Sharif Digital Repository

In this article, we investigate the limiting spectral distribution of the sample covariance matrix (SCM) of weighted/windowed complex data. We use recent advances in random matrix theory and describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We obtain an approximation for the spectral distribution of the SCM obtained from windowed data. We also determine a condition on the coefficients of the window, under which the fragmentation of the support of noise eigenvalues can be avoided, in the noise-only data case. For the commonly used exponential window, we derive an explicit expression for the l.s.d of the noise-only data. In addition, we present a method to... 

In this paper, a novel nonlinear joint dynamical model is presented, which is based on a set of coupled ordinary differential equations of motion and a Gaussian mixture model representation of pulsatile cardiovascular (CV) signals. In the proposed framework, the joint interdependences of CV signals are incorporated by assuming a unique angular frequency that controls the limit cycle of the heart rate. Moreover, the time consequence of CV signals is controlled by the same phase parameter that results in the space dimensionality reduction. These joint equations together with linear assignments to observation are further used in the Kalman filter structure for estimation and tracking. Moreover,... 

In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central machine is then responsible for learning the structure based on received messages from the other nodes. We present a set of communication-efficient strategies, which are theoretically proved to convey sufficient information for reliable learning of the structure. In particular, our analyses show that even if each machine sends only the signs of its local data samples to the central node, the tree structure can still be recovered with high accuracy. Our... 

In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central machine is then responsible for learning the structure based on received messages from the other nodes. We present a set of communication-efficient strategies, which are theoretically proved to convey sufficient information for reliable learning of the structure. In particular, our analyses show that even if each machine sends only the signs of its local data samples to the central node, the tree structure can still be recovered with high accuracy. Our... 

In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central machine is then responsible for learning the structure based on received messages from the other nodes. We present a set of communication-efficient strategies, which are theoretically proved to convey sufficient information for reliable learning of the structure. In particular, our analyses show that even if each machine sends only the signs of its local data samples to the central node, the tree structure can still be recovered with high accuracy. Our... 

This paper introduces a new method for improving the inertial navigation system errors using information provided by the camera. An unscented Kalman filter is used for integrating the inertial measurement unit data with the features’ constraints extracted from the camera’s image. The constraints, in our approach, comprise epipolar geometry of two consecutive images with more than 65% coverage. Tracking down a known feature in two consecutive images results in emergence of stochastic epipolar constraint. It emerges in the form of an implicit measurement equation of the Kalman filter. Correctly matching features of the two images is necessary for reducing the navigation system errors because... 

In this paper we consider the problem of improving unknown node localization by using differential received signal strength (DRSS). Many existing localization approaches, especially those using the least squares methods, either ignore nonlinear constraint among model parameters or utilize them inefficiently. In this paper, we develop four DRSS-based localization methods by utilizing different combinations of covariance and weight matrices. Each method constructs a two-stage procedure. During the first stage, an initial coarse position estimate is obtained. The second stage results the refined localization by accounting for nonlinear dependency among estimator variables. The proper choice... 

Contamination of ictal Electroencephalogram (EEG) signals by muscle artifacts is one of the critical issues related to clinically diagnosing seizure. Over the past decade, several methods have been proposed in time, frequency and time-frequency domain to accurately isolate ictal EEG activities from artifacts. Among denoising approaches Canonical Correlation Analysis (CCA) and Independent Component Analysis (ICA) are widely used. Denoising based on Generalized EigenValue Decomposition (GEVD) is one of the Semi-Blind Source Separation (SBSS) methods which has been recently proposed. In the GEVD-based method, a couple of time-frequency covariance matrices are used. These time-frequency (TF)... 

Human motion tracking has many applications in biomedical and industrial services. Low-cost inertial/magnetic sensors are widely used in human motion capture systems to obtain the orientation of the human body segments. In this paper, we have presented a quaternion-based unscented Kalman filter algorithm to fuse inertial/magnetic sensors measurements for tracking human arm movements. In order to have a better estimation of the orientation of the forearm and the upper arm, a constraint equation was developed based on the relative velocity of the elbow joint with respect to the inertial sensors attached to the forearm and the upper arm. Also to compensate for fast body motions, we adapted the... 

Human motion tracking has many applications in biomedical and industrial services. Low-cost inertial/magnetic sensors are widely used in human motion capture systems to obtain the orientation of the human body segments. In this paper, we have presented a quaternion-based unscented Kalman filter algorithm to fuse inertial/magnetic sensors measurements for tracking human arm movements. In order to have a better estimation of the orientation of the forearm and the upper arm, a constraint equation was developed based on the relative velocity of the elbow joint with respect to the inertial sensors attached to the forearm and the upper arm. Also to compensate for fast body motions, we adapted the... 

Identification of modulation and space-time block code (STBC) is an important task of receivers in applications such as military, civilian, and commercial communications. Here, we consider multiple-input multiple-output (MIMO) systems. We propose two methods for STBC identification when the modulation is known. We also introduce a method for joint identification of code and modulation. Additionally, we present an enhanced zero-forcing (ZF) equaliser to improve the separation between the features of different classes. Higher order cumulants are used as the statistical features. In the first method of STBC identification, after the proposed equalisation, received data samples are segmented,... 

