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A distributed Subgradient Method for Dynamic Convex Optimization Problems Under Noisy Information Exchange

IEEE JOURNAL OF SELECTED TOPICS IN signal processing 2013年第2期7卷 243-256页

作者： Cavalcante, Renato L. G. Stanczak, Slawomir Fraunhofer Heinrich Hertz Inst D-10587 Berlin Germany Tech Univ Berlin Heinrich Hertz Lehrstuhl Informat Theorie & Theor D-10623 Berlin Germany

We consider a convex optimization problem for non-hierarchical agent networks where each agent has access to a local or private time-varying function, and the network-wide objective is to find a time-invariant minimizer of the sum of these functions, provided that such a minimizer exists. Problems of this type are common in dynamic systems where the objective function is time-varying because of, for instance, the dependency on measurements that arrive continuously to each agent. A typical outer-loop optimization iteration for optimization problems of this type consists of a local optimization step based on the information provided by neighboring agents, followed by a consensus step to exchange and fuse local estimates of the agents. A great deal of research effort has been directed towards developing and better understanding such algorithms, which find many applications in distinct areas such as cognitive radio networks, distributed acoustic source localization, coordination of unmanned vehicles, and environmental modeling. Contrasting with existing work, which considers either dynamic systems or noisy links (but not both jointly), in this study we devise and analyze a novel distributed online algorithm for dynamic optimization problems in noisy communication environments. The main result of the study proves sufficient conditions for almost sure convergence of the algorithm as the number of iterations tends to infinity. The algorithm is applicable to a wide range of distributed optimization problems with time-varying cost functions and consensus updates corrupted by additive noise. Our results therefore extend previous work to include recently proposed schemes that merge the processes of computation and data transmission over noisy wireless networks for fast and efficient consensus protocols. To give a concrete example of an application, we show how to apply our general technique to the problem of distributed detection with adaptive filters.

关键词： distributed signal processing decentralized optimization decentralized adaptive filtering decentralized estimation and detection cognitive radios

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Sensor data cryptography in wireless sensor networks

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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2008年第2期3卷 273-289页

作者： Aysal, Tuncer Can Barner, Kenneth E. Univ Delaware Dept Elect & Comp Engn Newark DE 19716 USA

We consider decentralized estimation of a noise-corrupted deterministic signal in a bandwidth-constrained sensor network communicating through an insecure medium. Each sensor collects a noise-corrupted version, performs a local quantization, and transmits a I-bit message to an ally fusion center through a wireless medium where the sensor outputs are vulnerable to unauthorized observation from enemy/third-party fusion centers. In this paper, we introduce an encrypted wireless sensor network (eWSN) concept where stochastic enciphers operating on binary sensor outputs are introduced to disguise the sensor outputs, creating an eWSN scheme. Noting that the plaintext (original) and ciphertext (disguised) messages are constrained to a single bit due to bandwidth constraints, we consider a binary channel-like scheme to probabilistically encipher (i.e., flip) the sensor outputs. We first consider a symmetric key encryption, case where the "0" and "1" enciphering probabilities are equal. The key is represented by the bit enciphering probability. Specifically, we derive the optimal estimator of the deterministic signal approached from a maximum-likelihood perspective and the Cramer-Rao lower bound for the estimation problem utilizing the key. Furthermore, we analyze the effect of the considered cryptosystem on enemy fusion centers that are unaware of the fact that the WSN is encrypted (i.e., we derive the bias, variance, and mean square error (MSE) of the enemy fusion center). We then extend the cryptosystem to admit unequal enciphering schemes for "0" and "1", and analyze the estimation problem from both the prospectives of ally (that has access to the enciphering keys) and (third-party) enemy fusion centers. The results show that when designed properly, a significant amount of bias and MSE can be introduced to an enemy fusion center with the cost to the ally fusion center being a marginal increase [factor of (1 - Omega(1) - Omega(0))(-2) where 1 - Omega(j), j = 0, 1 is the "

关键词： cryptography decentralized estimation distributed signal processing information security parameter estimation sensor networks

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Tree-Based Recursive Expectation-Maximization Algorithm for Localization of Acoustic Sources

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IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE processing 2015年第10期23卷 1692-1703页

作者： Dorfan, Yuval Gannot, Sharon Bar Ilan Univ Fac Engn IL-5290002 Ramat Gan Israel

The problem of distributed localization for ad hoc wireless acoustic sensor networks (WASNs) is addressed in this paper. WASNs are characterized by low computational resources in each node and by limited connectivity between the nodes. Novel bi-directional tree-based distributed estimation-maximization (DEM) algorithms are proposed to circumvent these inherent limitations. We show that the proposed algorithms are capable of localizing static acoustic sources in reverberant enclosures without a priori information on the number of sources. Unlike serial estimation procedures (like ring-based algorithms), the new algorithms enable simultaneous computations in the nodes and exhibit greater robustness to communication failures. Specifically, the recursive distributed EM (RDEM) variant is better suited to online applications due to its recursive nature. Furthermore, the RDEM outperforms the other proposed variants in terms of convergence speed and simplicity. Performance is demonstrated by an extensive experimental study consisting of both simulated and actual environments.

