specific penalty term chosen. In this paper we elucidate the source of this behavior, by relating the detection performance to the extreme value distribution of the maximum of the periodogram and of related random fields. Based on this relation, we propose a combined detection-estimation algorithm with a new penalty term. Our proposed penalty term is sharp in the sense that the resulting estimator achieves a nearly constant false alarm rate. A series of simulations support our theoretical analysis and show the superior detection performance of the suggested estimator. [ABSTRACT FROM PUBLISHER]

This paper proposes a technique for motion estimation of groups of targets based on evolving graph networks. The main novelty over alternative group tracking techniques stems from learning the network structure for the groups. Each node of the graph corresponds to a target within the group. The uncertainty of the group structure is estimated jointly with the group target states. New group structure evolving models are proposed for automatic graph structure initialization, incorporation of new nodes, unexisting nodes removal, and the edge update. Both the state and the graph structure are updated based on range and bearing measurements. This evolving graph model is propagated combined with a sequential Monte Carlo framework able to cope with measurement origin uncertainty. The effectiveness of the proposed approach is illustrated over scenarios for group motion estimation in urban environments. Results with challenging scenarios with merging, splitting, and crossing of groups are presented with high estimation accuracy. The performance of the algorithm is also evaluated and shown on real ground moving target indicator (GMTI) radar data and in the presence of data origin uncertainty. [ABSTRACT FROM AUTHOR]

Target tracking algorithms usually treat the probability of detection as independent of the target state. In most cases, this assumption is not true, with subsequent degradation in the target tracking performance from both expected and optimal levels. One typical example is the Doppler frequency based clutter rejection, the other is obfuscation (shadowing) of ground based targets, and the third is antijamming notch filtering. This dependence of the probability of target detection on the target trajectory state modulates the measurement likelihood, which, in turn, introduces measurement nonlinearity. In this paper, we first present a general algorithm for target tracking in clutter when the probability of detection is target state dependent, and then proceed to an algorithm where both target state estimate and the probability of detection are modeled by Gaussian mixtures. The probability of target existence is recursively updated as the track quality measure used for false track discrimination. A two-sensor-based ground maneuvering target tracking in clutter simulation validates this approach. [ABSTRACT FROM AUTHOR]

In this paper, a novel algorithm to blindly separate an instantaneous linear underdetermined mixture of nonstationary sources is proposed. It means that the number of sources exceeds the number of channels of the available data. The separation is based on the working assumption that the sources are piecewise stationary with a different variance in each block. It proceeds in two steps: 1) estimating the mixing matrix, and 2) computing the optimum beamformer in each block to maximize the signal-to-interference ratio of each separated signal with respect to the remaining signals. Estimating the mixing matrix is accomplished through a specialized tensor decomposition of the set of sample covariance matrices of the received mixture in each block. It utilizes optimum weighting, which allows statistically efficient (CRB attaining) estimation provided that the data obey the assumed Gaussian piecewise stationary model. In simulations, performance of the algorithm is successfully tested on blind separation of 16 speech signals from nine linear instantaneous mixtures of these signals. [ABSTRACT FROM AUTHOR]

In this paper, we consider mixture approaches that adaptively combine outputs of several parallel running adaptive algorithms. These parallel units can be considered as diversity branches that can be exploited to improve the overall performance. We study various mixture structures where the final output is constructed as the weighted linear combination of the outputs of several constituent filters. Although the mixture structure is linear, the combination weights can be updated in a highly nonlinear manner to minimize the final estimation error such as in Singer and Feder 1999; Arenas-Garcia, Figueiras-Vidal, and Sayed 2006; Lopes, Satorius, and Sayed 2006; Bershad, Bermudez, and Tourneret 2008; and Silva and Nascimento 2008. We distinguish mixture approaches that are convex combinations (where the linear mixture weights are constrained to be nonnegative and sum up to one) [Singer and Feder 1999; Arenas-Garcia, Figueiras-Vidal, and Sayed 2006], affine combinations (where the linear mixture weights are constrained to sum up to one) [Bershad, Bermudez, and Tourneret 2008] and, finally, unconstrained linear combinations of constituent filters [Kozat and Singer 2000]. We investigate mixture structures with respect to their final mean-square error (MSE) and tracking performance in the steady state for stationary and certain nonstationary data, respectively. We demonstrate that these mixture approaches can greatly improve over the performance of the constituent filters. Our analysis is also generic such that it can be applied to inhomogeneous mixtures of constituent adaptive branches with possibly different structures, adaptation methods or having different filter lengths. [ABSTRACT FROM AUTHOR]

