Observation-driven scheduling for remote estimation of two Gaussian sources

TL;DR

This paper develops and analyzes scheduling policies for remote estimation of two Gaussian sources, establishing optimality conditions and proposing numerical methods for correlated sources to minimize estimation error.

Contribution

It introduces the max-scheduling/mean-estimation policy and extends joint scheduling and estimation design to correlated sources with arbitrary correlation structures.

Findings

Max-scheduling/mean-estimation policy is person-by-person optimal for independent sources.

Optimal policies for correlated sources can be found via difference-of-convex programming.

Numerical procedures efficiently yield locally optimal scheduling and estimation policies.

Abstract

Joint estimation and scheduling for sensor networks is considered in a system formed by two sensors, a scheduler and a remote estimator. Each sensor observes a Gaussian source, which may be correlated. The scheduler observes the output of both sensors and chooses which of the two is revealed to the remote estimator. The goal is to jointly design scheduling and estimation policies that minimize a mean-squared estimation error criterion. The person-by-person optimality of a policy pair called "max-scheduling/mean-estimation" is established, where the measurement with the largest absolute value is revealed to the estimator, which uses a corresponding conditional mean operator. This result is obtained for independent sources, and in the case of correlated sources and symmetric variances. We also consider the joint design of scheduling and linear estimation policies for two correlated Gaussian sources with an arbitrary correlation structure. In this case, the optimization problem can be cast a difference-of-convex program, and locally optimal solutions can be efficiently found using a simple numerical procedure.