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 approximation that yields a finite-state MDP solved via the relative value iteration algorithm (RVIA). We further reformulate the original belief-MDP into a discounted version and solve it using incremental pruning algorithm (IPA). Numerical results demonstrate that the performance of the RVIA-based policy improves with the truncation depth at the expense of computational effort, and both proposed methods outperform low-complexity baselines across a wide range of system parameters. The results also reveal a switching-type structure of the RVIA-based policy over the belief simplex and quantify the impact of key system parameters, highlighting the importance of accounting for state-dependent sensing.