The S transform is useful in time-frequency analysis. Many inverse S transform algorithms have been proposed with different filtering properties in the time-frequency spectrum. In this paper, the transformation matrices of the S transform and two novel least square inverse algorithms are proposed. The first one minimizes the global mean square error of the entire time-frequency spectrum, and the second one considers only the specific interesting time-frequency regions and is more flexible. The proposed inverse algorithms can provide more stable and better performance than the existing ones. [ABSTRACT FROM AUTHOR]

Downstream (DS) crosstalk channels of digital subscriber line systems can be estimated based on the reported signal-to-noise ratio (SNR). In the case of an already active victim line (VL) impacted by the joining of a new disturber line (DL), sending perturbing signals on the VL and reporting the SNRs allow the estimation of the crosstalk channel from the DL to the VL. This paper generalizes that concept to include full startup, tracking and joining scenarios as well as the impact of different perturbation signal choices. Additionally, the sensitivity of the algorithm to different sources of imperfection is analyzed. Simulation results reveal that starting without precoding, and updating the precoder matrix based on the DS crosstalk channel estimates, the far-end crosstalk-free SNR can be reached in a limited number of iterations (e.g., 36 SNR measurements are needed for the four lines case). The SNR-assisted method is documented in an informative appendix of the draft G.vector recommendation as a backward compatible method for very high speed digital subscriber lines (VDSL2) and, hence, can be used for channel acquisition today. [ABSTRACT FROM AUTHOR]

This paper proposes a general framework to effectively estimate the unknown timing and channel parameters, as well as design efficient timing resynchronization algorithms for asynchronous amplify-and-forward (AF) cooperative communication systems. In order to obtain reliable timing and channel parameters, a least squares (LS) estimator is proposed for initial estimation and an iterative maximum-likelihood (ML) estimator is derived to refine the LS estimates. Furthermore, a timing and channel uncertainty analysis based on the Cramér-Rao bounds (CRB) is presented to provide insights into the system uncertainties resulted from estimation. Using the parameter estimates and uncertainty information in our analysis, timing resynchronization algorithms that are robust to estimation errors are designed jointly at the relays and the destination. The proposed framework is developed for different AF systems with varying degrees of timing misalignment and channel uncertainties and is numerically shown to provide excellent performances that approach the synchronized case with perfect channel information. [ABSTRACT FROM AUTHOR]

Orthogonal frequency-division multiplexing (OFDM) combines the advantages of high performance and relatively low implementation complexity. However, for reliable coherent detection of the input signal, the OFDM receiver needs accurate channel information. When the channel exhibits fast time variation as it is the case with several recent OFDM-based mobile broadband wireless standards (e.g., WiMAX, LTE, DVB-H), channel estimation at the receiver becomes quite challenging for two main reasons: 1) the receiver needs to perform this estimation more frequently and 2) channel time-variations introduce intercarrier interference among the OFDM subcarriers which can degrade the performance of conventional channel estimation algorithms significantly. In this paper, we propose a new pilot-aided algorithm for the estimation of fast time-varying channels in OFDM transmission. Unlike many existing OFDM channel estimation algorithms in the literature, we propose to perform channel estimation in the frequency domain, to exploit the structure of the channel response (such as frequency and time correlations and bandedness), optimize the pilot group size and perform most of the computations offline resulting in high performance at substantial complexity reductions. [ABSTRACT FROM AUTHOR]

