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In this paper, we study the estimation of a block covariance matrix with linearly structured off-diagonal blocks. We consider estimation based on the least squares method, which has some drawbacks. These estimates are not always well conditioned and may not even be definite. We propose a new estimation procedure providing a structured positive definite and well-conditioned estimator with good statistical properties. The least squares estimator is improved with the use of a shrinkage method and an additional algebraic approach. The resulting so-called quasi shrinkage estimator is compared with the structured maximum likelihood estimator. [ABSTRACT FROM AUTHOR]

In this paper, we present a statistical approach to evaluate the relationship between variables observed in a two-factors experiment. We consider a three-level model with covariance structure Σ ⊗ Ψ 1 ⊗ Ψ 2 , where Σ is an arbitrary positive definite covariance matrix, and Ψ 1 and Ψ 2 are both correlation matrices with a compound symmetric structure corresponding to two different factors. The Rao's score test is used to test the hypotheses that observations grouped by one or two factors are uncorrelated. We analyze a fermentation process to illustrate the results. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

We consider the implementation of ensemble-based Kalman filters (EnKF) in the framework of ensembles of different accuracies and sizes that are smaller than the number of degrees of freedom. From a noise-free ensemble and a noisy one assuming Gaussian errors for which the hyper-parameters of the distribution are known, we suggest a maximum likelihood approach on reduced-dimension subspaces to estimate forecast error pseudo-anomaly matrices. We show that they can be introduced in most of the widely-used EnKF analyses scheme with little intrusion into the data assimilation system. The performances of this approach are assessed by twin experiments done in the Lorenz-96 system and a quasi-geostrophic model. It is shown that the estimation of the forecast covariance error matrices with this approach did not damage the performance of the EnKF, and even resulted in an improvement of the analysis root mean square error for the QG model, highlighting the benefits of using optimized forecast error covariance matrices. [ABSTRACT FROM AUTHOR]

The complex Wishart distribution is a widely used statistical model for multilook polarimetric synthetic aperture radar (PolSAR) image data, of which the equivalent number of looks (ENL) is a critical parameter. Over the past decades, various estimators have been developed to estimate the ENL of complex Wishart distribution, of which the maximum likelihood (ML) estimator is important since it is asymptotically unbiased and has a small variance. However, this estimator is very time-consuming since it has no analytical solution and is usually solved numerically. To address this problem, this letter proposes an efficient ML estimator of ENL by deriving an approximate closed-form solution. Moreover, to estimate the ENL map of a PolSAR image, we also develop an efficient way to compute the local sample statistics parallelly. The experimental results on two PolSAR images show that our method yields highly approximate ENL values as the traditional ML estimator while is much more efficient. It costs less than 0.8 s on a general laptop to estimate the ENL map of a PolSAR image with 900 $\times $ 1024 pixels. [ABSTRACT FROM AUTHOR]

The maximum likelihood (ML) technique plays an important role in direction-of-arrival (DOA) estimation. In this paper, we employ and design the expectation–conditional maximization either (ECME) algorithm, a generalization of the expectation–maximization algorithm, for solving the ML direction finding problem of stochastic sources, which may be correlated, in unknown nonuniform noise. Unlike alternating maximization, the ECME algorithm updates both the source and noise covariance matrix estimates by explicit formulas, and can guarantee that both estimates are positive semi-definite and definite, respectively. Thus, the ECME algorithm is computationally efficient and operationally stable. Simulation results confirm that the ECME algorithm can efficiently obtain the ML based DOA estimate of each stochastic source. [ABSTRACT FROM AUTHOR]

Gaussian random fields (GRF) are a fundamental stochastic model for spatiotemporal data analysis. An essential ingredient of GRF is the covariance function that characterizes the joint Gaussian distribution of the field. Commonly used covariance functions give rise to fully dense and unstructured covariance matrices, for which required calculations are notoriously expensive to carry out for large data. In this work, we propose a construction of covariance functions that result in matrices with a hierarchical structure. Empowered by matrix algorithms that scale linearly with the matrix dimension, the hierarchical structure is proved to be efficient for a variety of random field computations, including sampling, kriging, and likelihood evaluation. Specifically, with n scattered sites, sampling and likelihood evaluation has an O(n) cost and kriging has an O ( log n) cost after preprocessing, particularly favorable for the kriging of an extremely large number of sites (e.g., predicting on more sites than observed). We demonstrate comprehensive numerical experiments to show the use of the constructed covariance functions and their appealing computation time. Numerical examples on a laptop include simulated data of size up to one million, as well as a climate data product with over two million observations. [ABSTRACT FROM AUTHOR]

Multistate transition models (MSTMs) are valuable tools depicting disease progression. However, due to the complexity of MSTMs, larger sample size and longer follow-up time in real-world data, the computation of statistical estimation and inference for MSTMs becomes challenging. A bounded Taylor series in Newton–Raphson procedure is proposed which leverages the uniformization technique to derive maximum likelihood estimates and corresponding covariance matrix. The proposed method, namely uniformization Taylor-bounded Newton–Raphson, is validated in three simulation studies, which demonstrate the accuracy in parameter estimation, the efficiency in computation time and robustness in terms of different situations. This method is also illustrated using a large electronic medical record data related to statin-induced side effects and discontinuation. [ABSTRACT FROM AUTHOR]

