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Remote Estimation over Packet-Dropping Wireless Channels with Partial State Information

Ioannis Tzortzis, Evagoras Makridis, Charalambos D. Charalambous, Themistoklis Charalambous

TL;DR

This work addresses remote state estimation over packet-dropping wireless channels with imperfect channel state information. It casts the problem as a finite-horizon POMDP that jointly considers age of information and an unknown channel state, and introduces an information (belief) state to enable optimal decision making. The authors derive a dynamic programming framework and compute the optimal transmission policy using PBVI, accounting for HARQ dynamics via a retransmission-dependent error model. The approach balances estimation accuracy, information freshness, and energy consumption, and is demonstrated through numerical experiments showing HARQ's impact on MSE and AoI under channel uncertainty.

Abstract

In this paper, we study the design of an optimal transmission policy for remote state estimation over packet-dropping wireless channels with imperfect channel state information. A smart sensor uses a Kalman filter to estimate the system state and transmits its information to a remote estimator. Our objective is to minimize the state estimation error and energy consumption by deciding whether to transmit new information or retransmit previously failed packets. To balance the trade-off between information freshness and reliability, the sensor applies a hybrid automatic repeat request protocol. We formulate this problem as a finite horizon partially observable Markov decision process with an augmented state-space that incorporates both the age of information and the unknown channel state. By defining an information state, we derive the dynamic programming equations for evaluating the optimal policy. This transmission policy is computed numerically using the point-based value iteration algorithm.

Remote Estimation over Packet-Dropping Wireless Channels with Partial State Information

TL;DR

This work addresses remote state estimation over packet-dropping wireless channels with imperfect channel state information. It casts the problem as a finite-horizon POMDP that jointly considers age of information and an unknown channel state, and introduces an information (belief) state to enable optimal decision making. The authors derive a dynamic programming framework and compute the optimal transmission policy using PBVI, accounting for HARQ dynamics via a retransmission-dependent error model. The approach balances estimation accuracy, information freshness, and energy consumption, and is demonstrated through numerical experiments showing HARQ's impact on MSE and AoI under channel uncertainty.

Abstract

In this paper, we study the design of an optimal transmission policy for remote state estimation over packet-dropping wireless channels with imperfect channel state information. A smart sensor uses a Kalman filter to estimate the system state and transmits its information to a remote estimator. Our objective is to minimize the state estimation error and energy consumption by deciding whether to transmit new information or retransmit previously failed packets. To balance the trade-off between information freshness and reliability, the sensor applies a hybrid automatic repeat request protocol. We formulate this problem as a finite horizon partially observable Markov decision process with an augmented state-space that incorporates both the age of information and the unknown channel state. By defining an information state, we derive the dynamic programming equations for evaluating the optimal policy. This transmission policy is computed numerically using the point-based value iteration algorithm.
Paper Structure (11 sections, 1 theorem, 31 equations, 3 figures)

This paper contains 11 sections, 1 theorem, 31 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Dynamical System and Smart Sensor
  4. Wireless Channel and Remote Estimator
  5. Problem Setup
  6. Problem Formulation
  7. Finite horizon POMDP
  8. Performance Criterion
  9. Problem Solution
  10. Numerical Experiments
  11. Conclusions

Key Result

Theorem 1

Define recursively the functions $V_k(\pi,s^r)$, $0\leq k\leq N$, $\pi\in \Pi_1({\@fontswitch\mathcal{S}}^c)$, $s^r\in {\@fontswitch\mathcal{S}}^r$ by

Figures (3)

  • Figure 1: Remote state estimation scheme.
  • Figure 2: Evolution of the POMDP states and the MSE per iteration $k$.
  • Figure 3: MSE for different realizations of $T^c_1$ and $T^c_2$ .

Theorems & Definitions (3)

  • Remark 1
  • Theorem 1
  • proof