This paper presents a hierarchical Bayesian modeling framework for the uncertainty quantification in modal identification of linear dynamical systems using multiple vibration data sets. This novel framework integrates the state-of-the-art Bayesian formulations into a hierarchical setting aiming to capture both the identification precision and the variability prompted due to modeling errors. Such developments have been absent from the modal identification literature, sustained as a long-standing problem at the research spotlight. Central to this framework is a Gaussian hyper probability model, whose mean and covariance matrix are unknown, encapsulating the uncertainty of the modal parameters.... 

In this paper, statistical speech enhancement using hidden Markov model (HMM) is studied and new techniques for applying non-Gaussian distributions are proposed. The superiority of using non-Gaussian distributions in online adaptive noise suppression algorithms has been proven; however, in this study, this approach is formulated in an HMM-based mean-square error estimator (MMSE) estimator in which a priori models are trained in an off-line manner. In addition, an analytical study of using different distributions other than autoregressive (AR) Gaussian distribution, such as Laplace, is presented in order to construct an accurate HMM as a priori model for discrete Fourier transform and... 

In this paper a novel method called Extended Two-Dimensional PCA (E2DPCA) is proposed which is an extension to the original 2DPCA. We state that the covariance matrix of 2DPCA is equivalent to the average of the main diagonal of the covariance matrix of PCA. This implies that 2DPCA eliminates some covariance information that can be useful for recognition. E2DPCA instead of just using the main diagonal considers a radius of r diagonals around it and expands the averaging so as to include the covariance information within those diagonals. The parameter r unifies PCA and 2DPCA. r=1 produces the covariance of 2DPCA, r=n that of PCA. Hence, by controlling r it is possible to control the... 

Gaussian approximation filters have increasingly been developed to enhance the accuracy of attitude estimation in space missions. The effective employment of these algorithms demands accurate knowledge of system dynamics and measurement models, as well as their noise characteristics, which are usually unavailable or unreliable. An innovation-based adaptive filtering approach has been adopted as a solution to this problem; however, it exhibits two major challenges, namely appropriate window size selection and guaranteed assurance of positive definiteness for the estimated noise covariance matrices. The current work presents two novel techniques based on relative entropy and confidence level... 

This paper presents an improved stochastic simulation method for calculating current dependent energy losses in distribution networks. The method is based on power load curves and integrates the stochastic nature of the load curves with power and voltage covariance matrices. The method reduces calculation effort using the factor analysis of covariance matrices and provides a few quantities needed to calculate energy losses. The method has no limitation for network configuration and gives accurate results several times faster than other existing methods. Therefore, it is appropriate for considering losses in optimization and decision making purposes in operating and planning of distribution... 

In this paper, we consider an exponentially windowed sample covariance matrix (EWSCM) and propose an improved estimator for its eigenvalues. We use new advances in random matrix theory, which describe the limiting spectral distribution of the large dimensional doubly correlated Wishart matrices to find the support and distribution of the eigenvalues of the EWSCM. We then employ the complex integration and residue theorem to design an estimator for the eigenvalues, which satisfies the cluster separability condition, assuming that the eigenvalue multiplicities are known. We show that the proposed estimator is consistent in the asymptotic regime and has good performance in finite sample size... 

This letter investigates the problem of threedimensional (3-D) target localization in multiple-input multipleoutput (MIMO) radars with distributed antennas, using hybrid timedelay (TD) and angle of arrival (AOA) measurements. We propose a closed-form positioning method based on weighted least squares (WLS) estimation. The proposed estimator is shown theoretically to achieve the Cramer-Rao lower bound (CRLB) under mild noise conditions. Numerical simulations also verify the theoretical developments. IEEE  

An approach based on unitary transformation for the problem of estimating the number of signals is proposed in this study. Among the information theoretic criteria, the authors focus on the conventional Bayesian information criterion (BIC) in the presence of a uniform linear array. The sample covariance matrix of this array is transformed into the real symmetric one by using a unitary transformation. This real symmetric matrix has real eigenvalues and eigenvectors. Therefore its eigenvalue decomposition needs only real computations. Since the eigenvalues of this real symmetric matrix are equal to the eigenvalues of the sample covariance matrix, by replacing them in BIC formula, the term... 

Optomechanical and electromechanical cavities have been widely used in quantum memories and quantum transducers. We theoretically investigate the robustness of optomechanical and electromechanical quantum memories against the noise of the control laser. By solving the Langevin equations and using the covariance matrix formalism in the presence of laser noise, the storing fidelity of Gaussian states is obtained. It is shown that the destructive effect of phase noise is more significant in higher values of coupling laser amplitude and optomechanical coupling strength G. However, by further increasing the coupling coefficient, the interaction time between photons and phonons decreases below the...