Efficient calculation of sensor utility and sensor removal in wireless sensor networks for adaptive signal estimation and beamforming

Wireless sensor networks are often deployed over a large area of interest and therefore the quality of the sensor signals may vary significantly across the different sensors. In this case, it is useful to have a measure for the importance or the so-called "utility" of each sensor, e.g., for sensor subset selection, resource allocation or topology selection. In this paper, we consider the efficient calculation of sensor utility measures for four different signal estimation or beamforming algorithms in an adaptive context. We use the definition of sensor utility as the increase in cost (e.g., mean-squared error) when the sensor is removed from the estimation procedure. Since each possible sensor removal corresponds to a new estimation problem (involving less sensors), calculating the sensor utilities would require a continuous updating of different signal estimators (where is the number of sensors), increasing computational complexity and memory usage by a factor. However, we derive formulas to efficiently calculate all sensor utilities with hardly any increase in memory usage and computational complexity compared to the signal estimation algorithm already in place. When applied in adaptive signal estimation algorithms, this allows for on-line tracking of all the sensor utilities at almost no additional cost. Furthermore, we derive efficient formulas for sensor removal, i.e., for updating the signal estimator coefficients when a sensor is removed, e.g., due to a failure in the wireless link or when its utility is too low. We provide a complexity evaluation of the derived formulas, and demonstrate the significant reduction in computational complexity compared to straightforward implementations

Kontextsensitive Modellhierarchien für Quantifizierung der höherdimensionalen Unsicherheit

We formulate four novel context-aware algorithms based on model hierarchies aimed to enable an efficient quantification of uncertainty in complex, computationally expensive problems, such as fluid-structure interaction and plasma microinstability simulations. Our results show that our algorithms are more efficient than standard approaches and that they are able to cope with the challenges of quantifying uncertainty in higher-dimensional, complex problems.Wir formulieren vier kontextsensitive Algorithmen auf der Grundlage von Modellhierarchien um eine effiziente Quantifizierung der Unsicherheit bei komplexen, rechenintensiven Problemen zu ermöglichen, wie Fluid-Struktur-Wechselwirkungs- und Plasma-Mikroinstabilitätssimulationen. Unsere Ergebnisse zeigen, dass unsere Algorithmen effizienter als Standardansätze sind und die Herausforderungen der Quantifizierung der Unsicherheit in höherdimensionalen, komplexen Problemen bewältigen können

Diffusion Adaptation Strategies for Distributed Estimation over Gaussian Markov Random Fields

The aim of this paper is to propose diffusion strategies for distributed estimation over adaptive networks, assuming the presence of spatially correlated measurements distributed according to a Gaussian Markov random field (GMRF) model. The proposed methods incorporate prior information about the statistical dependency among observations, while at the same time processing data in real-time and in a fully decentralized manner. A detailed mean-square analysis is carried out in order to prove stability and evaluate the steady-state performance of the proposed strategies. Finally, we also illustrate how the proposed techniques can be easily extended in order to incorporate thresholding operators for sparsity recovery applications. Numerical results show the potential advantages of using such techniques for distributed learning in adaptive networks deployed over GMRF.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin note: text overlap with arXiv:1206.309

Group-Lasso on Splines for Spectrum Cartography

The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and control. Towards this goal, the present paper develops a spline-based approach to field estimation, which relies on a basis expansion model of the field of interest. The model entails known bases, weighted by generic functions estimated from the field's noisy samples. A novel field estimator is developed based on a regularized variational least-squares (LS) criterion that yields finitely-parameterized (function) estimates spanned by thin-plate splines. Robustness considerations motivate well the adoption of an overcomplete set of (possibly overlapping) basis functions, while a sparsifying regularizer augmenting the LS cost endows the estimator with the ability to select a few of these bases that ``better'' explain the data. This parsimonious field representation becomes possible, because the sparsity-aware spline-based method of this paper induces a group-Lasso estimator for the coefficients of the thin-plate spline expansions per basis. A distributed algorithm is also developed to obtain the group-Lasso estimator using a network of wireless sensors, or, using multiple processors to balance the load of a single computational unit. The novel spline-based approach is motivated by a spectrum cartography application, in which a set of sensing cognitive radios collaborate to estimate the distribution of RF power in space and frequency. Simulated tests corroborate that the estimated power spectrum density atlas yields the desired RF state awareness, since the maps reveal spatial locations where idle frequency bands can be reused for transmission, even when fading and shadowing effects are pronounced.Comment: Submitted to IEEE Transactions on Signal Processin

Detection of a signal in linear subspace with bounded mismatch

We consider the problem of detecting a signal of interest in a background of noise with unknown covariance matrix, taking into account a possible mismatch between the actual steering vector and the presumed one. We assume that the former belongs to a known linear subspace, up to a fraction of its energy. When the subspace of interest consists of the presumed steering vector, this amounts to assuming that the angle between the actual steering vector and the presumed steering vector is upper bounded. Within this framework, we derive the generalized likelihood ratio test (GLRT). We show that it involves solving a minimization problem with the constraint that the signal of interest lies inside a cone. We present a computationally efficient algorithm to find the maximum likelihood estimator (MLE) based on the Lagrange multiplier technique. Numerical simulations illustrate the performance and the robustness of this new detector, and compare it with the adaptive coherence estimator which assumes that the steering vector lies entirely in a subspace

Reliability-based design optimization of shells with uncertain geometry using adaptive Kriging metamodels

Optimal design under uncertainty has gained much attention in the past ten years due to the ever increasing need for manufacturers to build robust systems at the lowest cost. Reliability-based design optimization (RBDO) allows the analyst to minimize some cost function while ensuring some minimal performances cast as admissible failure probabilities for a set of performance functions. In order to address real-world engineering problems in which the performance is assessed through computational models (e.g., finite element models in structural mechanics) metamodeling techniques have been developed in the past decade. This paper introduces adaptive Kriging surrogate models to solve the RBDO problem. The latter is cast in an augmented space that "sums up" the range of the design space and the aleatory uncertainty in the design parameters and the environmental conditions. The surrogate model is used (i) for evaluating robust estimates of the failure probabilities (and for enhancing the computational experimental design by adaptive sampling) in order to achieve the requested accuracy and (ii) for applying a gradient-based optimization algorithm to get optimal values of the design parameters. The approach is applied to the optimal design of ring-stiffened cylindrical shells used in submarine engineering under uncertain geometric imperfections. For this application the performance of the structure is related to buckling which is addressed here by means of a finite element solution based on the asymptotic numerical method