We consider the maximum likelihood estimation of a covariance matrix that is known to be Toeplitz. The corresponding optimization problem is nonconvex, and to compute a local minimizer we propose an efficient implementation of Newton's method. The cost per iteration of a straightforward implementation is of order O (n 4) , where n + 1 is the dimension of the covariance matrix. By exploiting fast Fourier transforms to assemble the gradient and Hessian we reduce the iteration cost to order O (n 3). Through extensive simulations we demonstrate that for direction-of-arrival estimation, the performance of MUSIC is significantly enhanced by using it together with the maximum likelihood Toeplitz covariance estimate. The simulations also demonstrate that our open-source implementation is orders of magnitude faster than two existing Toeplitz covariance estimators. • Maximum likelihood estimation of a Toeplitz covariance matrix can be done efficiently. • The Toeplitz maximum likelihood estimate significantly enhances MUSIC. • We provide an open-source implementation of our method. [ABSTRACT FROM AUTHOR]

Estimating the parameters of spatial models for large spatial datasets can be computationally challenging, as it involves repeated evaluation of sizable spatial covariance matrices. In this paper, we aim to develop Krylov subspace‐based methods that are computationally efficient for large spatial data. Specifically, we approximate the inverse and the log‐determinant of the spatial covariance matrix in the log‐likelihood function via conjugate gradient and stochastic Lanczos on a Krylov subspace. These methods reduce the computational complexity from O(N3) to O(N2logN) and O(NlogN) for dense and sparse matrices, respectively. Moreover, we quantify the difference between the approximated log‐likelihood function and the original log‐likelihood function and establish the consistency of parameter estimates. Simulation studies are conducted to examine the computational efficiency as well as the finite‐sample properties. For illustration, our methodology is applied to analyze a large dataset comprising LiDAR estimates of forest canopy height in western Alaska. [ABSTRACT FROM AUTHOR]

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This article deals with the problem of adaptive radar detection in a missing-data context, where the complete observations (i.e., downstream information loss mechanisms) are characterized by homogeneous Gaussian disturbance with an unknown but possibly structured covariance matrix. The detection problem, formulated as a composite hypothesis test, is tackled by resorting to suboptimal design strategies, leveraging the generalized likelihood ratio criterion demanding appropriate maximum likelihood estimates (MLEs) of the unknowns under both hypotheses. Capitalizing on some possible a priori knowledge about the interference covariance matrix structure, the optimization problems involved in the MLE computation are handled by employing the expectation–maximization (EM) algorithm or its expectation–conditional maximization and multicycle EM variants. At the analysis stage, the performance of the devised architectures is assessed both via Monte Carlo simulations and on measured data for some covariance matrix structures of practical interest. [ABSTRACT FROM AUTHOR]

This communication presents an efficient iterative approach for locating the near-field (NF) coherent sources. In each iteration, the covariance matrices only containing single source information are constructed by using alternating oblique projection. Then based on the principle of vector dot products, a new iterative direction-of-arrival (DOA) estimator is proposed. After the DOA of each separated signal is estimated, the paired ranges are obtained from the 1-D maximum likelihood (ML) estimator. The proposed algorithm avoids high-dimensional spectral searches, subspace extraction, and any preprocessing such as spatial smoothing, leading to low computational complexities and high estimation accuracy. Comparative simulations show the efficiency and merits of the proposed method. [ABSTRACT FROM AUTHOR]

Standard noise radars, as well as noise-type radars such as quantum two-mode squeezing (QTMS) radar, are characterized by a covariance matrix with a very specific structure. This matrix has four independent parameters: the amplitude of the received signal, the amplitude of the internal signal used for matched filtering, the correlation between the two signals, and the relative phase between them. In this article, we derive estimators for these four parameters using two techniques. The first is based on minimizing the Frobenius norm between the structured covariance matrix and the sample covariance matrix; the second is maximum likelihood (ML) parameter estimation. The two techniques yield the same estimators. We then give probability density functions (pdf’s) for all four estimators. Because some of these pdf’s are quite complicated, we also provide approximate pdf’s. Finally, we apply our results to the problem of target detection and derive expressions for the receiver operating characteristic (ROC) curves of two different noise radar detectors. In summary, our work gives a broad overview of the basic statistical behavior of noise-type radars. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of adaptive detection of a multichannel subspace signal in the presence of constrained interference, which is assumed to be orthogonal to the signal in the whitened space. We derive the gradient test, which is found to have the same form as the existing subspace-based generalized likelihood ratio test (SGLRT). In addition, we derive the statistical performance of the SGLRT in the presence of orthogonal interference for the case of signal mismatch, which means that the actual signal does not completely belong to the presumed signal subspace. Numerical examples are provided to verify the theoretical results. It is shown that both the orthogonal interference and signal mismatch can degrade the detection performance of the detectors. [ABSTRACT FROM AUTHOR]

Causal analysis plays a vital role in determining the underlying relationship among the variables in a system from the data. In this article, the sparse inverse covariance (SIC) estimation is coupled with likelihood score, and a two-step approach is proposed to address the problem of causal analysis. The estimation of SIC matrix for undirected sparse network reconstruction is performed with the $L_{0}$ -norm constraint in the framework of greedy sparse simplex (GSS) algorithm. Furthermore, the GSS algorithm is suitably modified to incorporate the additional constraint of positive semidefiniteness of the inverse covariance matrix. To determine the causal direction among the variables, the likelihood score is computed for the associated variables in the reconstructed network in the second step. The efficacy of the proposed approach for causal analysis is illustrated using numerical examples and an industrial application on prediction of flooding and weeping in a deethanizer column associated with a fluid catalytic cracking unit. From these studies, it is observed that the proposed approach is able to recover causal connections accurately in both cases. Furthermore, the probable reasons for the occurrence of flooding and weeping phenomena in an industrial deethanizer unit are also inferred from the identified causal network. [ABSTRACT FROM AUTHOR]

