pith. sign in

arxiv: 1907.07018 · v1 · pith:DNWV22PBnew · submitted 2019-07-16 · 📡 eess.SY · cs.SY

Transmission Power Control for Remote State Estimation in Industrial Wireless Sensor Networks

Samuele Zoppi , Touraj Soleymani , Markus Kl\"ugel , Mikhail Vilgelm , Sandra Hirche , Wolfgang Kellerer This is my paper

Pith reviewed 2026-05-24 20:47 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords wirelesscontrolindustrialnetworkspowertransmissionalgorithmdynamics
0
0 comments X

The pith

A minimum transmission power control policy computed by approximate value iteration adapts to arbitrary interference scenarios and NCS dynamics for remote state estimation over shared packet-erasure channels.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper casts the coordination of multiple sensors transmitting to remote estimators as an infinite-horizon Markov decision process whose state includes the estimators' error covariances and whose actions are discrete transmission power levels. Approximate value iteration solves the resulting optimization for the lowest average power that keeps estimation error below target thresholds. The computed policy is evaluated across multiple interference levels and plant dynamics, showing that it meets the accuracy requirements while using less power than fixed or heuristic baselines. The results indicate that the same policy structure works without retuning for the tested range of conditions.

Core claim

By modeling joint estimation error evolution and channel access as an infinite-horizon MDP and solving it with approximate value iteration, a minimum-power transmission policy is obtained that coordinates sensors on a shared erasure channel while adapting to different interference conditions and control-system dynamics.

What carries the argument

Infinite-horizon Markov decision process whose state tracks remote estimator error covariances and whose actions are transmission power levels, solved by approximate value iteration.

If this is right

  • The policy achieves the target estimation accuracy with lower average transmission power than constant-power or myopic alternatives.
  • The same policy structure coordinates multiple NCSs on one shared channel without requiring separate resource partitions.
  • Performance remains consistent across a range of packet-erasure probabilities induced by different interference levels.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • An online learning extension could update the MDP transition model when channel statistics drift, allowing continued operation without full recomputation.
  • Pairing the power policy with event-triggered sensing might reduce transmissions further while preserving the same error bounds.
  • The MDP formulation could be reused for power allocation in other shared-medium remote estimation settings such as multi-agent monitoring.
  • keywords:[

Load-bearing premise

The wireless channel statistics, interference model, and NCS dynamics are known in advance and remain stationary enough for the infinite-horizon MDP formulation and its approximate solution to stay valid over the operating horizon.

What would settle it

A deployment in which the interference statistics or plant dynamics change after policy computation, causing the long-run average estimation error to exceed the design threshold.

Figures

Figures reproduced from arXiv: 1907.07018 by Markus Kl\"ugel, Mikhail Vilgelm, Samuele Zoppi, Sandra Hirche, Touraj Soleymani, Wolfgang Kellerer.

Figure 1
Figure 1. Figure 1: System model of an industrial WSN deployed for the [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Exemplary PSR feasibility region Λκ of 3 sensors with equal distances, for sensors 1 and 2 (κk,1, κk,2) as the PSR req. of sensor 3 (κk,3) decreases (left to right: 0.1, 0.5, 0.9). In this work, we apply the Foschini-Miljanic algorithm [20] to coordinate the simultaneous transmission of measure￾ments. Given the PSR requirements of the network ~κk = [κk,1, . . . , κk,L], it is possible to calculate the corr… view at source ↗
Figure 3
Figure 3. Figure 3: Visualization of exemplary PSR policies of two senso [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Circular (left) and assembly-line (right) topologi [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: shows the mean network covariance and transmission power for different relative distances d2/d1, d1 = 10 m and α = 1. In this configuration of the circular topology ( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Impact of the trade-off parameter λ on the system’s performance for 3 sensors in a circular topology with d2/d1 = 1.2 and for increasing values of α (arrow). increases, the mean transmission powers increase, decreasing the mean estimation error covariances [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Impact of the discount factor α on the system’s perfor￾mance for 3 sensors in a circular topology with d2/d1 = 1.2 and for increasing values of λ (arrow). -5 0 5 1 2 3 4 -14 -12 0 10 20 30 40 50 5 10 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Time evolution of the estimation error (top), transm [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

