1,310 research outputs found

    Distributed Optimal Quantization and Power Allocation for Sensor Detection Via Consensus

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    We address the optimal transmit power allocation problem (from the sensor nodes (SNs) to the fusion center (FC)) for the decentralized detection of an unknown deterministic spatially uncorrelated signal which is being observed by a distributed wireless sensor network. We propose a novel fully distributed algorithm, in order to calculate the optimal transmit power allocation for each sensor node (SN) and the optimal number of quantization bits for the test statistic in order to match the channel capacity. The SNs send their quantized information over orthogonal uncorrelated channels to the FC which linearly combines them and makes a final decision. What makes this scheme attractive is that the SNs share with their neighbours just their individual transmit powers at the current states. As a result, the SN processing complexity is further reduced

    Distributed Detection and Estimation in Wireless Sensor Networks

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    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

    Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability

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    Distributed consensus and other linear systems with system stochastic matrices WkW_k emerge in various settings, like opinion formation in social networks, rendezvous of robots, and distributed inference in sensor networks. The matrices WkW_k are often random, due to, e.g., random packet dropouts in wireless sensor networks. Key in analyzing the performance of such systems is studying convergence of matrix products WkWk−1...W1W_kW_{k-1}... W_1. In this paper, we find the exact exponential rate II for the convergence in probability of the product of such matrices when time kk grows large, under the assumption that the WkW_k's are symmetric and independent identically distributed in time. Further, for commonly used random models like with gossip and link failure, we show that the rate II is found by solving a min-cut problem and, hence, easily computable. Finally, we apply our results to optimally allocate the sensors' transmission power in consensus+innovations distributed detection

    Distributed detection and estimation in wireless sensor networks: resource allocation, fusion rules, and network security

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    This thesis addresses the problem of detection of an unknown binary event. In particular, we consider centralized detection, distributed detection, and network security in wireless sensor networks (WSNs). The communication links among SNs are subject to limited SN transmit power, limited bandwidth (BW), and are modeled as orthogonal channels with path loss, flat fading and additive white Gaussian noise (AWGN). We propose algorithms for resource allocations, fusion rules, and network security. In the first part of this thesis, we consider the centralized detection and calculate the optimal transmit power allocation and the optimal number of quantization bits for each SN. The resource allocation is performed at the fusion center (FC) and it is referred as a centralized approach. We also propose a novel fully distributeddistributed algorithm to address this resource allocation problem. What makes this scheme attractive is that the SNs share with their neighbors just their individual transmit power at the current states. Finally, the optimal soft fusion rule at the FC is derived. But as this rule requires a-priori knowledge that is difficult to attain in practice, suboptimal fusion rules are proposed that are realizable in practice. The second part considers a fully distributed detection framework and we propose a two-step distributed quantized fusion rule algorithm where in the first step the SNs collaborate with their neighbors through error-free, orthogonal channels. In the second step, local 1-bit decisions generated in the first step are shared among neighbors to yield a consensus. A binary hypothesis testing is performed at any arbitrary SN to optimally declare the global decision. Simulations show that our proposed quantized two-step distributed detection algorithm approaches the performance of the unquantized centralized (with a FC) detector and its power consumption is shown to be 50% less than the existing (unquantized) conventional algorithm. Finally, we analyze the detection performance of under-attack WSNs and derive attacking and defense strategies from both the Attacker and the FC perspective. We re-cast the problem as a minimax game between the FC and Attacker and show that the Nash Equilibrium (NE) exists. We also propose a new non-complex and efficient reputation-based scheme to identify these compromised SNs. Based on this reputation metric, we propose a novel FC weight computation strategy ensuring that the weights for the identified compromised SNs are likely to be decreased. In this way, the FC decides how much a SN should contribute to its final decision. We show that this strategy outperforms the existing schemes

    Distributed Two-Step Quantized Fusion Rules via Consensus Algorithm for Distributed Detection in Wireless Sensor Networks