Space-time adaptive processing (STAP) is an important airborne radar technique used to improve target detection in environments of clutter and jammers. Effective STAP implementations are dependent on an accurate estimate of the space-time covariance matrix, which characterizes noise and interference in the radar signal. Inside-looking monostatic radar systems, the estimate based on secondary radar observations is rather straight forward as all the samples in secondary data can be argued to be from a single distribution, and the sample covariance can be used as an estimate of the space-time covariance matrix. However, in many other radar configurations, the vital underlying STAP training assumption that secondary data are identically distributed is violated, which implies that detection performance can be significantly degraded. This article develops a new method that can be used when secondary data do not share a common distribution due to geometry-induced range dependencies. This phenomenon is of particular concern in bistatic radar systems. We propose a model-based approach, where the distribution of noise and clutter for each range bin is parameterized by a set of scenario parameters. Using secondary data, the scenario parameters are estimated by maximizing the likelihood function. Based on the estimated scenario parameters, the STAP covariance estimate is formed for the cell under test. The presented method is compared with other state-of-the-art methods for bistatic radar STAP via numerical simulations. The simulations indicate that the presented method, with a proper initialization, yields an estimate of the STAP covariance matrix that significantly increases the signal-to-interference-plus-noise ratio compared to the other investigated methods. [ABSTRACT FROM AUTHOR]

Geostatistical modeling, one of the prime motivating applications for exascale computing, is a technique for predicting desired quantities from geographically distributed data, based on statistical models and optimization of parameters. Spatial data are assumed to possess properties of stationarity or non-stationarity via a kernel fitted to a covariance matrix. A primary workhorse of stationary spatial statistics is Gaussian maximum log-likelihood estimation (MLE), whose central data structure is a dense, symmetric positive definite covariance matrix of the dimension of the number of correlated observations. Two essential operations in MLE are the application of the inverse and evaluation of the determinant of the covariance matrix. These can be rendered through the Cholesky decomposition and triangular solution. In this contribution, we reduce the precision of weakly correlated locations to single- or half- precision based on distance. We thus exploit mathematical structure to migrate MLE to a three-precision approximation that takes advantage of contemporary architectures offering BLAS3-like operations in a single instruction that are extremely fast for reduced precision. We illustrate application-expected accuracy worthy of double-precision from a majority half-precision computation, in a context where uniform single-precision is by itself insufficient. In tackling the complexity and imbalance caused by the mixing of three precisions, we deploy the PaRSEC runtime system. PaRSEC delivers on-demand casting of precisions while orchestrating tasks and data movement in a multi-GPU distributed-memory environment within a tile-based Cholesky factorization. Application-expected accuracy is maintained while achieving up to $1.59X$ 1. 59 X by mixing FP64/FP32 operations on 1536 nodes of HAWK or 4096 nodes of Shaheen II, and up to $2.64X$ 2. 64 X by mixing FP64/FP32/FP16 operations on 128 nodes of Summit, relative to FP64-only operations. This translates into up to 4.5, 4.7, and 9.1 (mixed) PFlop/s sustained performance, respectively, demonstrating a synergistic combination of exascale architecture, dynamic runtime software, and algorithmic adaptation applied to challenging environmental problems. [ABSTRACT FROM AUTHOR]

This paper addresses adaptive detection of range spread targets in the presence of thermal noise, jammer, and clutter. After motivating the study, a set of clutter-free training (CFT) data is considered to assist radar detection in absence of conventional secondary data sharing the same spectral properties as the interference of the cells under test. To this end, a maximum likelihood (ML) estimate of the unknown parameters is derived under the alternative hypothesis by leveraging the primary data and the CFT data simultaneously. Subsequently, the ML estimate is used to design decision rules based on generalized likelihood ratio, complex parameter Wald, and complex parameter Gradient test criteria. Furthermore, conditions guaranteeing the constant false alarm rate (CFAR) property of the proposed detectors are discussed. At the analysis stage, numerical examples are presented to evaluate the effectiveness of the proposed detectors in comparison with other detection schemes available in the literature. [ABSTRACT FROM AUTHOR]

This article investigates regularized estimation of Kronecker-structured covariance matrices (CMs) for polarization radar in sea clutter scenarios where the data are assumed to follow the complex elliptically symmetric (CES) distributions with a Kronecker-structured CM. To obtain a well-conditioned estimate of the CM, we add penalty terms of Kullback–Leibler divergence to the negative log-likelihood function of the associated complex angular Gaussian (CAG) distribution. This is shown to be equivalent to regularizing Tyler’s fixed-point equations by shrinkage. A sufficient condition that the solution exists is discussed. An iterative algorithm is applied to solve the resulting fixed-point iterations, and its convergence is proven. In order to solve the critical problem of tuning the shrinkage factors, we then introduce two methods by exploiting oracle approximating shrinkage (OAS) and cross-validation (CV). The proposed estimator, referred to as the robust shrinkage Kronecker estimator (RSKE), is shown to achieve better performance compared with several existing methods when the training samples are limited. Simulations are conducted for validating the RSKE and demonstrating its high performance by using the IPIX 1998 real sea data. [ABSTRACT FROM AUTHOR]

This paper considers a massive random access problem in which a large number of sporadically active devices wish to communicate with a base station (BS) equipped with massive multiple-input multiple-output (MIMO) antennas. Each device is preassigned a unique signature sequence, and the BS identifies the active devices by detecting which sequences are transmitted. This device activity detection problem can be formulated as a maximum likelihood estimation (MLE) problem for which the sample covariance matrix of the received signal is a sufficient statistic. The goal of this paper is to characterize the feasible set of problem parameters under which this covariance based approach is able to successfully recover the device activities in the massive MIMO regime. Through an analysis of the asymptotic behaviors of MLE via its associated Fisher information matrix, this paper derives a necessary and sufficient condition on the Fisher information matrix to ensure a vanishing probability of detection error as the number of antennas goes to infinity, based on which a numerical phase transition analysis is obtained. This condition is also examined from a perspective of covariance matching, which relates the phase transition analysis to a recently derived scaling law. Further, we provide a characterization of the distribution of the estimation error in MLE, based on which the error probabilities in device activity detection can be accurately predicted. Finally, this paper studies a random access scheme with joint device activity and data detection and analyzes its performance in a similar way. [ABSTRACT FROM AUTHOR]

The geometric unscented Kalman filter (GUF) is an effective method for state estimation due to its advantages of high precision, reasonable efficiency, and good stability. In order to further improve the filtering performance of GUF, multiple rotation matrices are first designed by optimizing the rotation angles of their corresponding sampling points with maximum likelihood estimation, leading to a novel sampling strategy, namely, rotating geometric unscented sampling (RGUS). Then, applying RGUS to the GUF framework generates a rotating geometric unscented Kalman filter (RGUF). Since observable measurements are generally corrupted by non-Gaussian noise, RGUF may suffer from performance degradation due to the used minimum mean square error (MMSE) criterion. To improve the robustness of RGUF against non-Gaussian noises, we propose a novel maximum correntropy rotating geometric unscented Kalman filter (MCRGUF) using the maximum correntropy criterion (MCC). Finally, a Cramér–Rao lower bound (CRLB) of MCRGUF is introduced as a performance indicator. Simulations on three examples validate the high filtering accuracy and strong robustness of MCRGUF in the presence of non-Gaussian noise. [ABSTRACT FROM AUTHOR]

In the problem of multichannel signal detection, when it comes to the detector design criteria apart from the generalized likelihood ratio test, the traditional method is to cascade the real and imaginary parts of the parameters, and then substitute them into the real parameter statistics. This method is not succinct, and sometimes may be cumbersome and difficult to handle. Recently, a complex parameter Rao test was introduced by Kay and Zhu without the need of cascading the real and imaginary parts of the complex parameters when there is no nuisance parameter. Inspired by this work, we move a further step toward the complex parameter statistics of the Rao, Wald, gradient, and Durbin tests both with and without nuisance parameters, and derive the relationships between their real and complex parameter statistics. Moreover, for a special Fisher information matrix which often holds in practice, we derive a series of simple forms of the complex parameter statistics for the above four criteria, and discuss their application conditions in linear multivariate complex circular Gaussian distribution. Finally, several application examples are given to confirm the proposed schemes. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of adaptive moving target detection, embedded in homogeneous Gaussian noise with unknown covariance matrix, for frequency diverse array multiple-input multiple-output (FDA-MIMO) radar operating in interference-dominant environment. Unlike traditional adaptive moving target detectors that need training data to estimate the jamming covariance matrix (JCM), we present the Rao and Wald test based adaptive detector, which requires no training data. Furthermore, we proposed a two-stage approach to obtain maximum likelihood estimate (MLE) of the joint range, angle and Doppler, respectively. The corresponding signal-to-jamming-plus-noise ratio (SJNR) is derived to evaluate the FDA-MIMO radar performance. All proposed methods are validated by numerical results, which show that the proposed detector outperforms the existing generalized likelihood ratio test (GLRT). [ABSTRACT FROM AUTHOR]

Note. The best result in each experiment is highlighted in bold.The optimal solutions of many decision problems such as the Markowitz portfolio allocation and the linear discriminant analysis depend on the inverse covariance matrix of a Gaussian random vector. In "Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator," Nguyen, Kuhn, and Mohajerin Esfahani propose a distributionally robust inverse covariance estimator, obtained by robustifying the Gaussian maximum likelihood problem with a Wasserstein ambiguity set. In the absence of any prior structural information, the estimation problem has an analytical solution that is naturally interpreted as a nonlinear shrinkage estimator. Besides being invertible and well conditioned, the new shrinkage estimator is rotation equivariant and preserves the order of the eigenvalues of the sample covariance matrix. If there are sparsity constraints, which are typically encountered in Gaussian graphical models, the estimation problem can be solved using a sequential quadratic approximation algorithm. We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a p-dimensional Gaussian random vector from n independent samples. The proposed model minimizes the worst case (maximum) of Stein's loss across all normal reference distributions within a prescribed Wasserstein distance from the normal distribution characterized by the sample mean and the sample covariance matrix. We prove that this estimation problem is equivalent to a semidefinite program that is tractable in theory but beyond the reach of general-purpose solvers for practically relevant problem dimensions p. In the absence of any prior structural information, the estimation problem has an analytical solution that is naturally interpreted as a nonlinear shrinkage estimator. Besides being invertible and well conditioned even for p>n , the new shrinkage estimator is rotation equivariant and preserves the order of the eigenvalues of the sample covariance matrix. These desirable properties are not imposed ad hoc but emerge naturally from the underlying distributionally robust optimization model. Finally, we develop a sequential quadratic approximation algorithm for efficiently solving the general estimation problem subject to conditional independence constraints typically encountered in Gaussian graphical models. [ABSTRACT FROM AUTHOR]

In this work, we addressthe MIMO semi-blindchannel estimation problem. We propose an eigenvalue decomposition based technique to significantly reduce the dimensionality of the EM based algorithm when the imposed prior on the data is Gaussian, greatly lowering the computational complexity. In addition to that, we apply the Minimum Power Distortionless Response (MPDR) decoupling principle to derive a tractable EM algorithm that uses the actual discrete prior of the data symbols. Our results show that the proposed MPDR based algorithm has superior performance over other EM based algorithms in both low and high SNR regions. The results also show that a faster version of the algorithm can be obtained by initializing it using the eigenvalue decomposition based Gaussian algorithm. [ABSTRACT FROM AUTHOR]

This article proposes an enhanced coarray transformation model (EDCTM) and a mixed greedy maximum likelihood algorithm called list-based maximum likelihood orthogonal matching pursuit (LBML-OMP) for direction-of-arrival estimation with nonuniform linear arrays (NLAs). The proposed EDCTM approach obtains improved estimates when Khatri–Rao product-based models are used to generate difference coarrays under the assumption of uncorrelated sources. In the proposed LBML-OMP technique, for each iteration a set of candidates is generated based on the correlation-maximization between the dictionary and the residue vector. LBML-OMP then chooses the best candidate based on a reduced-complexity asymptotic maximum likelihood decision rule. Simulations show the improved results of EDCTM over existing approaches and that LBML-OMP outperforms existing sparse recovery algorithms as well as spatial smoothing multiple signal classification with NLAs. [ABSTRACT FROM AUTHOR]

We derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics when sampling from complex elliptical distributions. We then use this result to derive the variance-covariance matrix of the sample covariance matrix (SCM) as well as its theoretical mean squared error (MSE) when finite fourth-order moments exist. Finally, illustrative examples of the formulas are presented. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so degrades when the noise is heteroscedastic across samples, as occurs, e.g., when samples come from sources of heterogeneous quality. This paper develops a probabilistic PCA variant that estimates and accounts for this heterogeneity by incorporating it in the statistical model. Unlike in the homoscedastic setting, the resulting nonconvex optimization problem is not seemingly solved by singular value decomposition. This paper develops a heteroscedastic probabilistic PCA technique (HePPCAT) that uses efficient alternating maximization algorithms to jointly estimate both the underlying factors and the unknown noise variances. Simulation experiments illustrate the comparative speed of the algorithms, the benefit of accounting for heteroscedasticity, and the seemingly favorable optimization landscape of this problem. Real data experiments on environmental air quality data show that HePPCAT can give a better PCA estimate than techniques that do not account for heteroscedasticity. [ABSTRACT FROM AUTHOR]

We consider a modern radar system which has a general antenna array configuration consisting of primary channels with high-gain beams and reference channels with low-gain beams. A generalized likelihood ratio test (GLRT) was proposed in this context for target detection and direction of arrival estimation. However, the analytical performance of the GLRT has not been provided yet. In this paper, we derive finite-sum expressions for the probabilities of false alarm and detection. It is proven that the GLRT exhibits a constant false alarm rate against the overall interference disturbance covariance matrix. Numerical examples show that the detection performance of the GLRT may not necessarily improve when the number of sensors increases [ABSTRACT FROM AUTHOR]

In this paper, the uplink sparse code multiple access over universal filtered multicarrier (SCMA-UFMC) is studied. In SCMA-UFMC, each sub-band of UFMC is occupied by multiple users through SCMA. Note that the even-component of frequency domain (FD) received signal suffers from neither inter-sub-band interference nor inter-sub-carrier interference while the odd-component suffers from both. The message passing algorithm (MPA) is first employed to perform multiuser detection by utilizing only the even-component. Next, to improve the performance, the odd-component is further utilized. In this improvement, reliable estimates obtained by MPA over even-component are reconstructed and cancelled from odd-component, and then only a very small number of most-unreliable user data are refined by maximum likelihood method. Moreover, the union bound of the average symbol error probability (ASEP) of maximum likelihood detection using only even-component is derived, from which it is shown that ASEP is sub-band-independent. Finally, simulation results are given to demonstrate the performance of the proposed scheme and the effectiveness of the analytical ASEP result. [ABSTRACT FROM AUTHOR]

Gaussian graphical models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: the nodewise approach and the penalised likelihood maximisation. We demonstrate on synthetic data that, when the sample size is small, the two methods produce graphs with either too few or too many edges when compared to the real one. As a result, we propose a composite procedure that explores a family of graphs with a nodewise numerical scheme and selects a candidate among them with an overall likelihood criterion. We demonstrate that, when the number of observations is small, this selection method yields graphs closer to the truth and corresponding to distributions with better KL divergence with regards to the real distribution than the other two. Finally, we show the interest of our algorithm on two concrete cases: first on brain imaging data, then on biological nephrology data. In both cases our results are more in line with current knowledge in each field. [ABSTRACT FROM AUTHOR]

In this brief, we investigate the robust state estimation of nonlinear systems with heavy-tailed noise. Based on the fact that the multivariate Laplace (ML) distribution has heavier tails than Gaussian distribution but is only determined by its mean and covariance, we utilize the ML distribution to model the heavy-tailed measurement noise. Based on the Gaussian mixture form of ML distribution, the system state and the covariance of ML distribution are inferred by variational Bayesian method, and then a closed recursive robust nonlinear Kalman filter is obtained with the nonlinear integrations calculated by numerical integration methods. Simulation results demonstrate that the proposed algorithm is insensitive to its free parameters and can obtain better estimation accuracy than related robust algorithms. [ABSTRACT FROM AUTHOR]

