Multi-hop Diffusion LMS for Energy-constrained Distributed Estimation

We propose a multi-hop diffusion strategy for a sensor network to perform distributed least mean-squares (LMS) estimation under local and network-wide energy constraints. At each iteration of the strategy, each node can combine intermediate parameter estimates from nodes other than its physical neighbors via a multi-hop relay path. We propose a rule to select combination weights for the multi-hop neighbors, which can balance between the transient and the steady-state network mean-square deviations (MSDs). We study two classes of networks: simple networks with a unique transmission path from one node to another, and arbitrary networks utilizing diffusion consultations over at most two hops. We propose a method to optimize each node's information neighborhood subject to local energy budgets and a network-wide energy budget for each diffusion iteration. This optimization requires the network topology, and the noise and data variance profiles of each node, and is performed offline before the diffusion process. In addition, we develop a fully distributed and adaptive algorithm that approximately optimizes the information neighborhood of each node with only local energy budget constraints in the case where diffusion consultations are performed over at most a predefined number of hops. Numerical results suggest that our proposed multi-hop diffusion strategy achieves the same steady-state MSD as the existing one-hop adapt-then-combine diffusion algorithm but with a lower energy budget.Comment: 14 pages, 12 figures. Submitted for publicatio

Source Coding Optimization for Distributed Average Consensus

Consensus is a common method for computing a function of the data distributed among the nodes of a network. Of particular interest is distributed average consensus, whereby the nodes iteratively compute the sample average of the data stored at all the nodes of the network using only near-neighbor communications. In real-world scenarios, these communications must undergo quantization, which introduces distortion to the internode messages. In this thesis, a model for the evolution of the network state statistics at each iteration is developed under the assumptions of Gaussian data and additive quantization error. It is shown that minimization of the communication load in terms of aggregate source coding rate can be posed as a generalized geometric program, for which an equivalent convex optimization can efficiently solve for the global minimum. Optimization procedures are developed for rate-distortion-optimal vector quantization, uniform entropy-coded scalar quantization, and fixed-rate uniform quantization. Numerical results demonstrate the performance of these approaches. For small numbers of iterations, the fixed-rate optimizations are verified using exhaustive search. Comparison to the prior art suggests competitive performance under certain circumstances but strongly motivates the incorporation of more sophisticated coding strategies, such as differential, predictive, or Wyner-Ziv coding.Comment: Master's Thesis, Electrical Engineering, North Carolina State Universit

High Dimensional Separable Representations for Statistical Estimation and Controlled Sensing.

This thesis makes contributions to a fundamental set of high dimensional problems in the following areas: (1) performance bounds for high dimensional estimation of structured Kronecker product covariance matrices, (2) optimal query design for a centralized collaborative controlled sensing system used for target localization, and (3) global convergence theory for decentralized controlled sensing systems. Separable approximations are effective dimensionality reduction techniques for high dimensional problems. In multiple modality and spatio-temporal signal processing, separable models for the underlying covariance are exploited for improved estimation accuracy and reduced computational complexity. In query- based controlled sensing, estimation performance is greatly optimized at the expense of query design. Multi-agent controlled sensing systems for target localization consist of a set of agents that collaborate to estimate the location of an unknown target. In the centralized setting, for a large number of agents and/or high- dimensional targets, separable representations of the fusion center’s query policies are exploited to maintain tractability. For large-scale sensor networks, decentralized estimation methods are of primary interest, under which agents obtain new noisy information as a function of their current belief and exchange local beliefs with their neighbors. Here, separable representations of the temporally evolving information state are exploited to improve robustness and scalability. The results improve upon the current state-of-the-art.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107110/1/ttsili_1.pd

1 Toward Resource-Optimal Consensus over the Wireless Medium

Abstract—We carry out a comprehensive study of the resource cost of averaging consensus in wireless networks. Most previous approaches suppose a graphical network, which abstracts away crucial features of the wireless medium, and measure resource consumption only in terms of the total number of transmissions required to achieve consensus. Under a pathloss dominated model, we study the resource requirements of consensus with respect to three wireless-appropriate metrics: total transmit energy, elapsed time, and time-bandwidth product. First we characterize the performance of several popular gossip algorithms, showing that they may be order-optimal with respect to transmit energy but are strictly suboptimal with respect to elapsed time and time-bandwidth product. Further, we propose a new consensus scheme, termed hierarchical averaging, and show that it is nearly order-optimal with respect to all three metrics. Finally, we examine the effects of quantization, showing that hierarchical averaging provides a nearly order-optimal tradeoff between resource consumption and quantization error. I