Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is @math , where @math is the number of nodes. As the size of the network increases, this makes global convergence over the entire network less practical. On the other hand, for several applications, such as load balancing or detection of local events, global convergence may not be necessary or even relevant. We introduce simple distributed iterative processes which limit the scope of the computational task to a smaller subnetwork of the entire network. This is achieved using one additional local parameter which controls the size of the subnetwork. We establish termination and convergence rate of such processes in theory, in experiment, in comparison to the well understood behavior of Markov processes, and for a variety of network topologies and initial conditions.
@cite_28: 1 Introduction.- 1.1 Distributed Detection Systems.- 1.2 Outline of the Book.- 2 Elements of Detection Theory.- 2.1 Introduction.- 2.2 Bayesian Detection Theory.- 2.3 Minimax Detection.- 2.4 Neyman-Pearson Test.- 2.5 Sequential Detection.- 2.6 Constant False Alarm Rate (CFAR) Detection.- 2.7 Locally Optimum Detection.- 3 Distributed Bayesian Detection: Parallel Fusion Network.- 3.1 Introduction.- 3.2 Distributed Detection Without Fusion.- 3.3 Design of Fusion Rules.- 3.4 Detection with Parallel Fusion Network.- 4 Distributed Bayesian Detection: Other Network Topologies.- 4.1 Introduction.- 4.2 The Serial Network.- 4.3 Tree Networks.- 4.4 Detection Networks with Feedback.- 4.5 Generalized Formulation for Detection Networks.- 5 Distributed Detection with False Alarm Rate Constraints.- 5.1 Introduction.- 5.2 Distributed Neyman-Pearson Detection.- 5.3 Distributed CFAR Detection.- 5.4 Distributed Detection of Weak Signals.- 6 Distributed Sequential Detection.- 6.1 Introduction.- 6.2 Sequential Test Performed at the Sensors.- 6.3 Sequential Test Performed at the Fusion Center.- 7 Information Theory and Distributed Hypothesis Testing.- 7.1 Introduction.- 7.2 Distributed Detection Based on Information Theoretic Criterion.- 7.3 Multiterminal Detection with Data Compression.- Selected Bibliography.
@cite_1: This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations
@cite_17: In order to monitor a region for traffic traversal, sensors can be deployed to perform collaborative target detection. Such a sensor network achieves a certain level of detection performance with an associated cost of deployment. This paper addresses this problem by proposing path exposure as a measure of the goodness of a deployment and presents an approach for sequential deployment in steps. It illustrates that the cost of deployment can be minimized to achieve the desired detection performance by appropriately choosing the number of sensors deployed in each step.
@cite_6: Collaboration in sensor networks must be fault-tolerant due to the harsh environmental conditions in which such networks can be deployed. We focus on finding algorithms for collaborative target detection that are efficient in terms of communication cost, precision, accuracy, and number of faulty sensors tolerable in the network. Two algorithms, namely, value fusion and decision fusion, are identified first. When comparing their performance and communication overhead, decision fusion is found to become superior to value fusion as the ratio of faulty sensors to fault free sensors increases. As robust data fusion requires agreement among nodes in the network, an analysis of fully distributed and hierarchical agreement is also presented. The impact of hierarchical agreement on communication cost and system failure probability is evaluated and a method for determining the number of tolerable faults is identified.
@cite_15: The problem of distributed Kalman filtering (DKF) for sensor networks is one of the most fundamental distributed estimation problems for scalable sensor fusion. This paper addresses the DKF problem by reducing it to two separate dynamic consensus problems in terms of weighted measurements and inverse-covariance matrices. These to data fusion problems are solved is a distributed way using low-pass and band-pass consensus filters. Consensus filters are distributed algorithms that allow calculation of average-consensus of time-varying signals. The stability properties of consensus filters is discussed in a companion CDC ’05 paper [24]. We show that a central Kalman filter for sensor networks can be decomposed into n micro-Kalman filters with inputs that are provided by two types of consensus filters. This network of micro-Kalman filters collectively are capable to provide an estimate of the state of the process (under observation) that is identical to the estimate obtained by a central Kalman filter given that all nodes agree on two central sums. Later, we demonstrate that our consensus filters can approximate these sums and that gives an approximate distributed Kalman filtering algorithm. A detailed account of the computational and communication architecture of the algorithm is provided. Simulation results are presented for a sensor network with 200 nodes and more than 1000 links.
@cite_10: In this paper, we address the problem of optimizing the detection performance of sensor networks under communication constraints on the common access channel. Our work helps understanding tradeoffs between sensor network para-meters like number of sensors, degree of quantization at each local sensor, and SNR. Traditionally, this problem is tack-led using asymptotic assumptions on the number of sensors, an approach that leads to the abstraction of important details such as the structure of the fusion center. We adopt a non-asymptotic approach and optimize both, the sensing and the fusion sides with respect to the probability of detection error. We show that the optimal fusion rule has an interesting structure similar to themajority-voting rule. In addition, we study the convergence with respect to the number of sensors of the performance of the fusion rule. We show that convergence is SNR dependent and that, in low-SNR environments, asymptotics may require a large number of sensors.
@cite_25: We consider a network of distributed sensors, where where each sensor takes a linear measurement of some unknown parameters, corrupted by independent Gaussian noises. We propose a simple distributed iterative scheme, based on distributed average consensus in the network, to compute the maximum-likelihood estimate of the parameters. This scheme doesn't involve explicit point-to-point message passing or routing; instead, it diffuses information across the network by updating each node's data with a weighted average of its neighbors' data (they maintain the same data structure). At each step, every node can compute a local weighted least-squares estimate, which converges to the global maximum-likelihood solution. This scheme is robust to unreliable communication links. We show that it works in a network with dynamically changing topology, provided that the infinitely occurring communication graphs are jointly connected.
@cite_11: We propose a new iterative distributed algorithm for linear minimum mean-squared-error (LMMSE) estimation in sensor networks whose measurements follow a Gaussian hidden Markov graphical model with cycles. The embedded polygons algorithm decomposes a loopy graphical model into a number of linked embedded polygons and then applies a parallel block Gauss-Seidel iteration comprising local LMMSE estimation on each polygon (involving inversion of a small matrix) followed by an information exchange between neighboring nodes and polygons. The algorithm is robust to temporary communication faults such as link failures and sleeping nodes and enjoys guaranteed convergence under mild conditions. A simulation study indicates that energy consumption for iterative estimation increases substantially as more links fail or nodes sleep. Thus, somewhat surprisingly, energy conservation strategies such as low-powered transmission and aggressive sleep schedules could actually be counterproductive.
It is important to combine the data from different sensors for the purpose of event detection or other applications such as consensus @cite_28 . Some common data fusion functions include mean distributed averaging @cite_1 , Kalman filter @cite_15 , Maximum likelihood estimator @cite_25 and linear least-squares estimator @cite_11 . Nodes often collaborate for a better performance @cite_10 . There are many applications in event detection that require data fusion @cite_10 @cite_17 @cite_6 .