This paper considers the problem of time difference-of-arrival (TDOA) source localization when the TDOA measurements from multiple disjoint sources are subject to the same sensor position displacements from the available sensor positions. This is a challenging problem and closed-form solution with good localization accuracy has yet to be found. This paper proposes an estimator that can achieve this purpose. The pro- posed algorithm jointly estimates the unknown source and sensor positions to take the advantage that the TDOAs from different sources have the same sensor position displacements. The joint estimation is a highly nonlinear problem due to the coupling of source and sensor positions in the measurement equations. We introduce the novel idea of hypothesized source locations in the algorithm development to enable the formulation of psuedolinear equations, thereby leading to the establishment of closed-form solution for source location estimates. Besides the advantage of closed-form, the newly developed algorithm is shown analytically, under the condition that the TDOA measurement noise and the sensor position errors are sufficiently small, to reach the CRLB accuracy. For clarity, the localization of two disjoint sources is used in the algorithm development. The developed algorithm is then examined under the special case of a single source and extended to the more general case of more than two unknown sources. The theoretical developments are supported by simulations. [ABSTRACT FROM AUTHOR]

This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for nonnegativity and fulladditivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution.. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images. [ABSTRACT FROM AUTHOR]

The Chinese remainder theorem (CRT) allows to reconstruct a large integer from its remainders modulo several moduli. In this paper, we propose a robust reconstruction algorithm called robust CRT when the remainders have errors. We show that, using the proposed robust CRT, the reconstruction error is upper bounded by the maximal remainder error range named remainder error bound, if the remainder error bound is less than one quarter of the greatest common divisor (gcd) of all the moduli. We then apply the robust CRT to estimate frequencies when the signal waveforms are undersampled multiple times. It shows that with the robust CRT, the sampling frequencies can be significantly reduced. [ABSTRACT FROM AUTHOR]

Compressive sensing (CS) is a framework whereby one performs N nonadaptive measurements to constitute a vector v ϵ RN, with v used to recover an approximation û ϵ RM to a desired signal u ϵ ℝM, with N ⪡ M; this is performed under the assumption that u is sparse in the basis represented by the matrix Ψ ϵ RM×M. It has been demonstrated that with appropriate design of the compressive measurements used to define v, the decompressive mapping v → û may be performed with error ∥u - û∥22having asymptotic properties analogous to those of the best adaptive transform-coding algorithm applied in the basis Ψ. The mapping v → û constitutes an inverse problem, often solved using ē1 regularization or related techniques. In most previous re- search, if L > 1 sets of compressive measurements {vi} i=1, L are performed, each of the associated {ûi}i=1, L are recovered one at a time, independently. In many applications the L "tasks" defined by the mappings v, → ûiare not statistically independent, and it may be possible to improve the performance of the inversion if statistical interrelationships are exploited. In this paper, we address this problem within a multitask learning setting, wherein the map- ping v, → ûi for each task corresponds to inferring the parameters (here, wavelet coefficients) associated with the desired signal ui, and a shared prior is placed across all of the L tasks. Under this hierarchical Bayesian modeling, data from all L tasks con- tribute toward inferring a posterior on the hyperparameters, and once the shared prior is thereby inferred, the data from each of the L individual tasks is then employed to estimate the task-dependent wavelet coefficients. An empirical Bayesian procedure for the estimation of hyperparameters is considered; two fast inference algorithms extending the relevance vector machine (RVM) are developed. Example results on several data sets demonstrate the effectiveness and robustness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a self-synchronization mechanism among linearly coupled integrators initialized with local measurements. We model the interaction among the nodes as a directed graph with weights (possibly) dependent on the radio channels, and we pose special attention to the effect of the propagation delay occurring in the exchange of data among sensors, as a function of the network geometry. We derive necessary and sufficient conditions for the proposed system to reach a consensus on globally optimal decision statistics. One of the major results proved in this work is that a consensus is reached with exponential convergence speed for any bounded delay condition if and only if the directed graph is quasi-strongly connected. We provide a closed form expression for the global consensus, showing that the effect of delays is, in general, the introduction of a bias in the final decision. Finally, we exploit our closed form expression to devise a double-step consensus mechanism able to provide an unbiased estimate with minimum extra complexity, without the need to know or estimate the channel parameters. [ABSTRACT FROM AUTHOR]

