Structural Monotonicity in Transmission Scheduling for Remote State Estimation with Hidden Channel Mode
This addresses the problem of efficient resource allocation in networked control systems for applications like IoT or robotics, though it is incremental as it extends known monotonicity results to partially observable settings.
The paper tackles transmission scheduling for remote state estimation over unreliable channels with hidden modes, formulating it as a POMDP, and introduces a state-space folding technique to establish monotonicity, enabling a threshold-structured optimal policy.
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.