Novel low-power wireless technologies and IoT applications open the door to the Industrial Internet of Things (IIoT). In this new paradigm, Wireless Sensor Networks (WSNs) must fulfil, despite energy and transmission power limitations, the challenging communication requirements of advanced manufacturing processes and technologies. In industrial networks, this is possible thanks to the availability of network infrastructure and the presence of a network coordinator that efficiently allocates the available radio resources. In this work, we consider a WSN that simultaneously transmits measurements of Networked Control Systems' (NCSs) dynamics to remote state estimators over a shared packet-erasure channel. We develop a minimum transmission power control (TPC) policy for the coordination of the wireless medium by formulating an infinite horizon Markov decision process (MDP) optimization problem. We compute the policy using an approximate value iteration algorithm and provide an extensive evaluation of its parameters in different interference scenarios and NCSs dynamics. The evaluation results present a comprehensive characterization of the algorithm's performance, proving that it can flexibly adapt to arbitrary use cases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript formulates an infinite-horizon MDP for minimum transmission power control of sensors transmitting NCS state measurements over a shared packet-erasure channel in an industrial WSN. The MDP is solved via approximate value iteration; the resulting policy is evaluated across multiple interference scenarios and NCS dynamics to characterize performance and demonstrate flexible adaptation to different use cases.

Significance. If the quantitative evaluation and policy computation hold, the work provides a concrete MDP-based method for power-efficient resource allocation in IIoT settings that must satisfy remote estimation requirements under interference. The emphasis on parameter evaluation across scenarios is a positive contribution for practical applicability, though the approach relies on standard MDP techniques without novel theoretical guarantees.

major comments (3)
  1. [Abstract, §3] Abstract and §3 (MDP formulation): the claim that the computed policy 'can flexibly adapt to arbitrary use cases' is load-bearing for the contribution, yet the infinite-horizon formulation and offline approximate value iteration presuppose known, stationary channel statistics, interference model, and NCS dynamics. The manuscript should clarify whether the policy is recomputed for each new scenario or whether a single policy is shown to generalize without re-solving.
  2. [Evaluation] Evaluation section: the abstract states that 'extensive evaluation' and 'comprehensive characterization' prove flexible adaptation, but no quantitative performance tables, convergence metrics for the approximate value iteration, or comparison against baselines (e.g., fixed-power or myopic policies) are referenced. Without these, it is impossible to verify that the reported adaptation is supported by the computed policy rather than by construction of the cost function.
  3. [§4] §4 (approximate value iteration): no derivation details, contraction-mapping arguments, or error bounds on the approximation are provided. This is load-bearing because the central claim rests on the policy obtained from the algorithm; without guarantees or reported iteration counts and value-function residuals, the soundness of the numerical results cannot be assessed.
minor comments (2)
  1. [System Model] Notation for the packet-erasure probability and interference model should be introduced consistently in the system model section before being used in the MDP transition probabilities.
  2. [Evaluation] The manuscript should include a brief statement on computational complexity of the approximate value iteration for the reported network sizes.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and will revise the manuscript accordingly to improve clarity and support for the claims.

read point-by-point responses

  1. Referee: [Abstract, §3] Abstract and §3 (MDP formulation): the claim that the computed policy 'can flexibly adapt to arbitrary use cases' is load-bearing for the contribution, yet the infinite-horizon formulation and offline approximate value iteration presuppose known, stationary channel statistics, interference model, and NCS dynamics. The manuscript should clarify whether the policy is recomputed for each new scenario or whether a single policy is shown to generalize without re-solving.

    Authors: The infinite-horizon MDP is formulated under the standard assumption of known and stationary statistics for the channel and NCS dynamics. The policy is computed offline via approximate value iteration for each specific parameter set (i.e., each interference scenario and NCS dynamics). The claim of flexible adaptation refers to the ability to obtain suitable policies by re-solving the MDP for new parameters, as demonstrated through the evaluation across scenarios. We will revise the abstract and §3 to explicitly state that the policy is recomputed for each use case. revision: yes

  2. Referee: [Evaluation] Evaluation section: the abstract states that 'extensive evaluation' and 'comprehensive characterization' prove flexible adaptation, but no quantitative performance tables, convergence metrics for the approximate value iteration, or comparison against baselines (e.g., fixed-power or myopic policies) are referenced. Without these, it is impossible to verify that the reported adaptation is supported by the computed policy rather than by construction of the cost function.

    Authors: The evaluation section presents results across multiple scenarios and NCS dynamics, but we agree that explicit quantitative tables, convergence metrics, and baseline comparisons are needed to strengthen the claims. We will revise the evaluation section to include performance tables, report value-iteration convergence metrics, and add comparisons against fixed-power and myopic policies. revision: yes

  3. Referee: [§4] §4 (approximate value iteration): no derivation details, contraction-mapping arguments, or error bounds on the approximation are provided. This is load-bearing because the central claim rests on the policy obtained from the algorithm; without guarantees or reported iteration counts and value-function residuals, the soundness of the numerical results cannot be assessed.

    Authors: We will expand §4 with additional implementation details on the approximate value iteration, including iteration counts and value-function residuals from the experiments. As the algorithm follows standard approximate dynamic programming methods, we will add references to established convergence results in the literature. We do not derive new theoretical error bounds, as the contribution centers on the application and empirical evaluation rather than novel MDP theory. revision: partial

Circularity Check

0 steps flagged

No circularity: standard MDP formulation and solution from known model

full rationale

The paper formulates an infinite-horizon MDP directly from the known wireless channel, interference, and NCS dynamics, then obtains the policy via approximate value iteration and evaluates it on varied but fixed scenarios. This is a direct optimization procedure whose output is the solution to the stated problem; no step reduces a claimed prediction or result to a fitted parameter, self-citation, or definitional tautology. The central claim of flexibility follows from re-solving the same well-defined optimization for different stationary parameters, which is independent of the paper's own outputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The approach rests on standard domain assumptions about channel and dynamics models plus the usual MDP formulation; no free parameters or invented entities are visible from the abstract.

free parameters (1)
  • MDP cost weights and transition probabilities
    These quantities must be chosen or estimated to define the optimization problem but are not quantified in the abstract.
axioms (2)
  • domain assumption The shared channel is a stationary packet-erasure channel whose erasure probability depends on chosen transmit power and interference level.
    Invoked to define the MDP transition kernel.
  • domain assumption NCS plant dynamics are linear and known to the remote estimator.
    Required for the state estimator model inside the MDP state.

pith-pipeline@v0.9.0 · 5728 in / 1290 out tokens · 23869 ms · 2026-05-24T20:47:18.641259+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages

  1. [1]

    K. J. ˚Astr¨ om,Introduction to Stochastic Control Theory . Dover Publications, 2006

    work page 2006

  2. [2]

    Network-Induced Constr aints in Networked Control SystemsA Survey,

    L. Zhang, H. Gao, and O. Kaynak, “Network-Induced Constr aints in Networked Control SystemsA Survey,” IEEE Transactions on Industrial Informatics, vol. 9, no. 1, pp. 403–416, Feb 2013

    work page 2013

  3. [3]

    Industrial Wireless Senso r Networks: Challenges, Design Principles, and Technical Approaches,

    V . C. Gungor and G. P . Hancke, “Industrial Wireless Senso r Networks: Challenges, Design Principles, and Technical Approaches, ” IEEE Trans- actions on Industrial Electronics , vol. 56, no. 10, pp. 4258–4265, Oct 2009

    work page 2009

  4. [4]

    Kalman Filtering with Intermittent Observat ions,

    B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M . I. Jordan, and S. S. Sastry, “Kalman Filtering with Intermittent Observat ions,” IEEE Transactions on Automatic Control , vol. 49, no. 9, pp. 1453–1464, Sep. 2004

    work page 2004

  5. [5]

    Infinite Horizon Optimal Transmission Power Control for Remote State Estima tion over Fading Channels,

    X. Ren, J. Wu, K. H. Johansson, G. Shi, and L. Shi, “Infinite Horizon Optimal Transmission Power Control for Remote State Estima tion over Fading Channels,” IEEE Transactions on Automatic Control , vol. 63, no. 1, pp. 85–100, 2018

    work page 2018

  6. [6]

    Data-drive n Power Control for State Estimation: A Bayesian inference ap proach,

    J. Wu, Y . Li, D. E. Quevedo, V . Lau, and L. Shi, “Data-drive n Power Control for State Estimation: A Bayesian inference ap proach,” Automatica, vol. 54, pp. 332–339, 2015

    work page 2015

  7. [7]

    Improved Results o n Transmission Power Control for Remote State Estimation,

    J. Wu, Y . Li, D. E. Quevedo, and L. Shi, “Improved Results o n Transmission Power Control for Remote State Estimation,” Systems and Control Letters, vol. 107, pp. 44–48, 2017

    work page 2017

  8. [8]

    Covariance-Based Transmission Power Control for E stimation over Wireless Sensor Networks,

    T. Soleymani, S. Zoppi, M. Vilgelm, S. Hirche, W. Kellere r, and J. S. Baras, “Covariance-Based Transmission Power Control for E stimation over Wireless Sensor Networks,” in 2018 European Control Conference (ECC), June 2018, pp. 857–862

    work page 2018

  9. [9]