Recently, a new adaptive scheme [Conte et al. (1995), Gini (1997)] has been introduced for covariance structure matrix estimation in the context of adaptive radar detection under non-Gaussian noise. This latter has been modeled by compound-Gaussian noise, which is the product c of the square root of a positive unknown variable τ (deterministic or random) and an independent Gaussian vector x, c = √τx Because of the implicit algebraic structure of the equation to solve, we called the corresponding solution, the fixed point (FP) estimate. When τ is assumed deterministic and unknown, the FP is the exact maximum-likelihood (ML) estimate of the noise covariance structure, while when τ is a positive random variable, the FP is an approximate maximum likelihood (AML). This estimate has been already used for its excellent statistical properties without proofs of its existence and uniqueness. The major contribution of this paper is to fill these gaps. Our derivation is based on some likelihood functions general properties like homogeneity and can be easily adapted to other recursive contexts. Moreover, the corresponding iterative algorithm used for the FP estimate practical determination is also analyzed and we show the convergence of this recursive scheme, ensured whatever the initialization. [ABSTRACT FROM AUTHOR]

The advent of waveform-agile sensors has enabled the design of tracking systems where the transmitted waveform is changed on-the-fly in response to the tracker's requirements. This approach can provide performance improvements over individual optimization of the sensor waveform or the tracking algorithm. In this paper, we consider joint sensor configuration and tracking for the problem of tracking a single target in the presence of clutter using range and range-rate measurements obtained by waveform-agile, active sensors in a narrowband environment. We propose an algorithm to select and configure linear and nonlinear frequency-modulated waveforms to minimize the predicted mean square error (MSE) in the target state estimate; the MSE is predicted using the Cramér-Rao lower bound on the measurement error in conjunction with the unscented transform. We further extend our algorithm to match wideband environments, and we demonstrate the algorithm performance through a Monte Carlo simulation of a radar tracking example. [ABSTRACT FROM AUTHOR]

In this paper we study two fourth-order cumulant-based techniques for the estimation of the mixing matrix in underdetermined independent component analysis. The first method is based on a simultaneous matrix diagonalization. The second is based on a simultaneous off-diagonalization. The number of sources that can be allowed is roughly quadratic in the number of observations. For both methods, explicit expressions for the maximum number of sources are given. Simulations illustrate the performance of the techniques. [ABSTRACT FROM AUTHOR]

In this paper, we propose a particle filter acoustic direction-of-arrival (DOA) tracker to track multiple maneuvering targets using a state space approach. The particle filter determines its state vector using a batch of DOA estimates. The filter likelihood treats the observations as an image, using template models derived from the state update equation, and also incorporates the possibility of missing data as well as spurious DOA observations. Multiple targets are handled using a partitioned state-vector approach. The particle filter solution is compared with three other methods: the extended Kalman filter, Laplacian filter, and another particle filter that uses the acoustic microphone outputs directly. In addition, we demonstrate an autonomous system for multiple target DOA tracking with automatic target initialization and deletion. The initialization system uses a track-before-detect approach and employs matching pursuit to initialize multiple targets. Computer simulations are presented to compare the performance of the algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider the distributed parameter estimation in wireless sensor networks where a total bit rate constraint is imposed. We study the optimal tradeoff between the number of active sensors and the quantization bit rate for each active sensor to minimize the estimation mean-square error (MSE). To facilitate the solution, we first introduce a concept of equivalent 1-bit MSE function. Next, we present an optimal distributed estimation algorithm for homogeneous sensor networks based on minimizing the equivalent 1-bit MSE function. Then, we present a quasi-optimal distributed estimation algorithm for heterogeneous sensor networks, which is also based on the equivalent 1-bit MSE function, and the upper bound of the estimation MSE of the proposed algorithm is addressed. Furthermore, a theoretical nonachievable lower bound of the estimation MSE under the total bit rate constraint is stated and it is shown that our proposed algorithm is quasi-optimal within a factor 2.2872 of the theoretical lower bound. Simulation results also show that significant reduction in estimation MSE is achieved by our proposed algorithm when compared with other uniform methods. [ABSTRACT FROM AUTHOR]

