Real-time Tracking System with Partially Coupled Sources

TL;DR

The paper tackles real-time tracking of $K$ partially coupled sources in a pull-based system where the sink requests updates from a single source per slot over an unreliable wireless channel. The coupling is modeled via a mixture $P=\lambda P^C+(1-\lambda)P^I$, and the objective minimizes the time-average distortion $\frac{1}{K}\sum_k D(X_k(t),\hat{X}_k(t))$ plus a transmission cost with weight $\gamma$, i.e., ${\lim\sup}_{T\to\infty} \frac{1}{T} \sum_t \mathbb{E}\Big\{ \frac{1}{K}\sum_k D(X_k(t),\hat{X}_k(t)) + \gamma \tilde{c}(t) \Big\}$. Due to partial observability at the sink, the problem is formulated as a POMDP and recast as a belief-MDP, which is solved approximately using Relative Value Iteration after truncating the belief space. The resulting POMDP-based policy outperforms a maximum-age-first baseline, with costs decreasing as the coupling factor $\lambda$ increases, indicating that information from updates propagates more efficiently across correlated sources. The approach provides a principled framework for joint estimation and scheduling in networks with partially coupled dynamics and unreliable channels, enabling adaptive, cost-aware updates in real time.

Abstract

We consider a pull-based real-time tracking system consisting of multiple partially coupled sources and a sink. The sink monitors the sources in real-time and can request one source for an update at each time instant. The sources send updates over an unreliable wireless channel. The sources are partially coupled, and updates about one source can provide partial knowledge about other sources. We study the problem of minimizing the sum of an average distortion function and a transmission cost. Since the controller is at the sink side, the controller (sink) has only partial knowledge about the source states, and thus, we model the problem as a partially observable Markov decision process (POMDP) and then cast it as a belief-MDP problem. Using the relative value iteration algorithm, we solve the problem and propose a control policy. Simulation results show the proposed policy's effectiveness and superiority compared to a baseline policy.

Figures (5)

• Figure 1: The considered system model.
• Figure 2: The average cost of different policies with respect to coupling factor $\lambda$, where $p_s=0.8$, $p = 0.8$, $\gamma = 0.15$, $N = 6$.
• Figure 3: The average cost of different policies with respect to transmission cost weight $\gamma$, where $p_s=0.8$, $p = 0.8$, $K=2$, $N = 6$.
• Figure 4: The average cost of different policies with respect to the probability of successful delivery $p_s$, where $\lambda=0.6$, $p = 0.8$, $\gamma = 0.05$, $N = 6$.
• Figure 5: The average cost of different policies for different probability of successful delivery with respect to the probability of self-transition $p$, where $\lambda = 0.4$, $K=2$, $\gamma=0.05$, $N = 6$.