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Bayesian filtering is a statistical approach that naturally appears in many signal processing problems. Ranging from Kalman filter to particle filters, there is a plethora of alternatives depending on model assumptions. With the exception of very few tractable cases, one has to resort to suboptimal methods due to the inability to analytically compute the Bayesian recursion in general dynamical systems. This is why it has attracted the attention of many researchers in order to develop efficient algorithms to implement it. We focus our interest into a recently developed algorithm known as the Quadrature Kalman filter (QKF). Under the Gaussian assumption, the QKF can tackle arbitrary nonlinearities by resorting to the Gauss-Hermite quadrature rules. However, its complexity increases exponentially with the state-space dimension. In this paper we study a complexity reduction technique for the QKF based on the partitioning of the state-space, referred to as the Multiple QKF. We prove that partitioning schemes can effectively be used to reduce the curse of dimensionality in the QKF. Simulation results are also provided to show that a nearly-optimal performance can be attained, while drastically reducing the computational complexity with respect to state-of-the-art algorithms that are able to deal with such nonlinear filtering problems. [ABSTRACT FROM PUBLISHER]

This work proposes a new tensor-based approach to solve the problem of blind identification of underdetermined mixtures of complex-valued sources exploiting the cumulant generating function (CGF) of the observations. We show that a collection of second-order derivatives of the CGF of the observations can be stored in a third-order tensor following a constrained factor (CONFAC) decomposition with known constrained structure. In order to increase the diversity, we combine three derivative types into an extended third-order CONFAC decomposition. A detailed uniqueness study of this decomposition is provided, from which easy-to-check sufficient conditions ensuring the essential uniqueness of the mixing matrix are obtained. From an algorithmic viewpoint, we develop a CONFAC-based enhanced line search (CONFAC-ELS) method to be used with an alternating least squares estimation procedure for accelerated convergence, and also analyze the numerical complexities of two CONFAC-based algorithms (namely, CONFAC-ALS and CONFAC-ELS) in comparison with the Levenberg-Marquardt (LM)-based algorithm recently derived to solve the same problem. Simulation results compare the proposed approach with some higher-order methods. Our results also corroborate the advantages of the CONFAC-based approach over the competing LM-based approach in terms of performance and computational complexity. [ABSTRACT FROM PUBLISHER]

Estimation of the covariance matrix and its inverse, the precision matrix, in high-dimensional situations is of great interest in many applications. In this paper, we focus on the estimation of a class of sparse precision matrices which are assumed to be approximately inversely closed for the case that the dimensionality p can be much larger than the sample size n, which is fundamentally different from the classical case that p < n. Different in nature from state-of-the-art methods that are based on penalized likelihood maximization or constrained error minimization, based on the truncated Neumann series representation, we propose a computationally efficient precision matrix estimator that has a computational complexity of O(p^3). We prove that the proposed estimator is consistent in probability and in L^2 under the spectral norm. Moreover, its convergence is shown to be rate-optimal in the sense of minimax risk. We further prove that the proposed estimator is model selection consistent by establishing a convergence result under the entry-wise \infty-norm. Simulations demonstrate the encouraging finite sample size performance and computational advantage of the proposed estimator. The proposed estimator is also applied to a real breast cancer data and shown to outperform existing precision matrix estimators. [ABSTRACT FROM AUTHOR]

We consider the problem of sensor selection for event detection in wireless sensor networks (WSNs). We want to choose a subset of p out of n sensors that yields the best detection performance. As the sensor selection optimality criteria, we propose the Kullback–Leibler and Chernoff distances between the distributions of the selected measurements under the two hypothesis. We formulate the maxmin robust sensor selection problem to cope with the uncertainties in distribution means. We prove that the sensor selection problem is NP hard, for both Kullback–Leibler and Chernoff criteria. To (sub)optimally solve the sensor selection problem, we propose an algorithm of affordable complexity. Extensive numerical simulations on moderate size problem instances (when the optimum by exhaustive search is feasible to compute) demonstrate the algorithm's near optimality in a very large portion of problem instances. For larger problems, extensive simulations demonstrate that our algorithm outperforms random searches, once an upper bound on computational time is set. We corroborate numerically the validity of the Kullback–Leibler and Chernoff sensor selection criteria, by showing that they lead to sensor selections nearly optimal both in the Neyman–Pearson and Bayes sense. [ABSTRACT FROM PUBLISHER]

This paper proposes a new paradigm for adaptive Volterra filtering using a time-variant size of the quadratic kernel memory in order to optimally identify any unknown transversal second-order nonlinear system. To this end, competing Volterra structures of different sizes are employed in a hierarchical combination scheme so as to find the best configuration of the second-order kernel memory, using the already known diagonal-coordinate representation. The length and number of required quadratic kernel diagonals can be concurrently estimated by monitoring the combination performance. Subsequently, the memory size of the involved models is dynamically increased or decreased, following a set of intuitive rules. Since this automatic memory adaptation is performed along with the coefficient updates, an efficient Volterra filter is realized, offering great flexibility and minimizing the risk of under- or overmodeling any given quadratic nonlinearity. Besides the straightforward scheme, a simplified version is presented, greatly reducing the algorithmic demands. This efficient version is based on a virtualization of the competing Volterra filters by jointly using common coefficients and hence exhibits a computational complexity suitable for practical implementations. The robust estimation performance of the approach is demonstrated by various examples for a nonlinear acoustic echo cancellation scenario, involving stationary noise, real speech signals and realistic Volterra kernels. [ABSTRACT FROM AUTHOR]

In this correspondence, we focus on blind estimation of the chip duration of time-hopping signals by introducing a cost function based on time-of-arrival (ToA) folding over multiple observation sets. An optimization algorithm that takes advantage of the highly oscillatory behavior in the nearby of the global minimum is proposed and a performance bound for the chip time estimate is derived. The pertinence of our approach is shown through numerical results, considering alternative methods like periodogram and separable least squares line search. The proposed technique enables a good tradeoff between statistical accuracy and computational complexity. [ABSTRACT FROM AUTHOR]