In this paper we present properties of an algorithm to determine the maximum likelihood estimators of the covariance matrix when two processes jointly affect the observations. Additionally, one process is partially modeled by a compound symmetry structure. We perform a simulation study of the properties of an iteratively determined estimator of the covariance matrix. [ABSTRACT FROM AUTHOR]

This paper addresses the source location problem by using time-difference-of-arrival (TDOA) measurements. The two-stage weighted least squares (TWLS) algorithm has been widely used in the TDOA location. However, the estimation accuracy of the source location is poor and the bias is significant when the measurement noise is large. Owing to the nonlinear nature of the system model, we reformulate the localization problem as a constrained weighted least squares problem and derive the theoretical bias of the source location estimate from the maximum-likelihood (ML) estimation. To reduce the location bias and improve location accuracy, a novel bias-reduced method is developed based on an iterative constrained weighted least squares algorithm. The new method imposes a set of linear equality constraints instead of the quadratic constraints to suppress the bias. Numerical simulations demonstrate the significant performance improvement of the proposed method over the traditional methods. The bias is reduced significantly and the Cramér–Rao lower bound accuracy can also be achieved. [ABSTRACT FROM AUTHOR]

Detection of cyclostationary (CS) signals has been addressed by means of generalized likelihood ratio test criteria. However, an accurate maximum likelihood estimator requires the estimation of cycle period (CP) as a priori information, which has not yet been correctly addressed in the literature. In this correspondence, an estimator of CP is devised under the information theoretic criterion(ITC) framework for long observation regime. In particular, we formulate asymptotic log-likelihood function in discrete frequency domain. From the evidence that direct implementation of ITC leads to a high probability of CP overestimation, we reformulate ITC by Bayesian information criterion (BIC), and derive an accurate penalty function. The proposed BIC variant appears to be consistent as signal-to-noise ratio increases. Numerical simulations corroborate the feasibility of the proposed estimator and show its superiority over state-of-the-art schemes. [ABSTRACT FROM AUTHOR]

This paper provides a precise error analysis for the maximum likelihood estimate $\hat {\textit a}_{\text {ML}}({\textit u}_{1}^{\textit n})$ of the parameter ${\textit a}$ given samples ${\textit u}_{1}^{\textit n} = ({\textit u}_{1}, \ldots, {\textit u}_{\textit n})'$ drawn from a nonstationary Gauss-Markov process ${\textit U}_{\textit i} = {\textit a} {\textit U}_{\textit i-1} + {\textit Z}_{\textit i},\,\,{\textit i}\geq 1$ , where ${\textit U}_{0} = 0$ , ${\textit a}> 1$ , and ${\textit Z}_{\textit i}$ ’s are independent Gaussian random variables with zero mean and variance $\sigma ^{2}$. We show a tight nonasymptotic exponentially decaying bound on the tail probability of the estimation error. Unlike previous works, our bound is tight already for a sample size of the order of hundreds. We apply the new estimation bound to find the dispersion for lossy compression of nonstationary Gauss-Markov sources. We show that the dispersion is given by the same integral formula that we derived previously for the asymptotically stationary Gauss-Markov sources, i.e., $|{\textit a}| < 1$. New ideas in the nonstationary case include separately bounding the maximum eigenvalue (which scales exponentially) and the other eigenvalues (which are bounded by constants that depend only on a) of the covariance matrix of the source sequence, and new techniques in the derivation of our estimation error bound. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of estimating the location and velocity of a moving source using a distributed passive radar sensor network. We first derive the maximum likelihood estimator (MLE) using direct sensor observations, when the source signal is unknown and modeled as a deterministic process. Since the MLE obtains the source location and velocity estimates through a search process over the parameter space and is quite computationally intensive, we also developed an efficient algorithm to solve the problem using a two-step approach. The first step finds the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimates for each sensor with respect to a reference sensor by using a two-dimensional fast Fourier transform and interpolation, while the second step employs an iterative reweighted least square (IRLS) approach with a varying weighting matrix to determine the source location and velocity. To benchmark the performance of the proposed methods, a constrained Cramér–Rao bound (CRB) for the considered source localization problem is derived. Numerical results show that the IRLS approach has a lower signal-to-noise ratio threshold phenomenon compared with several recent TDOA/FDOA-based methods, especially when the source is considerably farther away from some sensors than others, creating a larger disparity in the quality of sensors observations. [ABSTRACT FROM AUTHOR]