关键词： Bi-directional tree topologies distributed signal processing recursive expectation-maximization (REM) speaker localization wireless acoustic sensor networks (WASNs)

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Accelerated distributed Average Consensus via Localized Node State Prediction

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IEEE TRANSACTIONS ON signal processing 2009年第4期57卷 1563-1576页

作者： Aysal, Tuncer Can Oreshkin, Boris N. Coates, Mark J. McGill Univ Telecommun & Signal Proc Comp Networks Lab Dept Elect & Comp Engn Montreal PQ H3A 2A7 Canada Cornell Univ Dept Elect & Comp Engn Ithaca NY 14850 USA

This paper proposes an approach to accelerate local, linear iterative network algorithms asymptotically achieving distributed average consensus. We focus on the class of algorithms in which each node initializes its "state value" to the local measurement and then at each iteration of the algorithm, updates this state value by adding a weighted sum or its, own and its neighbors' state values. Provided the weight matrix satisfies certain convergence conditions, the state values asymptotically converge to the average of the measurements, but the convergence is generally slow, Impeding the practical application of these algorithms. In order to improve the rate of convergence, we propose a novel method where each node employs a linear predictor to predict future node values. The local update then becomes a convex (weighted) sum of the original consensus update and the prediction, convergence is faster because redundant states are bypassed. The method is linear and poses a small computational burden. For a concrete theoretical analysis, we prove the existence of a convergent solution in the general case and then focus on one-step prediction based on the current state, and derive the optimal mixing parameter in the convex sum for this case. Evaluation of the optimal mixing parameter requires knowledge or the eigenvalues of the weight matrix, so we present a bound on the optimal parameter. Calculation or this bound requires only local information. We provide simulation results that demonstrate the validity and effectiveness of the proposed scheme. The results indicate that the incorporation of a multistep predictor call lead to convergence rates that are much faster than those achieved by an optimum weight matrix in the standard consensus framework.

关键词： Average consensus distributed signal processing linear prediction

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Realization using the Roesser model for implementations in distributed grid sensor networks

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MULTIDIMENSIONAL SYSTEMS AND signal processing 2011年第1-3期22卷 131-146页

作者： Sumanasena, Buddika Bauer, Peter H. Univ Notre Dame Dept Elect Engn Notre Dame IN 46556 USA

Using the Roesser model, a method for distributed information processing in grid sensor networks is presented by Sumanasena and Bauer (A Roesser model based multidimensional systems approach for grid sensor networks. Pacific Grove, California, 2009). The method can be used to implement linear systems in grid sensor networks. Unless information originating in a node can be conveyed over the entire sensor network in a single time slot, for a system described by the Roesser model to be implementable in real-time on a sensor network, the system matrices of the Roesser model have to assume a particular form. A necessary and sufficient condition for a proper transfer matrix to be realizable in the constrained Roesser model is established in this paper. A realization algorithm to derive the Roesser model of the desired form, given an admissible transfer matrix is derived. The analogues problem for the realization of non-proper transfer matrices is also addressed.

关键词： Grid sensor networks Roesser model Realization distributed signal processing

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distributed Kalman Filtering Over Massive Data Sets: Analysis Through Large Deviations of Random Riccati Equations

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第3期61卷 1351-1372页

作者： Li, Di Kar, Soummya Moura, Jose M. F. Poor, H. Vincent Cui, Shuguang Texas A&M Univ Dept Elect & Comp Engn College Stn TX 77843 USA Carnegie Mellon Univ Dept Elect & Comp Engn Pittsburgh PA 15213 USA Princeton Univ Dept Elect Engn Princeton NJ 08544 USA King Abdulaziz Univ Jeddah 22254 Saudi Arabia

This paper studies the convergence of the estimation error process and the characterization of the corresponding invariant measure in distributed Kalman filtering for potentially unstable and large linear dynamic systems. A gossip network protocol termed modified gossip interactive Kalman filtering ( M-GIKF) is proposed, where sensors exchange their filtered states ( estimates and error covariances) and propagate their observations via intersensor communications of rate. (gamma) over bar;(gamma) over bar is defined as the averaged number of intersensor message passages per signal evolution epoch. The filtered states are interpreted as stochastic particles swapped through local interaction. This paper shows that the conditional estimation error covariance sequence at each sensor under M-GIKF evolves as a random Riccati equation ( RRE) with Markov modulated switching. By formulating the RRE as a random dynamical system, it is shown that the network achieves weak consensus, i. e., the conditional estimation error covariance at a randomly selected sensor converges weakly ( in distribution) to a unique invariant measure. Further, it is proved that as.(gamma) over bar -> infinity this invariant measure satisfies the large deviation ( LD) upper and lower bounds, implying that this measure converges exponentially fast ( in probability) to the Dirac measure delta P*, where P* is the stable error covariance of the centralized ( Kalman) filtering setup. The LD results answer a fundamental question on how to quantify the rate at which the distributed scheme approaches the centralized performance as the intersensor communication rate increases.

