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High-Accuracy and Efficient DV-Hop Localization for IoT Using Hop Loss

Zhengdi Shen, Qiran Wang

TL;DR

This work tackles IoT localization by reformulating DV-Hop with a novel hop-loss model called distance-based connectivity consistency ($HL^{DCC}$). It introduces an activation condition based on connectivity consistency $AC^{CC}$ and a continuous distance-based individual loss $IL^{DST}$, combining them into $HL^{DCC}$ to avoid expensive predicted hop-count calculations while ensuring full coverage of hop errors. The approach yields higher localization accuracy and significant reductions in computation time (about 30–40% over a hop-loss baseline) across multiple network topologies, with ablation showing the necessity of both components. Overall, DCC enhances DV-Hop performance for large-scale IoT localization, offering practical benefits for real-time and scalable deployments.

Abstract

Accurate localization is critical for Internet of Things (IoT) applications. Using hop loss in DV-Hop-based algorithms is a promising approach. Nevertheless, challenges lie in overcoming the computational complexity caused by re-calculating the predicted hop-counts, and how to further optimize the modeling for better accuracy. In this paper, a novel hop loss modeling, distance-based connectivity consistency (DCC), is proposed. By focusing on the first order connectivity, DCC avoids computing predicted hop-counts, and significantly reduces the time complexity. We also provide a proof to theoretically guarantee that this design achieves a full coverage of all hop errors. In addition, by computing a continuous loss function instead of the discrete hop-count errors, DCC further improves the localization accuracy. In the evaluations, DCC demonstrates notable improvements in accuracy over other highly regarded algorithms, and reduces 30% to 40% total computation time compared with the baseline algorithm using hop loss.

High-Accuracy and Efficient DV-Hop Localization for IoT Using Hop Loss

TL;DR

This work tackles IoT localization by reformulating DV-Hop with a novel hop-loss model called distance-based connectivity consistency (). It introduces an activation condition based on connectivity consistency and a continuous distance-based individual loss , combining them into to avoid expensive predicted hop-count calculations while ensuring full coverage of hop errors. The approach yields higher localization accuracy and significant reductions in computation time (about 30–40% over a hop-loss baseline) across multiple network topologies, with ablation showing the necessity of both components. Overall, DCC enhances DV-Hop performance for large-scale IoT localization, offering practical benefits for real-time and scalable deployments.

Abstract

Accurate localization is critical for Internet of Things (IoT) applications. Using hop loss in DV-Hop-based algorithms is a promising approach. Nevertheless, challenges lie in overcoming the computational complexity caused by re-calculating the predicted hop-counts, and how to further optimize the modeling for better accuracy. In this paper, a novel hop loss modeling, distance-based connectivity consistency (DCC), is proposed. By focusing on the first order connectivity, DCC avoids computing predicted hop-counts, and significantly reduces the time complexity. We also provide a proof to theoretically guarantee that this design achieves a full coverage of all hop errors. In addition, by computing a continuous loss function instead of the discrete hop-count errors, DCC further improves the localization accuracy. In the evaluations, DCC demonstrates notable improvements in accuracy over other highly regarded algorithms, and reduces 30% to 40% total computation time compared with the baseline algorithm using hop loss.
Paper Structure (14 sections, 1 theorem, 14 equations, 7 figures, 8 tables)

This paper contains 14 sections, 1 theorem, 14 equations, 7 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. High Accuracy Hop Loss with Optimized Efficiency
  4. Activation Condition Based on Connectivity Consistency
  5. Individual Loss Based on Distance between Nodes
  6. Total Hop Loss with High Accuracy and Optimized Efficiency
  7. Simulation Results
  8. Data, Algorithm Settings and Evaluation Metric
  9. Simulation Data
  10. Algorithm Settings
  11. Evaluation Metric
  12. Comparison Results
  13. Ablation Study
  14. Conclusion

Key Result

Proposition 1

If there are two nodes $i, j$ in a network making $Hop^{real}_{i,j} \neq Hop^{pred}_{i,j}$, then there exist $i', j'$ in the network making $AC^{CC}_{i', j'}=1$.

Figures (7)

  • Figure 1: An example of the DV-Hop localization. A node has a communication radius $R$, and can directly communicate with other nodes within the communication radius. The hop-count between two directly connected nodes is 1, and the hop-counts between other nodes can be derived by information propagation.
  • Figure 2: An example network with a hop-count inconsistency between $Hop^{real}_{1,4}$ and $Hop^{pred}_{1,4}$. Each dot represents a node, and each segment between nodes represents the nodes are connected. $HL^{base}$ cannot catch this hop error because $AC^{base}_{1,4}=0$. On the other hand, $AC^{CC}_{1,4}=1$, making the modified hop loss capable of catching the error.
  • Figure 3: The relation between $IL_{i,j}^{DST}$ and $Dist_{i,j}^{pred}$ in the two conditions.
  • Figure 4: The types of the network topology in simulations: randomly distributed, C-shaped, O-shaped and X-shaped. Each blue dot $\bullet$ represents an unknown node, and each red dot $\bullet$ represents an anchor nodes.
  • Figure 5: The $95\%$ confidence interval of $MLEs$. ${N}_{a}=20$, $R=25$.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof