Structural Monotonicity in Transmission Scheduling for Remote State Estimation with Hidden Channel Mode

TL;DR

This paper develops a novel state-space folding technique to analyze monotonicity in transmission scheduling for remote state estimation with hidden channel modes, revealing threshold-based optimal policies.

Contribution

Introduces a new state-space folding method to establish monotonicity in POMDPs for remote estimation, enabling threshold policy characterization.

Findings

Monotonicity of the value function is established using state-space folding.

Optimal scheduling policies have a threshold structure.

The approach applies to partially observable channel modes.

Abstract

This study treats transmission scheduling for remote state estimation over unreliable channels with a hidden mode. A local Kalman estimator selects scheduling actions, such as power allocation and resource usage, and communicates with a remote estimator based on acknowledgement feedback, balancing estimation performance and communication cost. The resulting problem is naturally formulated as a partially observable Markov decision process (POMDP). In settings with observable channel modes, it is well known that monotonicity of the value function can be established via investigating order-preserving property of transition kernels. In contrast, under partial observability, the transition kernels generally lack this property, which prevents the direct application of standard monotonicity arguments. To overcome this difficulty, we introduce a novel technique, referred to as state-space folding, which induces transformed transition kernels recovering order preservation on the folded space. This transformation enables a rigorous monotonicity analysis in the partially observable setting. As a representative implication, we focus on an associated optimal stopping formulation and show that the resulting optimal scheduling policy admits a threshold structure.