The performance of the IEEE 802.11 protocol based on the distributed coordination function (DCF) has been shown to be dependent on the number of competing terminals and the backoff parameters. Better performance can be expected if the parameters are adapted to the number of active users. In this paper we develop both off-line and online Bayesian signal processing algorithms to estimate the number of competing terminals. The estimation is based on the observed use of the channel and the number of competing terminals is modeled as a Markov chain with unknown transition matrix. The off-line estimator makes use of the Gibbs sampler whereas the first online estimator is based on the sequential Monte Carlo (SMC) technique. A deterministic variant of the SMC estimator is then developed, which is simpler to implement and offers superior performance. Finally a novel approximate maximum a posteriori (MAP) algorithm for hidden Markov models (HMM) with unknown transition matrix is proposed. Realistic IEEE 802.11 simulations using the ns-2 network simulator are provided to demonstrate the excellent performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

In this paper, we derive a stochastic maximum-likelihood (ML) method for estimating spatio-temporal parameters for multiple-input multiple-output (M1MO) channels. Such estimators are needed in propagation studies where extensive channel measurements and sounding are required. These are seminal tasks in the process of developing advanced channel models. The proposed method employs an angular von Mises distribution model which is appropriate for angular data observed in channel measurement campaigns. The signal model is stochastic, and consequentially the method is particularly useful for estimation of the diffuse scattering component. This approach leads to lower complexity and faster convergence in comparison to deterministic models. These benefits are due to lower dimensionality of the model, leading to a simpler optimization problem. The statistical performance of the estimator is studied by establishing the Cramér-Rao lower bound (CRLB) and comparing the variances. The simulations show that the variance of the proposed estimation technique reaches the CRLB for relatively small sample size. The estimator is robust in the sense that meaningful results are obtained when applied to data generated by channel models other than the one used in its derivation. [ABSTRACT FROM AUTHOR]