    Online Sensor Tra nsmission Power Schedule for Remote State Estimation,

    Y . Li, D. E. Quevedo, V . Lau, and L. Shi, “Online Sensor Tra nsmission Power Schedule for Remote State Estimation,” in 52nd IEEE Conference on Decision and Control , Dec 2013, pp. 4000–4005

    work page 2013

  10. [10]

    Power Control of an Energy Harvesting Sensor for Remote State Esti mation,

    Y . Li, F. Zhang, D. E. Quevedo, V . Lau, S. Dey, and L. Shi, “ Power Control of an Energy Harvesting Sensor for Remote State Esti mation,” IEEE Transactions on Automatic Control , vol. 62, no. 1, pp. 277–290, Jan 2017

    work page 2017

  11. [11]

    Multi-Sensor Tr ansmission Power Scheduling for Remote State Estimation Under SINR Mod el,

    Y . Li, D. E. Quevedo, V . Lau, and L. Shi, “Multi-Sensor Tr ansmission Power Scheduling for Remote State Estimation Under SINR Mod el,” in 53rd IEEE Conference on Decision and Control , Dec 2014, pp. 1055– 1060

    work page 2014

  12. [12]

    Mu lti-Sensor Scheduling for State Estimation With Event-Based, Stochas tic Triggers,

    S. Weerakkody, Y . Mo, B. Sinopoli, D. Han, and L. Shi, “Mu lti-Sensor Scheduling for State Estimation With Event-Based, Stochas tic Triggers,” IEEE Transactions on Automatic Control , vol. 61, no. 9, pp. 2695–2701, Sep. 2016

    work page 2016

  13. [13]

    Optimal Scheduling of M ultiple Sensors over Shared Channels with Packet Transmission Cons traint,

    S. Wu, X. Ren, S. Dey, and L. Shi, “Optimal Scheduling of M ultiple Sensors over Shared Channels with Packet Transmission Cons traint,” Automatica, vol. 96, pp. 22–31, 2018

    work page 2018

  14. [14]

    Channel Allocation and Power Contr ol Scheme over Interference Channels with QoS Constraints,

    L. Zhang and J. Sun, “Channel Allocation and Power Contr ol Scheme over Interference Channels with QoS Constraints,” in 2017 13th IEEE International Conference on Control Automation (ICCA) , July 2017, pp. 794–798

    work page 2017

  15. [15]

    Multi-sensor Transmissi on Power Control for Remote Estimation Through a SINR-based Communi cation Channel,

    Y . Li, A. S. Mehr, and T. Chen, “Multi-sensor Transmissi on Power Control for Remote Estimation Through a SINR-based Communi cation Channel,” Automatica, vol. 101, pp. 78–86, 2019

    work page 2019

  16. [16]

    Transmit Power Control and Rem ote State Estimation with Sensor Networks: A Bayesian Inference Appr oach,

    Y . Li, J. Wu, and T. Chen, “Transmit Power Control and Rem ote State Estimation with Sensor Networks: A Bayesian Inference Appr oach,” Automatica, vol. 97, pp. 292–300, 2018

    work page 2018

  17. [17]

    Power Control for Multi - sensor Remote State Estimation over Interference Channel,

    Y . Li, C. S. Chen, and W. S. Wong, “Power Control for Multi - sensor Remote State Estimation over Interference Channel, ” Systems and Control Letters, vol. 126, pp. 1–7, 2019

    work page 2019

  18. [18]

    Power Control in Wireless Cellular Networks,

    M. Chiang, P . Hande, T. Lan, and C. W. Tan, “Power Control in Wireless Cellular Networks,” F oundations and Trends in Networking, vol. 2, no. 4, pp. 381–533, 2008

    work page 2008

  19. [19]

    Review of Some Fundament al Approaches for Power Control in Wireless Networks,

    V . G. Douros and G. C. Polyzos, “Review of Some Fundament al Approaches for Power Control in Wireless Networks,” Computer Com- munications, vol. 34, no. 13, pp. 1580–1592, 2011

    work page 2011

  20. [20]

    A Simple Distributed Au tonomous Power Control Algorithm and Its Convergence,

    G. J. Foschini and Z. Miljanic, “A Simple Distributed Au tonomous Power Control Algorithm and Its Convergence,” IEEE Transactions on V ehicular Technology, vol. 42, no. 4, pp. 641–646, Nov 1993

    work page 1993

  21. [21]