A blind Direction-of-Arrivals (DOAs)estimate of narrowband signals for Acoustic Vector-Sensor (AVS) arrays is proposed. Building upon the special structure of the signal measured by an AVS, we show that the covariance matrix of all the received signals from the array admits a natural low-rank 4-way tensor representation. Thus, rather than estimating the DOAs directly from the raw data, our estimate arises from the unique parametric Canonical Polyadic Decomposition (CPD) of the observations’ Second-Order Statistics (SOSs) tensor. By exploiting results from fundamental statistics and the recently re-emerging tensor theory, we derive a consistent blind CPD-based DOAs estimate without prior assumptions on the array configuration. We show that this estimate is a solution to an equivalent approximate joint diagonalization problem, and propose an ad hoc iterative solution. Additionally, we derive the Cramér-Rao lower bound for Gaussian signals, and use it to derive the iterative Fisher scoring algorithm for the computation of the Maximum Likelihood Estimate (MLE) in this particular signal model. We then show that the MLE for the Gaussian model can in fact be used to obtain improved DOAs estimates for non-Gaussian signals as well (under mild conditions), which are optimal under the Kullback-Leibler divergence covariance fitting criterion, harnessing additional information encapsulated in the SOSs. Our analytical results are corroborated by simulation experiments in various scenarios, which also demonstrate the considerable improved accuracy w.r.t. a previously proposed state-of-the-art blind DOAs estimate for AVS arrays, reducing the resulting root mean squared error by up to more than an order of magnitude. [ABSTRACT FROM AUTHOR]

A highly popular regularized (shrinkage) covariance matrix estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward the grand mean of the eigenvalues of the SCM. In this paper, a more general approach is considered in which the SCM is replaced by an M-estimator of scatter matrix and a fully automatic data adaptive method to compute the optimal shrinkage parameter with minimum mean squared error is proposed. Our approach permits the use of any weight function such as Gaussian, Huber's, Tyler's, or t weight functions, all of which are commonly used in M-estimation framework. Our simulation examples illustrate that shrinkage M-estimators based on the proposed optimal tuning combined with robust weight function do not loose in performance to shrinkage SCM estimator when the data is Gaussian, but provide significantly improved performance when the data is sampled from an unspecified heavy-tailed elliptically symmetric distribution. Also, real-world and synthetic stock market data validate the performance of the proposed method in practical applications. [ABSTRACT FROM AUTHOR]

Synthetic aperture radar (SAR) interferometry (InSAR) has shown great potential in the monitoring of Earth’s surface and detection of the possible slow temporal deformations. Within the framework of multibaseline SAR interferometry, the availability of multiple interferograms obtained from multipass satellite observations can significantly improve the accuracy of the estimated target parameters, i.e., the residual height and the mean deformation velocity. The parameters can be estimated in the maximum likelihood (ML) sense and through the data covariance matrix. However, the presence of artifact and outliers may impair the parameter estimation, specifically when the candidate cells are subject to temporal decorrelation and atmospheric phase noise effects. In this letter, the exploitation of contextual spatial information is proposed to reduce the possible ambiguity and improve the accuracy of ML-based parameter estimation. The proposed approach adds a regularization term (or a constraint) to the ML’s model in order to include the information about the scene velocity variation. Hence, the resulted nonconvex optimization is resolved using the graph-cut concept. The method is evaluated using the simulated and two real data sets acquired by Constellation of Small Satellites for Mediterranean basin Observation (COSMO-SkyMed) and Sentinel-1A sensors over Tehran, Iran; and the results are validated using the global positioning system-based measurements. [ABSTRACT FROM AUTHOR]

We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the cardinality constrained likelihood problem to certifiable optimality. The approach uses techniques from mixed-integer optimization and convex optimization, and provides a high-quality solution with a guarantee on its suboptimality, even if the algorithm is terminated early. Using a variety of synthetic and real datasets, we demonstrate that our approach can solve problems where the dimension of the inverse covariance matrix is up to 1000 s. We also demonstrate that our approach produces significantly sparser solutions than Glasso and other popular learning procedures, makes less false discoveries, while still maintaining state-of-the-art accuracy. [ABSTRACT FROM AUTHOR]

Modelling the covariance structure of multivariate longitudinal data is more challenging than its univariate counterpart, owing to the complex correlated structure among multiple responses. Furthermore, there are little methods focusing on the robustness of estimating the corresponding correlation matrix. In this paper, we propose an alternative Cholesky block decomposition (ACBD) for the covariance matrix of multivariate longitudinal data. The new unconstrained parameterization is capable to automatically eliminate the positive definiteness constraint of the covariance matrix and robustly estimate the correlation matrix with respect to the model misspecifications of the nested prediction error covariance matrices. The entries of the new decomposition are modelled by regression models, and the maximum likelihood estimators of the regression parameters in joint mean–covariance models are computed by a quasi-Fisher iterative algorithm. The resulting estimators are shown to be consistent and asymptotically normal. Simulations and real data analysis illustrate that the new method performs well. [ABSTRACT FROM AUTHOR]

This paper presents a joint synchronization and localization algorithm based on the time-difference-of-arrival (TDOA) for asynchronous Wireless Sensor Networks (WSNs), where the positions of anchors are relatively fixed but unknown. To obtain time synchronization and anchor positions, each anchor broadcasts signals periodically, while other anchors receive the broadcasting signals and stamp times-of-arrival (TOAs). Based on these TOAs, we estimate the internal clock parameters and anchor positions in three steps: least square estimation (LSE) of the relative clock skew based on TDOAs, maximum likelihood localization (MLE) of anchors using biased time of flight (TOF), and LSE estimation of relative clock offsets. Anchor pairs stamp the TDOAs when a tag (a wireless sensor node that requires localization) transmits a signal. The biased TDOAs, due to asynchronous local clocks, are compensated by relative clock offset estimation. The maximum likelihood estimation is used for the tag localization based on the Gaussian noise model. We evaluate the performance of the proposed synchronization and localization algorithm using the Cramér-Rao lower bound (CRLB). Simulations are carried out to verify the validity of the algorithm in this paper. [ABSTRACT FROM AUTHOR]