DNA microarray technology relies on the hybridization process, which is stochastic in nature. Currently, probabilistic cross hybridization of nonspecific targets, as well as the shot noise (Poisson noise) originating from specific targets binding, are among the main obstacles for achieving high accuracy in DNA microarray analysis. In this paper, statistical techniques are used to model the hybridization and cross-hybridization processes and, based on the model, optimal algorithms are employed to detect the targets and to estimate their quantities. To verify the theory, two sets of microarray experiments are conducted: one with oligonucleotide targets and the other with complementary DNA (cDNA) targets in the presence of biological background. Both experiments indicate that, by appropriately modeling the cross-hybridization interference, significant improvement in the accuracy over conventional methods such as direct readout can be obtained. This substantiates the fact that the accuracy of microarrays can become exclusively noise limited, rather than interference (i.e., cross-hybridization) limited. The techniques presented in this paper potentially increase considerably the signal-to-noise ratio (SNR), dynamic range, and resolution of DNA and protein microarrays as well as other affinity-based biosensors. A preliminary study of the Cramer-Rao bound for estimating the target concentrations suggests that, in some regimes, cross hybridization may even be beneficial-a result with potential ramifications for probe design, which is currently focused on minimizing cross hybridization. Finally, in its current form, the proposed method is best suited to low-density arrays arising in diagnostics, single nucleotide polymorphism (SNP) detection, toxicology, etc. How to scale it to high-density arrays (with many thousands of spots) is an interesting challenge. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new Direction-of-Arrival (DOA) estimator called Conjugate Augmented MUSIC (CAM). The basic idea of CAM is to use the second-order statistics of the received signals to get the conjugate steering matrix. This, together with the steering matrix, is used to find the fourth-order cumulants. From that the source directions are obtained using the MUSIC-like algorithm. CAM can resolve two times the number of directions when compared to MUSIC-like estimator. Moreover, simulation results show that the estimation capacity, angle resolution, immunity to noise, and the number of required snapshots are all better than MUSIC-like algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel approach to implement the robust minimum variance distortionless response (MVDR) beamformer. This beamformer is based on worst-case performance optimization and has been shown to provide an excellent robustness against arbitrary but norm-bounded mismatches in the desired signal steering vector. However, the existing algorithms to solve this problem do not have direct computationally efficient online implementations. In this paper, we develop a new algorithm for the robust MVDR beamformer, which is based on the constrained Kalman filter and can be implemented online with a low computational cost. Our algorithm is shown to have a similar performance to that of the original second-order cone programming (SOCP)-based implementation of the robust MVDR beamformer. We also present two improved modifications of the proposed algorithm to additionally account for nonstationary environments. These modifications are based on model switching and hypothesis merging techniques that further improve the robustness of the beamformer against rapid (abrupt) environmental changes. [ABSTRACT FROM AUTHOR]

Parallel factor (PARAFAC) analysis is an extension of low-rank matrix decomposition to higher way arrays, also referred to as. It decomposes a given array in a sum of multi- linear terms, analogous to the familiar bilinear vector outer products that appear In matrix decomposition. PARAFAC analysis generalizes and unifies common array processing models, like joint diagonalization and ESPRIT; it has found numerous applications from blind multiuser detection and multidimensional harmonic retrieval, to clustering and nuclear magnetic resonance. The prevailing fitting algorithm in all these applications is based on (alternating) least squares, which is optimal for Gaussian noise. In many cases, however, measurement errors are far from being Gaussian. In this paper, we develop two iterative algorithms for the least absolute error fitting of general multilinear models. The first is based on efficient interior point methods for linear programming, employs in an alternating fashion. The second is based on a weighted median filtering iteration, which is particularly appealing from a simplicity viewpoint. Both are guaranteed to converge in terms of absolute error. Performance is illustrated by means of simulations, and compared to the pertinent Cramér-Rao bounds (CRBs). [ABSTRACT FROM AUTHOR]

This paper is concerned with recursive estimation using augmented data. We study two recursive procedures closely linked with the well-known expectation and maximization (EM) and space alternating generalized EM (SAGE) algorithms. Unlike iterative methods, the recursive EM and SAGE-inspired algorithms give a quick update on estimates given new data. Under mild conditions, estimates generated by these procedures are strongly consistent and asymptotically normally distributed. These mathematical properties are valid for a broad class of problems. When applied to direction of arrival (DOA) estimation, the recursive EM and SAGE-inspired algorithms lead to a very simple and fast implementation of the maximum-likelihood (ML) method. The most complicated computation in each recursion is inversion of the augmented information matrix. Through data augmentation, this matrix is diagonal and easy to invert. More importantly, there is no search in such recursive procedures. Consequently, the computational time is much less than that associated with existing numerical methods for finding ML estimates. This feature greatly increases the potential of the ML approach in real-lime processing. Numerical experiments show that both algorithms provide good results with low computational cost. [ABSTRACT FROM AUTHOR]

