Remote Tracking with State-Dependent Sensing in Pull-Based Systems: A POMDP Framework

We consider real-time remote tracking of a Markov source observed by multiple heterogeneous sensors with state-dependent sensing accuracy, motivated by distributed camera networks with overlapping coverage and spatial blind spots. Upon commands from a remote sink, sensors transmit their observations over error-prone channels. We aim to minimize the long-term average of a weighted sum of goal-aware distortion and transmission costs. The problem is formulated as a partially observable Markov decision process (POMDP) and cast into an equivalent belief-MDP. To address the intractability of the infinite and continuous belief space, we develop a truncation-based method that yields a finite-state MDP which can be solved via standard methods such as relative value iteration. We further use a discounted reformulation to derive a theoretical lower bound for the optimal average cost, which is tightened via the incremental pruning algorithm (IPA) and also induces a comparison policy. Numerical results demonstrate that the performance of the proposed policy improves with the truncation depth at the expense of computational effort, and also outperforms low-complexity baselines across a wide range of system parameters. The results also reveal a switching-type structure of the truncation-based policy over the belief simplex and quantify the impact of key system parameters, highlighting the importance of accounting for state-dependent~sensing.