Hierarchical diffusion algorithms for distributed estimation

We study the problem of distributed estimation, where a set of nodes are required to collectively estimate some parameter of interest from their measurements. Distributed implementations avoid the use of a fusion center and distribute the processing and communication across the entire network. Among distributed solutions, diffusion algorithms have been shown to achieve good performance, increased robustness and are amenable for ad-hoc implementation. In this work we focus on hierarchical diffusion algorithms, where we allow different nodes to have different responsibilities, as opposed to our previous work where every node performed exactly the same type of operations. Our results are general in the sense that they apply to any diffusion algorithm. We illustrate the concept using diffusion LMS, provide performance analysis for hierarchical collaboration and present simulation results showing improved performance over non-hierarchical methods

Diffusion LMS algorithms with information exchange

We consider the problem of distributed estimation, where a set of nodes are required to collectively estimate some parameter of interest. We motivate and propose new versions of the diffusion LMS algorithm, including a version that outperforms previous solutions without increasing the complexity or communications, and others that obtain even better performance by allowing additional communications. We analyze their performance and compare with simulation results

Distributed nonlinear Kalman filtering with applications to wireless localization

We study the problem of distributed state-space estimation, where a set of nodes are required to estimate the state of a nonlinear state-space system based on their observations. We extend our previous work on distributed Kalman filtering to the nonlinear case, and propose algorithms for Extended and Unscented Kalman filtering. The resulting algorithms are robust to node and link failure, scalable, and fully distributed, in the sense that no fusion center is required, and nodes communicate with their neighbors only. We apply the algorithms to the problem of estimating the position of every node in an ad-hoc network, also known as wireless localization. Simulation results illustrate the performance of the proposed algorithms

Analysis of Spatial and Incremental LMS Processing for Distributed Estimation

Consider a set of nodes distributed spatially over some region forming a network, where every node takes measurements of an underlying process. The objective is for every node in the network to estimate some parameter of interest from these measurements by cooperating with other nodes. In this work we compare the performance of four adaptive implementations. Two of the implementations are distributed and network-based; they are spatial LMS and incremental LMS. In both algorithms, the nodes share information in a cyclic manner and both algorithms differ by the amount of information shared (less information is shared in the incremental case). The two other adaptive algorithms that we study deal with centralized implementations of spatial and incremental LMS. In these latter cases, all nodes exchange data with a fusion center where the computations are performed. In the centralized approach, all nodes receive the same estimates back from the fusion center, while these estimates differ among the nodes in the distributed implementation. We analyze and compare the performance of fusion-based and network-based versions of spatial LMS and incremental LMS processing and reveal some interesting conclusions. The results indicate that incremental LMS can outperform spatial LMS, and that network-based implementations can outperform the aforementioned fusion-based solutions in some revealing ways

Modeling Bird Flight Formations Using Diffusion Adaptation

Flocks of birds self-organize into V-formations when they need to travel long distances. It has been shown that this formation allows the birds to save energy, by taking advantage of the upwash generated by the neighboring birds. In this work we use a model for the upwash generated by a flying bird, and show that a flock of birds can self-organize into a V-formation if every bird were to process spatial and network information through an adaptive diffusive process. The diffusion algorithm requires the birds to obtain measurements of the upwash, and also to use information from neighboring birds. The result has interesting implications. First, a simple diffusion algorithm can account for self-organization in birds. The algorithm is fully distributed and runs in real time. Second, according to the model, that birds can self-organize based on the upwash generated by the other birds. Third, that some form of information sharing among birds is necessary to achieve flight formation. We also propose a modification to the algorithm that allows birds to organize into a U-formation, starting from a V-formation. We show that this type of formation leads to an equalization effect, where every bird in the flock observes approximately the same upwash

Multi-level diffusion adaptive networks

We study the problem of distributed estimation, where a set of nodes are required to collectively estimate some parameter of interest from their measurements. Diffusion algorithms have been shown to achieve good performance, increased robustness and are amenable for real-time implementations. In this work we focus on multi-level diffusion algorithms, where a network running a diffusion algorithm is enhanced by adding special nodes that can perform different processing. These special nodes form a second network where a second diffusion algorithm is implemented. We illustrate the concept using diffusion LMS, provide performance analysis for multi-level collaboration and present simulation results showing improved performance over conventional diffusion

Distributed adaptive learning mechanisms

The chapter describes recent developments in distributed processing over adaptive networks. The resulting adaptive learning rules rely on local data at the individual nodes and on collaborations among neighboring nodes in order to exploit the space-time dimension of the data more fully. The ideas are illustrated by considering algorithms of the least mean-squares type, although more general adaptation rules are also possible including least-squares rules and Kalman-type rules. Both incremental and diffusion collaboration strategies are considere

Distributed detection over adaptive networks based on diffusion estimation schemes

We study the problem of distributed detection, where a set of nodes are required to decide between two hypotheses based on their measurements. We seek fully distributed implementations, where all nodes make individual decisions by communicating with their immediate neighbors, and no fusion center is necessary. This scheme provides the network with more flexibility, saves energy for communication and networking resources. Our distributed detection algorithm is based on a previously proposed distributed estimation algorithm. We establish the connection between the detection and estimation problems, propose a distributed detection algorithm, and analyze the performance of the algorithm in terms of its probabilities of detection and false alarm. We also provide simulation results comparing with other cooperation schemes

Distributed Detection Over Adaptive Networks Using Diffusion Adaptation

We study the problem of distributed detection, where a set of nodes is required to decide between two hypotheses based on available measurements. We seek fully distributed and adaptive implementations, where all nodes make individual real-time decisions by communicating with their immediate neighbors only, and no fusion center is necessary. The proposed distributed detection algorithms are based on diffusion strategies [C. G. Lopes and A. H. Sayed, “Diffusion Least-Mean Squares Over Adaptive Networks: Formulation and Performance Analysis,” IEEE Trans. Signal Process., vol. 56, no. 7, pp. 3122-3136, July 2008; F. S. Cattivelli and A. H. Sayed, “Diffusion LMS Strategies for Distributed Estimation,” IEEE Trans. Signal Process., vol. 58, no. 3, pp. 1035-1048, March 2010; F. S. Cattivelli, C. G. Lopes, and A. H. Sayed, “Diffusion Recursive Least-Squares for Distributed Estimation Over Adaptive Networks,” IEEE Trans. Signal Process., vol. 56, no. 5, pp. 1865-1877, May 2008] for distributed estimation. Diffusion detection schemes are attractive in the context of wireless and sensor networks due to their scalability, improved robustness to node and link failure as compared to centralized schemes, and their potential to save energy and communication resources. The proposed algorithms are inherently adaptive and can track changes in the active hypothesis. We analyze the performance of the proposed algorithms in terms of their probabilities of detection and false alarm, and provide simulation results comparing with other cooperation schemes, including centralized processing and the case where there is no cooperation. Finally, we apply the proposed algorithms to the problem of spectrum sensing in cognitive radios