Optimal Sensor Scheduling and Remote Estimation over an Additive Noise Channel

TL;DR

This paper addresses optimal sensor scheduling and remote estimation over a noisy channel, deriving solutions for minimizing combined communication and estimation costs with specific distribution assumptions.

Contribution

It introduces a framework considering additive channel noise, extending prior models, and derives optimal strategies under certain distributional conditions.

Findings

Optimal encoding and scheduling policies derived for specific distributions.

Reduction in total expected cost achieved with proposed strategies.

Enhanced understanding of sensor communication over noisy channels.

Abstract

We consider a sensor scheduling and remote estimation problem with one sensor and one estimator. At each time step, the sensor makes an observation on the state of a source, and then decides whether to transmit its observation to the estimator or not. The sensor is charged a cost for each transmission. The remote estimator generates a real-time estimate on the state of the source based on the messages received from the sensor. The estimator is charged for estimation error. As compared with previous works from the literature, we further assume that there is an additive communication channel noise. As a consequence, the sensor needs to encode the message before transmitting it to the estimator. For some specific distributions of the underlying random variables, we obtain the optimal solution to the problem of minimizing the expected value of the sum of communication cost and estimation cost over the time horizon.