# Optimal scheduling strategy for networked estimation with energy harvesting

## TL;DR

This paper develops an optimal scheduling and estimation strategy for a networked system with energy-harvesting sensors transmitting over bandwidth-limited wireless channels, ensuring minimal mean-squared error.

## Contribution

It introduces a globally optimal scheduling and estimation framework for energy-harvesting sensors with a threshold-based policy structure under symmetric unimodal data distributions.

## Key findings

- Optimal policies are derived under symmetry and unimodality assumptions.
- The scheduling policy is characterized by a threshold function depending on time and energy.
- A recursive algorithm for computing the threshold is provided.

## Abstract

Joint optimization of scheduling and estimation policies is considered for a system with two sensors and two non-collocated estimators. Each sensor produces an independent and identically distributed sequence of random variables, and each estimator forms estimates of the corresponding sequence with respect to the mean-squared error sense. The data generated by the sensors is transmitted to the corresponding estimators, over a bandwidth-constrained wireless network that can support a single packet per time slot. The access to the limited communication resources is determined by a scheduler who decides which sensor measurement to transmit based on both observations. The scheduler has an energy-harvesting battery of limited capacity, which couples the decision-making problem in time. Despite the overall lack of convexity of the team decision problem, it is shown that this system admits globally optimal scheduling and estimation strategies under the assumption that the distributions of the random variables at the sensors are symmetric and unimodal. Additionally, the optimal scheduling policy has a structure characterized by a threshold function that depends on the time index and energy level. A recursive algorithm for threshold computation is provided.