Energy-aware Sparse Sensing of Spatial-temporally Correlated Random Fields

This dissertation focuses on the development of theories and practices of energy aware sparse sensing schemes of random fields that are correlated in the space and/or time domains. The objective of sparse sensing is to reduce the number of sensing samples in the space and/or time domains, thus reduce the energy consumption and complexity of the sensing system. Both centralized and decentralized sensing schemes are considered in this dissertation. Firstly we study the problem of energy efficient Level set estimation (LSE) of random fields correlated in time and/or space under a total power constraint. We consider uniform sampling schemes of a sensing system with a single sensor and a linear sensor network with sensors distributed uniformly on a line where sensors employ a fixed sampling rate to minimize the LSE error probability in the long term. The exact analytical cost functions and their respective upper bounds of these sampling schemes are developed by using an optimum thresholding-based LSE algorithm. The design parameters of these sampling schemes are optimized by minimizing their respective cost functions. With the analytical results, we can identify the optimum sampling period and/or node distance that can minimize the LSE error probability. Secondly we propose active sparse sensing schemes with LSE of a spatial-temporally correlated random field by using a limited number of spatially distributed sensors. In these schemes a central controller is designed to dynamically select a limited number of sensing locations according to the information revealed from past measurements,and the objective is to minimize the expected level set estimation error.The expected estimation error probability is explicitly expressed as a function of the selected sensing locations, and the results are used to formulate the optimal sensing location selection problem as a combinatorial problem. Two low complexity greedy algorithms are developed by using analytical upper bounds of the expected estimation error probability. Lastly we study the distributed estimations of a spatially correlated random field with decentralized wireless sensor networks (WSNs). We propose a distributed iterative estimation algorithm that defines the procedures for both information propagation and local estimation in each iteration. The key parameters of the algorithm, including an edge weight matrix and a sample weight matrix, are designed by following the asymptotically optimum criteria. It is shown that the asymptotically optimum performance can be achieved by distributively projecting the measurement samples into a subspace related to the covariance matrices of data and noise samples

Distributed Detection and Estimation in Wireless Sensor Networks

In this article we consider the problems of distributed detection and estimation in wireless sensor networks. In the first part, we provide a general framework aimed to show how an efficient design of a sensor network requires a joint organization of in-network processing and communication. Then, we recall the basic features of consensus algorithm, which is a basic tool to reach globally optimal decisions through a distributed approach. The main part of the paper starts addressing the distributed estimation problem. We show first an entirely decentralized approach, where observations and estimations are performed without the intervention of a fusion center. Then, we consider the case where the estimation is performed at a fusion center, showing how to allocate quantization bits and transmit powers in the links between the nodes and the fusion center, in order to accommodate the requirement on the maximum estimation variance, under a constraint on the global transmit power. We extend the approach to the detection problem. Also in this case, we consider the distributed approach, where every node can achieve a globally optimal decision, and the case where the decision is taken at a central node. In the latter case, we show how to allocate coding bits and transmit power in order to maximize the detection probability, under constraints on the false alarm rate and the global transmit power. Then, we generalize consensus algorithms illustrating a distributed procedure that converges to the projection of the observation vector onto a signal subspace. We then address the issue of energy consumption in sensor networks, thus showing how to optimize the network topology in order to minimize the energy necessary to achieve a global consensus. Finally, we address the problem of matching the topology of the network to the graph describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R. Chellapa and S. Theodoridis, Eds., Elsevier, 201

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

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

Monte Carlo optimization of decentralized estimation networks over directed acyclic graphs under communication constraints

Motivated by the vision of sensor networks, we consider decentralized estimation networks over bandwidth–limited communication links, and are particularly interested in the tradeoff between the estimation accuracy and the cost of communications due to, e.g., energy consumption. We employ a class of in–network processing strategies that admits directed acyclic graph representations and yields a tractable Bayesian risk that comprises the cost of communications and estimation error penalty. This perspective captures a broad range of possibilities for processing under network constraints and enables a rigorous design problem in the form of constrained optimization. A similar scheme and the structures exhibited by the solutions have been previously studied in the context of decentralized detection. Under reasonable assumptions, the optimization can be carried out in a message passing fashion. We adopt this framework for estimation, however, the corresponding optimization scheme involves integral operators that cannot be evaluated exactly in general. We develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both the in–network processing strategies and their optimization. The proposed Monte Carlo optimization procedure operates in a scalable and efficient fashion and, owing to the non-parametric nature, can produce results for any distributions provided that samples can be produced from the marginals. In addition, this approach exhibits graceful degradation of the estimation accuracy asymptotically as the communication becomes more costly, through a parameterized Bayesian risk

Distributed Detection and Estimation in Wireless Sensor Networks

Wireless sensor networks (WSNs) are typically formed by a large number of densely deployed, spatially distributed sensors with limited sensing, computing, and communication capabilities that cooperate with each other to achieve a common goal. In this dissertation, we investigate the problem of distributed detection, classification, estimation, and localization in WSNs. In this context, the sensors observe the conditions of their surrounding environment, locally process their noisy observations, and send the processed data to a central entity, known as the fusion center (FC), through parallel communication channels corrupted by fading and additive noise. The FC will then combine the received information from the sensors to make a global inference about the underlying phenomenon, which can be either the detection or classification of a discrete variable or the estimation of a continuous one.;In the domain of distributed detection and classification, we propose a novel scheme that enables the FC to make a multi-hypothesis classification of an underlying hypothesis using only binary detections of spatially distributed sensors. This goal is achieved by exploiting the relationship between the influence fields characterizing different hypotheses and the accumulated noisy versions of local binary decisions as received by the FC, where the influence field of a hypothesis is defined as the spatial region in its surrounding in which it can be sensed using some sensing modality. In the realm of distributed estimation and localization, we make four main contributions: (a) We first formulate a general framework that estimates a vector of parameters associated with a deterministic function using spatially distributed noisy samples of the function for both analog and digital local processing schemes. ( b) We consider the estimation of a scalar, random signal at the FC and derive an optimal power-allocation scheme that assigns the optimal local amplification gains to the sensors performing analog local processing. The objective of this optimized power allocation is to minimize the L 2-norm of the vector of local transmission powers, given a maximum estimation distortion at the FC. We also propose a variant of this scheme that uses a limited-feedback strategy to eliminate the requirement of perfect feedback of the instantaneous channel fading coefficients from the FC to local sensors through infinite-rate, error-free links. ( c) We propose a linear spatial collaboration scheme in which sensors collaborate with each other by sharing their local noisy observations. We derive the optimal set of coefficients used to form linear combinations of the shared noisy observations at local sensors to minimize the total estimation distortion at the FC, given a constraint on the maximum average cumulative transmission power in the entire network. (d) Using a novel performance measure called the estimation outage, we analyze the effects of the spatial randomness of the location of the sensors on the quality and performance of localization algorithms by considering an energy-based source-localization scheme under the assumption that the sensors are positioned according to a uniform clustering process