# Remote State Estimation with Smart Sensors over Markov Fading Channels

arXiv: https://arxiv.org/abs/2005.07871 · HTML: https://mlsanity.com/paper/2005.07871/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2020.

## Built on by (most cited first, 8 of 8)

- [Structure-Enhanced DRL for Optimal Transmission Scheduling](https://mlsanity.com/paper/2212.12704/) (2022)
- [Deep Reinforcement Learning for Wireless Scheduling in Distributed Networked Control](https://mlsanity.com/paper/2109.12562/) (2021)
- [Structure-Enhanced Deep Reinforcement Learning for Optimal Transmission Scheduling](https://mlsanity.com/paper/2211.10827/) (2022)
- [Semantic-aware Transmission Scheduling: a Monotonicity-driven Deep Reinforcement Learning Approach](https://mlsanity.com/paper/2305.13706/) (2023)
- [Wireless Human-Machine Collaboration in Industry 5.0](https://mlsanity.com/paper/2410.14153/) (2024)
- [Wireless Resource Allocation with Collaborative Distributed and Centralized DRL under Control Channel Attacks](https://mlsanity.com/paper/2411.10702/) (2024)
- [Goal-oriented Transmission Scheduling: Structure-guided DRL with a Unified Dual On-policy and Off-policy Approach](https://mlsanity.com/paper/2501.11921/) (2025)
- [Adaptive Scheduling: A Reinforcement Learning Whittle Index Approach for Wireless Sensor Networks](https://mlsanity.com/paper/2601.01179/) (2026)

## Abstract (arXiv)

We consider a fundamental remote state estimation problem of discrete-time linear time-invariant (LTI) systems. A smart sensor forwards its local state estimate to a remote estimator over a time-correlated M-state Markov fading channel, where the packet drop probability is time-varying and depends on the current fading channel state. We establish a necessary and sufficient condition for mean-square stability of the remote estimation error covariance as ρ2(A)ρ(DM)<1, where ρ(·) denotes the spectral radius, A is the state transition matrix of the LTI system, D is a diagonal matrix containing the packet drop probabilities in different channel states, and M is the transition probability matrix of the Markov channel states. To derive this result, we propose a novel estimation-cycle based approach, and provide new element-wise bounds of matrix powers. The stability condition is verified by numerical results, and is shown more effective than existing sufficient conditions in the literature. We observe that the stability region in terms of the packet drop probabilities in different channel states can either be convex or concave depending on the transition probability matrix M. Our numerical results suggest that the stability conditions for remote estimation may coincide for setups with a smart sensor and with a conventional one (which sends raw measurements to the remote estimator), though the smart sensor setup achieves a better estimation performance.