In time-difference-of-arrival (TDOA) localization systems, the TDOA measurements and range-difference-of-arrival (RDOA) values can be used interchangeably if the signal propagation speed is known. In some scenarios like underwater acoustic localization, the signal propagation speed is often unknown. This letter addresses joint source location and propagation speed (unknown) estimation using signal TDOA measurements in the presence of sensor position errors. The maximum likelihood estimator (MLE) for this problem is optimal, but it requires a suitable initial value to obtain the global solution or needs exhaustive grid search. We develop a semidefinite programming (SDP) based localization algorithm to effectively solve the MLE problem. The accuracy of the proposed algorithm is close to the Cramér-Rao lower bound and has a superior performance than existing solutions. [ABSTRACT FROM AUTHOR]

This paper addresses the adaptive target detection problem in Gaussian clutter edges. We employ a two-step generalized likelihood ratio test (GLRT) for the detection problem. Our main contribution lies in devising an iterative algorithm in the second step of the GLRT to obtain the maximum likelihood estimation of the unknown clutter-plus-noise covariance matrix, with all available secondary samples in the clutter edge (including the homogeneous and heterogeneous ones). We prove that the proposed iterative algorithm has guaranteed convergence of the objective value. At the analysis stage, we evaluate the performance of the proposed detector and show the superiority over its counterparts. [ABSTRACT FROM AUTHOR]

In this study, a constant false alarm rate (CFAR) decision scheme is devised for frequency diversity multiple‐input–multiple‐output (MIMO) radar. Under the assumption that there exists not only the unstructured disturbance but also the structured interference, a double threshold detector (DT‐MGLRT) based on the modified generalised likelihood ratio test (MGLRT) algorithm is proposed, of which the first stage deals with the unknown parameters and the second stage determines the final decision. It is proved that the proposed detector possesses a CFAR with respect not only to the unknown spectral properties of the unstructured disturbance but also to the structured interference distribution. Finally, some experiment results indicate that the proposed detection algorithm has 2 dB signal‐to‐interference‐plus‐noise power ratio improvement on average in detection performance at a low computation and communication cost over conventional detection algorithms. [ABSTRACT FROM AUTHOR]

A central machine is interested in estimating the underlying structure of a sparse Gaussian Graphical Model (GGM) from a dataset distributed across multiple local machines. The local machines can communicate with the central machine through a wireless multiple access channel. In this paper, we are interested in designing effective strategies where reliable learning is feasible under power and bandwidth limitations. Two approaches are proposed: Signs and Uncoded methods. In the Signs method, the local machines quantize their data into binary vectors and an optimal channel coding scheme is used to reliably send the vectors to the central machine where the structure is learned from the received data. In the Uncoded method, data symbols are scaled and transmitted through the channel. The central machine uses the received noisy symbols to recover the structure. Theoretical results show that both methods can recover the structure with high probability for a large enough sample size. Experimental results indicate the superiority of the Signs method over the Uncoded method under several circumstances. [ABSTRACT FROM AUTHOR]

This work presents a generalization of classical factor analysis (FA). Each of $M$ channels carries measurements that share factors with all other channels, but also contains factors that are unique to the channel. Furthermore, each channel carries an additive noise whose covariance is diagonal, as is usual in factor analysis, but is otherwise unknown. This leads to a problem of multi-channel factor analysis with a specially structured covariance model consisting of shared low-rank components, unique low-rank components, and diagonal components. Under a multivariate normal model for the factors and the noises, a maximum likelihood (ML) method is presented for identifying the covariance model, thereby recovering the loading matrices and factors for the shared and unique components in each of the $M$ multiple-input multiple-output (MIMO) channels. The method consists of a three-step cyclic alternating optimization, which can be framed as a block minorization-maximization (BMM) algorithm. Interestingly, the three steps have closed-form solutions and the convergence of the algorithm to a stationary point is ensured. Numerical results demonstrate the performance of the proposed algorithm and its application to passive radar. [ABSTRACT FROM AUTHOR]

Location awareness is becoming essential for various wireless applications, and cooperation among nodes is highly beneficial for localization performance. However, the existing cooperative localization (CL) algorithms may suffer from major performance loss when applied to the mobile environments with fast changing network topologies. In this paper, we extend the joint spatial and temporal cooperation (JSTC) model to the range-based localization problem. Based on mobility constraints and the maximum likelihood estimation (MLE) criterion, we formulate the CL problems in both centralized and distributed cases. Different from the conventional distributed CL problems, the proposed one takes the transmission delay and the cooperation among multi-hop nodes into account, which is more practical. Moreover, the performance limits of the considered problems are investigated by the Cramér-Rao lower bound (CRLB). Finally, these two problems are solved by the Sequential Quadratic Programming (SQP) algorithm. Both simulation and experiment results show that the extended JSTC model can effectively improve the localization reliability and accuracy. [ABSTRACT FROM AUTHOR]

Common principal components (CPCs) are often estimated using maximum likelihood estimation through an algorithm called the Flury–Gautschi (FG) Algorithm. Krzanowski proposed a simpler estimation method via a principal component analysis of a weighted sum of the sample covariance matrices. These methods are compared for real-world datasets and in a Monte Carlo simulation. The real-world data is used to compare the selection of a common eigenvector model and the estimated coefficients. The simulation study investigates how the accuracy of the methods is affected by autocorrelation, the number of covariance matrices, dimensions, and sample sizes for multivariate normal and chi-square distributed data. The findings in this article support the use of Krzanowski's method in situations where the CPC assumption is appropriate. [ABSTRACT FROM AUTHOR]