This paper presents a general feedforward symbol-timing estimation framework based on the conditional maximum likelihood principle. The proposed timing estimator presents reduced implementation complexity and is obtained by performing an approximation on the Fourier series expansion of the conditional maximum likelihood function. The proposed algorithm is applied to linear modulations and two commonly used continuous phase modulations: minimum shift keying (MSK) and Gaussian MSK (GMSK). For the linear modulations, it is shown both analytically and via simulations that the performance of the proposed estimator is very close to the conditional CRB and modified CRB for signal-to-noise ratios (SNRs) in the range SNR ≤ 30 dB. Furthermore, the proposed estimator is shown to be asymptotically equivalent to the classic square-law nonlinearity estimator under certain conditions. In the case of MSK and GMSK modulations, although the proposed algorithm reaches the conditional CRB at certain SNRs, however, the conditional CRB is quite far away from the modified CRB, and there exists an alternative algorithm whose performance comes closer to the modified CRB. Therefore, the proposed estimator is more suitable for linear modulations than for MSK and GMSK modulations. [ABSTRACT FROM AUTHOR]

In this paper, the problem of blind spatial signature estimation using the parallel factor (PARAFAC) analysis model is addressed in application to wireless communications. A time-varying user power loading in the uplink mode is proposed to make the model identifiable and to enable application of PARAFAC analysis. Then, identifiability issues are studied in detail and closed-form expressions for the corresponding modified Cramér-Rao bound (CRB) are obtained. Furthermore, two blind spatial signature estimation algorithms are developed. The first technique is based on the PARAFAC fitting trilinear alternating least squares (TALS) regression procedure, whereas the second one makes use of the joint approximate diagonalization algorithm. These techniques do not require any knowledge of the propagation channel and/or sensor array manifold and are applicable to a more general class of scenarios than earlier approaches to blind spatial signature estimation. [ABSTRACT FROM AUTHOR]

This paper presents a multiresolution multisensor data fusion scheme for dynamic systems to be observed by several sensors of different resolutions. A state projection equation is Introduce at associate the states of a system at each resolution with others. This projection equation together with the state transition equation and the measurement equations at each of the resolutions construct a continuous-time model of the system. The model meets the requirements of Kalman filtering. In discrete time, the state transition is described at the finest resolution and the sampling frequencies of sensors decrease successively by a factor of two in resolution. We can build a discrete model of the system by using a linear projection operator to approximate the state space projection. This discrete model satisfies the requirements Of discrete Kalman filtering, which actually offers an optimal estimation algorithm Of the system. In time-invariant case, the Stability of the Kalman filter Is analyzed and a sufficient condition for the filtering stability is given. A Markov-process-based example is given to illustrate and evaluate the proposed scheme of multi- resolution modeling and estimation with multiple sensors. [ABSTRACT FROM AUTHOR]

Graphical models provide a powerful general frame- work for encoding the structure of large-scale estimation problems. However, the graphs describing typical real-world phenomena contain many cycles, making direct estimation procedures prohibitively costly. In. this paper, we develop an iterative Inference algorithm for general.. Gaussian graphical models. it operates by exactly solving a series of modified estimation problems on spanning trees embedded within the original cyclic graph. When these sub problems are suitably chosen, the algorithm, converges to the correct conditional means. Moreover, and in contrast to many other iterative methods, the tree-based procedures we propose can also be used to calculate exact error variances. Although the conditional mean iteration is effective for quite densely connected graphical models, the error variance computation is most efficient for sparser. graphs. In this context, we present a modeling example suggesting that very sparsely connected graphs with cycles may provide significant advantages relative to their tree-structured counterparts, thanks both to the expressive power of these models and to the efficient inference algorithms developed herein. The convergence properties of the proposed tree-based iterations are characterized both analytically and experimentally, in addition, by using the basic tree-based iteration . to precondition the conjugate gradient method, we develop an alternative, accelerated iteration is finitely convergent. Simulation results are presented that demonstrate this algorithm's effectiveness on several inference problems, including a prototype distributed sensing application. [ABSTRACT FROM AUTHOR]