Controlled Collaboration for Linear Coherent Estimation in Wireless Sensor Networks

TL;DR

This paper investigates energy-efficient collaboration strategies in wireless sensor networks for estimating both static and dynamic signals, analyzing network topologies and the benefits of frequent sampling under power constraints.

Contribution

It extends previous work by analyzing partially connected networks and incorporating time-varying signals modeled as Gaussian processes.

Findings

Partially connected networks like nearest-neighbor graphs are effective for energy-efficient estimation.

Sampling as frequently as possible improves estimation accuracy despite increased noise.

Simulation results support the analytical insights on collaboration and sampling strategies.

Abstract

We consider a wireless sensor network consisting of multiple nodes that are coordinated by a fusion center (FC) in order to estimate a common signal of interest. In addition to being coordinated, the sensors are also able to collaborate, i.e., share observations with other neighboring nodes, prior to transmission. In an earlier work, we derived the energy-optimal collaboration strategy for the single-snapshot framework, where the inference has to be made based on observations collected at one particular instant. In this paper, we make two important contributions. Firstly, for the single-snapshot framework, we gain further insights into partially connected collaboration networks (nearest-neighbor and random geometric graphs for example) through the analysis of a family of topologies with regular structure. Secondly, we explore the estimation problem by adding the dimension of time, where the goal is to estimate a time-varying signal in a power-constrained network. To model the time dynamics, we consider the stationary Gaussian process with exponential covariance (sometimes referred to as Ornstein-Uhlenbeck process) as our representative signal. For such a signal, we show that it is always beneficial to sample as frequently as possible, despite the fact that the samples get increasingly noisy due to the power-constrained nature of the problem. Simulation results are presented to corroborate our analytical results.