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    We consider the problem of distributed soft decision fusion in a bandwidth-constrained spatially uncorrelated wireless sensor network (WSN). The WSN is tasked with the detection of an intruder transmitting an unknown signal over a fading channel. Existing distributed consensus-based fusion rules algorithms only ensure equal combining of local data and in the case of bandwidth-constrained WSNs, we show that their performance is poor and does not converge across the sensor nodes (SNs). Motivated by this fact, we propose a two-step distributed quantized fusion rule algorithm where in the first step the SNs collaborate with their neighbors through error-free, orthogonal channels (the SNs exchange quantized information matched to the channel capacity of each link). In the second step, local 1-bit decisions generated in the first step are shared among neighbors to yield a consensus. A binary hypothesis testing is performed at any arbitrary SN to optimally declare the global decision. Simulations show that our proposed quantized two-step distributed detection algorithm approaches the performance of the unquantized centralized (with a fusion center) detector and its power consumption is shown to be 50% less than the existing (unquantized) conventional algorithm

    Distributed Estimation and Performance Limits in Resource-constrained Wireless Sensor Networks

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    Distributed inference arising in sensor networks has been an interesting and promising discipline in recent years. The goal of this dissertation is to investigate several issues related to distributed inference in sensor networks, emphasizing parameter estimation and target tracking with resource-constrainted networks. To reduce the transmissions between sensors and the fusion center thereby saving bandwidth and energy consumption in sensor networks, a novel methodology, where each local sensor performs a censoring procedure based on the normalized innovation square (NIS), is proposed for the sequential Bayesian estimation problem in this dissertation. In this methodology, each sensor sends only the informative measurements and the fusion center fuses both missing measurements and received ones to yield more accurate inference. The new methodology is derived for both linear and nonlinear dynamic systems, and both scalar and vector measurements. The relationship between the censoring rule based on NIS and the one based on Kullback-Leibler (KL) divergence is investigated. A probabilistic transmission model over multiple access channels (MACs) is investigated. With this model, a relationship between the sensor management and compressive sensing problems is established, based on which, the sensor management problem becomes a constrained optimization problem, where the goal is to determine the optimal values of probabilities that each sensor should transmit with such that the determinant of the Fisher information matrix (FIM) at any given time step is maximized. The performance of the proposed compressive sensing based sensor management methodology in terms of accuracy of inference is investigated. For the Bayesian parameter estimation problem, a framework is proposed where quantized observations from local sensors are not directly fused at the fusion center, instead, an additive noise is injected independently to each quantized observation. The injected noise performs as a low-pass filter in the characteristic function (CF) domain, and therefore, is capable of recoverving the original analog data if certain conditions are satisfied. The optimal estimator based on the new framework is derived, so is the performance bound in terms of Fisher information. Moreover, a sub-optimal estimator, namely, linear minimum mean square error estimator (LMMSE) is derived, due to the fact that the proposed framework theoretically justifies the additive noise modeling of the quantization process. The bit allocation problem based on the framework is also investigated. A source localization problem in a large-scale sensor network is explored. The maximum-likelihood (ML) estimator based on the quantized data from local sensors and its performance bound in terms of Cram\\u27{e}r-Rao lower bound (CRLB) are derived. Since the number of sensors is large, the law of large numbers (LLN) is utilized to obtain a closed-form version of the performance bound, which clearly shows the dependence of the bound on the sensor density, i.e.,i.e., the Fisher information is a linearly increasing function of the sensor density. Error incurred by the LLN approximation is also theoretically analyzed. Furthermore, the design of sub-optimal local sensor quantizers based on the closed-form solution is proposed. The problem of on-line performance evaluation for state estimation of a moving target is studied. In particular, a compact and efficient recursive conditional Posterior Cram\\u27{e}r-Rao lower bound (PCRLB) is proposed. This bound provides theoretical justification for a heuristic one proposed by other researchers in this area. Theoretical complexity analysis is provided to show the efficiency of the proposed bound, compared to the existing bound

    Distributed binary event detection under data-falsification and energy-bandwidth limitation

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    We address the problem of centralized detection of a binary event in the presence of falsifiable sensor nodes (SNs) (i.e., controlled by an attacker) for a bandwidth-constrained under-attack spatially uncorrelated distributed wireless sensor network (WSN). The SNs send their quantized test statistics over orthogonal channels to the fusion center (FC), which linearly combines them to reach a final decision. First (considering that the FC and the attacker do not act strategically), we derive (i) the FC optimal weight combining; (ii) the optimal SN to FC transmit power, and (iii) the test statistic quantization bits that maximize the probability of detection (Pd). We also derive an expression for the attacker strategy that causes the maximum possible FC degradation. But in these expressions, both the optimum FC strategy and the attacker strategy require
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