Observation-Driven Scheduling for Remote Estimation of Two Gaussian Random Variables

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.

Data-driven sensor scheduling for remote estimation in wireless networks

“…Our problem is based on the Observation-Driven Sensor Scheduling (ODSS) framework introduced in [18],…”

“…where the scheduling of sensors making correlated Gaussian observations is considered. The work in [18] uses team decision theory to obtain person-by-person optimal scheduling and estimation policies while seeking to prove the optimality of the so-called max-scheduler proposed in [19], which consists of letting the sensor with the measurement of largest magnitude transmit over the network. The subsequent work [10] considered a sequential ODSS framework with an energy-harvesting scheduler for sensors making independent observations distributed according to symmetric and unimodal PDFs.…”

“…Our approach follows the current state of the art in learning for controls and estimation, where models are not fully available to the system designer and must be learned from data [20]- [22]. The DoC decompositions of the objective function contained here were observed in [18] for the scheduling of two sensors making correlated Gaussian observations. Here we formally establish the results in full generality and in addition, we show the connection of the resulting CCP with subgradient methods with constant step sizes.…”

Optimal Scheduling of Multiple Spatio-temporally Dependent Observations using Age-of-Information

“…In [5], [9], [10], the authors investigate the optimal transmission frequency for sensors observing spatiotemporally correlated measurements. In [11], authors consider correlated sensor measurements when a scheduler can observe measurements before scheduling. Such a scheduling strategy may reduce estimation error but has implications on the system's privacy and latency.…”

“…This paper presents an optimal scheduling policy for multiple sensors that observe spatio-temporally correlated Gaussian processes. Our system model is similar to [11], [12], where observations are communicated via a network manager to the remote estimators. In contrast, we assume spatio-temporal dependence among the sensors, that multiple observations are broadcasted, and that a system-scheduler cannot read the measurements but utilizes the age-of-information (AoI) [13], [14] to decide on the scheduling.…”