    Wireless Link Schedul ing With Power Control and SINR Constraints,

    S. A. Borbash and A. Ephremides, “Wireless Link Schedul ing With Power Control and SINR Constraints,” IEEE Transactions on Informa- tion Theory , vol. 52, no. 11, pp. 5106–5111, Nov 2006

    work page 2006

  22. [22]

    Optimal Routing, Link Sc heduling and Power Control in Multihop Wireless Networks,

    R. L. Cruz and A. V . Santhanam, “Optimal Routing, Link Sc heduling and Power Control in Multihop Wireless Networks,” in IEEE INFO- COM 2003. 22nd Annual Joint Conference of the IEEE Computer a nd Communications Societies, vol. 1, March 2003, pp. 702–711 vol.1

    work page 2003

  23. [23]

    Distribute d Interference Compensation for Wireless Networks,

    Jianwei Huang, R. A. Berry, and M. L. Honig, “Distribute d Interference Compensation for Wireless Networks,” IEEE Journal on Selected Areas in Communications , vol. 24, no. 5, pp. 1074–1084, May 2006

    work page 2006

  24. [24]

    Bayesian Game-theoretic M odeling of Transmit Power Determination in a Self-organizing CDMA W ire- less Network,

    C. A. St Jean and B. Jabbari, “Bayesian Game-theoretic M odeling of Transmit Power Determination in a Self-organizing CDMA W ire- less Network,” in IEEE 60th V ehicular Technology Conference, 2004. VTC2004-Fall. 2004, vol. 5, Sep. 2004, pp. 3496–3500 V ol. 5

    work page 2004

  25. [25]

    Non-coope rative Power Control for Wireless Ad Hoc Networks with Repeated Gam es,

    C. Long, Q. Zhang, B. Li, H. Y ang, and X. Guan, “Non-coope rative Power Control for Wireless Ad Hoc Networks with Repeated Gam es,” IEEE Journal on Selected Areas in Communications , vol. 25, no. 6, pp. 1101–1112, August 2007

    work page 2007

  26. [26]

    A Game Theore tic Frame- work for Power Control in Wireless Sensor Networks,

    S. Sengupta, M. Chatterjee, and K. Kwiat, “A Game Theore tic Frame- work for Power Control in Wireless Sensor Networks,” IEEE Transac- tions on Computers , vol. 59, no. 2, pp. 231–242, Feb 2010

    work page 2010

  27. [27]

    A Joint Scheduling, Power Cont rol, and Routing Algorithm for Ad Hoc Wireless Networks,

    Y . Li and A. Ephremides, “A Joint Scheduling, Power Cont rol, and Routing Algorithm for Ad Hoc Wireless Networks,” Ad Hoc Networks , vol. 5, no. 7, pp. 959–973, 2007

    work page 2007

  28. [28]

    1–320, Sep

    “IEEE Standard for Information technology– Local and m etropolitan area networks– Specific requirements– Part 15.4: Wireless M edium Access Control (MAC) and Physical Layer (PHY) Specification s for Low Rate Wireless Personal Area Networks (WPANs),” IEEE Std 802.15.4-2006 (Revision of IEEE Std 802.15.4-2003) , pp. 1–320, Sep. 2006

    work page 2006

  29. [29]

    IEEE Standard for Local and metropolitan area network s–Part 15.4: Low-Rate Wireless Personal Area Networks (LR-WPANs) Amend ment 1: MAC sublayer,

    “IEEE Standard for Local and metropolitan area network s–Part 15.4: Low-Rate Wireless Personal Area Networks (LR-WPANs) Amend ment 1: MAC sublayer,” IEEE Std 802.15.4e-2012 (Amendment to IEEE Std 802.15.4-2011), pp. 1–225, April 2012

    work page 2012

  30. [30]

    I. F. Akyildiz and M. C. Vuran, Wireless Sensor Networks. John Wiley & Sons, 2010, vol. 4

    work page 2010

  31. [31]

    An Analysis of Unreliability and Asymmetry in Low-power Wireless Links,

    M. Z. n. Zamalloa and B. Krishnamachari, “An Analysis of Unreliability and Asymmetry in Low-power Wireless Links,” ACM Transactions on Sensor Networks (TOSN) , vol. 3, no. 2, Jun. 2007

    work page 2007

  32. [32]

    D. P . Bertsekas, Dynamic Programming and Optimal Control, V ol. II , 3rd ed. Athena Scientific, 2001

    work page 2001