Optimal Strategies for Communication and Remote Estimation with an Energy Harvesting Sensor (1205.6018v1)

Abstract: We consider a remote estimation problem with an energy harvesting sensor and a remote estimator. The sensor observes the state of a discrete-time source which may be a finite state Markov chain or a multi-dimensional linear Gaussian system. It harvests energy from its environment (say, for example, through a solar cell) and uses this energy for the purpose of communicating with the estimator. Due to the randomness of energy available for communication, the sensor may not be able to communicate all the time. The sensor may also want to save its energy for future communications. The estimator relies on messages communicated by the sensor to produce real-time estimates of the source state. We consider the problem of finding a communication scheduling strategy for the sensor and an estimation strategy for the estimator that jointly minimize an expected sum of communication and distortion costs over a finite time horizon. Our goal of joint optimization leads to a decentralized decision-making problem. By viewing the problem from the estimator's perspective, we obtain a dynamic programming characterization for the decentralized decision-making problem that involves optimization over functions. Under some symmetry assumptions on the source statistics and the distortion metric, we show that an optimal communication strategy is described by easily computable thresholds and that the optimal estimate is a simple function of the most recently received sensor observation.

• The paper introduces an optimal strategy that minimizes the joint cost of communication and estimation distortion through dynamic programming.
• It demonstrates that threshold-based methods simplify decentralized sensor decision-making under intermittent energy availability.
• The study offers practical insights for designing energy-efficient remote sensing applications such as environmental monitoring.

Optimal Strategies for Communication and Remote Estimation with an Energy Harvesting Sensor

The paper presents a comprehensive exploration and formulation of optimal strategies for communication scheduling and remote estimation involving an energy harvesting sensor. This paper is particularly relevant in scenarios where sensors collect energy from the environment, such as through solar cells, and use this energy for intermittent communications necessary to report observations. The core objective is to devise strategies that minimize the joint cost of communication and estimation distortion over a finite time duration.

The authors focus on a sensor observing the state of discrete-time sources—either a finite state Markov chain or a multi-dimensional linear Gaussian system. A significant challenge faced by the sensor is the irregular availability of energy to facilitate communication consistently. Therefore, the sensor must tactically conserve energy for future communications while maintaining effective estimation accuracy at the receiver—making this a decentralized decision-making problem.

A dynamic programming approach is used to characterize the decentralized decision-making problem, primarily from the estimator's perspective. By utilizing symmetry assumptions on source statistics and distortion metrics, the paper demonstrates that optimal sensor communication strategies can be elegantly reduced to easily computable threshold-based methods. An optimal estimation strategy is derived as a straightforward function dependent on the most recent received observation.

One of the salient results from this paper is the simplification it provides for both offline computation and online implementation of optimal strategies. The paper proposes leveraging specific properties of value functions, such as Schur concavity, within dynamic programming to characterize and, consequently, derive these optimal strategies in decentralized contexts.

Implications and Future Developments

The implications of this research extend into both theoretical and practical domains. From a theoretical perspective, the paper enriches the understanding of dynamic programming applications in decentralized decision-making scenarios, especially when the problem incorporates function minimization aspects.

Practically, the results aid in constructing energy-efficient sensors capable of dealing with energy constraints in real-time applications. Possible areas of application include environmental monitoring, remote surveillance, and systems where energy autonomy is pivotal.

Future research could expand upon varying distortion metrics or harvest energy models, possibly advancing towards adaptive strategies that incorporate machine learning techniques for contextually aware optimizations. Additionally, investigating the application of similar decentralized optimization strategies in other networked systems and under different resource constraints could prove beneficial.

In essence, this paper serves as a robust framework for designing optimal communication and estimation strategies across a spectrum of applications involving energy-limited sensing devices.