Sensor Scheduling in Variance Based Event Triggered Estimation with Packet Drops

TL;DR

This paper develops optimal sensor scheduling strategies for remote state estimation over unreliable channels, demonstrating the effectiveness of threshold policies in minimizing estimation error and energy use, with structural results applicable to various scenarios.

Contribution

It establishes structural properties and optimality of threshold-based scheduling policies for variance-based event-triggered estimation with packet drops, including extensions to Markovian drop models.

Findings

Threshold policies are optimal for single sensor cases.

Large error covariances trigger sensor transmissions.

Structural results hold for Markovian packet drops.

Abstract

This paper considers a remote state estimation problem with multiple sensors observing a dynamical process, where sensors transmit local state estimates over an independent and identically distributed (i.i.d.) packet dropping channel to a remote estimator. At every discrete time instant, the remote estimator decides whether each sensor should transmit or not, with each sensor transmission incurring a fixed energy cost. The channel is shared such that collisions will occur if more than one sensor transmits at a time. Performance is quantified via an optimization problem that minimizes a convex combination of the expected estimation error covariance at the remote estimator and expected energy usage across the sensors. For transmission schedules dependent only on the estimation error covariance at the remote estimator, this work establishes structural results on the optimal scheduling which show that 1) for unstable systems, if the error covariance is large then a sensor will always be scheduled to transmit, and 2) there is a threshold-type behaviour in switching from one sensor transmitting to another. Specializing to the single sensor case, these structural results demonstrate that a threshold policy (i.e. transmit if the error covariance exceeds a certain threshold and don't transmit otherwise) is optimal. We also consider the situation where sensors transmit measurements instead of state estimates, and establish structural results including the optimality of threshold policies for the single sensor, scalar case. These results provide a theoretical justification for the use of such threshold policies in variance based event triggered estimation. Numerical studies confirm the qualitative behaviour predicted by our structural results. An extension of the structural results to Markovian packet drops is also outlined.