Clock Synchronization and Distributed Estimation in Highly Dynamic Networks: An Information Theoretic Approach

TL;DR

This paper addresses clock synchronization in highly dynamic sensor networks using an information-theoretic approach, proposing a simple weighted averaging algorithm with performance guarantees close to the optimal, even under adversarial meeting patterns.

Contribution

It introduces a robust, resource-efficient clock synchronization algorithm for dynamic networks and provides theoretical performance bounds using Fisher information concepts.

Findings

Algorithm performs near-optimally under arbitrary meeting patterns.

Performance matches the best possible algorithms in Gaussian scenarios.

Fisher information and Cramer-Rao bounds are used to quantify information flow.

Abstract

We consider the External Clock Synchronization problem in dynamic sensor networks. Initially, sensors obtain inaccurate estimations of an external time reference and subsequently collaborate in order to synchronize their internal clocks with the external time. For simplicity, we adopt the drift-free assumption, where internal clocks are assumed to tick at the same pace. Hence, the problem is reduced to an estimation problem, in which the sensors need to estimate the initial external time. This work is further relevant to the problem of collective approximation of environmental values by biological groups. Unlike most works on clock synchronization that assume static networks, this paper focuses on an extreme case of highly dynamic networks. Specifically, we assume a non-adaptive scheduler adversary that dictates in advance an arbitrary, yet independent, meeting pattern. Such meeting patterns fit, for example, with short-time scenarios in highly dynamic settings, where each sensor interacts with only few other arbitrary sensors. We propose an extremely simple clock synchronization algorithm that is based on weighted averages, and prove that its performance on any given independent meeting pattern is highly competitive with that of the best possible algorithm, which operates without any resource or computational restrictions, and knows the meeting pattern in advance. In particular, when all distributions involved are Gaussian, the performances of our scheme coincide with the optimal performances. Our proofs rely on an extensive use of the concept of Fisher information. We use the Cramer-Rao bound and our definition of a Fisher Channel Capacity to quantify information flows and to obtain lower bounds on collective performance. This opens the door for further rigorous quantifications of information flows within collaborative sensors.