关键词： distributed signal processing massive data sets gossip Kalman filter consensus random dynamical systems random algebraic Riccati equation large deviations

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Local Interference Can Accelerate Gossip Algorithms

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IEEE JOURNAL OF SELECTED TOPICS IN signal processing 2011年第4期5卷 876-887页

作者： Nazer, Bobak Dimakis, Alexandros G. Gastpar, Michael Boston Univ Dept Elect & Comp Engn Boston MA 02215 USA Univ So Calif Dept Elect Engn Syst Los Angeles CA 90089 USA Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94720 USA Ecole Polytech Fed EPFL Sch Comp & Commun Sci CH-1015 Lausanne Switzerland

In this paper, we show how interference can be exploited to perform gossip computations for average-based consensus over a larger local neighborhood, rather than only pairs of nodes. We use a new channel coding technique called computation coding to compute sums reliably over the wireless medium. Since many nodes can simultaneously average in a single round, our neighborhood gossip algorithm converges faster than the standard nearest neighbor gossip algorithm. For a network with n nodes and size m neighborhoods, neighborhood gossip requires O(n(2)/m(2)) rounds while standard gossip requires circle dot(n(2)) rounds. Furthermore, we show that if the power path loss coefficient is less than 4, the total transmit energy employed by neighborhood gossip is polynomially smaller than that employed by standard gossip.

关键词： distributed signal processing gossip algorithms interference multiaccess communication wireless sensor networks

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distributed Frequency Estimation Over Sensor Network

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IEEE SENSORS JOURNAL 2015年第7期15卷 3973-3983页

作者： Li, Chunguang Wang, Heyu Zhejiang Univ Dept Informat Sci & Elect Engn Hangzhou 310027 Peoples R China

Frequency estimation is a common problem in a variety of applications. In recent years, adaptive notch filtering methods have been widely adopted for solving frequency estimation problems. For frequency estimation performed by a single node, the sampling time may not be long enough, the sampling rate may not be high enough, and the noise effect may be serious. In such situations, most existing algorithms for frequency estimation can not produce accurate enough results. Here, we propose using wireless sensor networks for sampling data distributedly, and using distributed notch filtering method for dealing with this problem. In particular, we propose two distributed algorithms over sensor network, a least mean square-based distributed notch filtering (dNF) algorithm and a total least square-based dNF algorithm. The communication cost of the new proposed algorithms is low, as each node exchanges only with its neighbors the estimates other than the original data. The proposed algorithms are applied to both synthetic and real examples. Simulation results demonstrate the effectiveness of the new proposed algorithms.

关键词： Frequency estimation distributed signal processing sensor network adaptive notch filter least-mean squares (LMS) total least squares (TLS) radar power system

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The incremental subgradient methods on distributed estimations in-network

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Science China(Information Sciences) 2014年第9期57卷 30-39页

作者： FENG Hui JIANG ZiDong HU Bo ZHANG JianQiu Department of Electronic Engineering Fudan University

A unified framework on distributed estimations in-network using incremental subgradient(IS)methods is *** IS methods meet the requirement of the asynchronously processing,which are efficient solvers developed recently focusing on separable non-differentiable convex optimization *** main contribution of this paper is to formalize distributed estimators as equivalent separable convex optimization problems,where general skills and several specific cases on signal estimations are *** and simulation results show that the IS framework can solve general nonlinear estimation problems in-network,and achieve comparable performances as the centralized estimators.

关键词： distributed signal processing signal processing in-network distributed estimation incremental subgradient optimization methods

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Geographic gossip: Efficient averaging for sensor networks

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IEEE TRANSACTIONS ON signal processing 2008年第3期56卷 1205-1216页

作者： Dimakis, Alexandros D. G. Sarwate, Anand D. Wainwright, Martin J. Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94720 USA Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA

Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste of energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of n and root n, respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy E using O((n(1.5)/root log n) log epsilon(-1)) radio transmissions, which yields a root n/log n factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.

关键词： aggregation problems consensus problems distributed signal processing gossip algorithms message-passing algorithms random geometric graphs sensor networks

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