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Optimizing Sensor Network Design for Multiple Coverage

Lukas Taus, Yen-Hsi Richard Tsai

TL;DR

This work tackles minimizing the number of sensors to achieve robust, multi-coverage in non-simply connected environments by formulating a greedy next-best-view approach with a novel gain function $\mathcal{G}_k$. It establishes monotonicity and submodularity properties of the objective $f_k$, provides approximation guarantees, and introduces a parallel greedy variant to accelerate computation. A deep learning strategy with a UNet-like architecture is developed to predict the gain function, enabling near real-time decisions, and a comprehensive data-generation pipeline (including $D_0$, $D_\epsilon$, and $D_+$) supports training. Extensive simulations demonstrate that the combination of greedy, parallelization, and learned gains achieves near-optimal coverage with fewer sensors, while revealing the importance of training data distribution on inference performance. The proposed framework advances practical, robust sensor-network design with potential impact on surveillance, robotics, and infrastructure planning.

Abstract

Sensor placement optimization methods have been studied extensively. They can be applied to a wide range of applications, including surveillance of known environments, optimal locations for 5G towers, and placement of missile defense systems. However, few works explore the robustness and efficiency of the resulting sensor network concerning sensor failure or adversarial attacks. This paper addresses this issue by optimizing for the least number of sensors to achieve multiple coverage of non-simply connected domains by a prescribed number of sensors. We introduce a new objective function for the greedy (next-best-view) algorithm to design efficient and robust sensor networks and derive theoretical bounds on the network's optimality. We further introduce a Deep Learning model to accelerate the algorithm for near real-time computations. The Deep Learning model requires the generation of training examples. Correspondingly, we show that understanding the geometric properties of the training data set provides important insights into the performance and training process of deep learning techniques. Finally, we demonstrate that a simple parallel version of the greedy approach using a simpler objective can be highly competitive.

Optimizing Sensor Network Design for Multiple Coverage

TL;DR

This work tackles minimizing the number of sensors to achieve robust, multi-coverage in non-simply connected environments by formulating a greedy next-best-view approach with a novel gain function . It establishes monotonicity and submodularity properties of the objective , provides approximation guarantees, and introduces a parallel greedy variant to accelerate computation. A deep learning strategy with a UNet-like architecture is developed to predict the gain function, enabling near real-time decisions, and a comprehensive data-generation pipeline (including , , and ) supports training. Extensive simulations demonstrate that the combination of greedy, parallelization, and learned gains achieves near-optimal coverage with fewer sensors, while revealing the importance of training data distribution on inference performance. The proposed framework advances practical, robust sensor-network design with potential impact on surveillance, robotics, and infrastructure planning.

Abstract

Sensor placement optimization methods have been studied extensively. They can be applied to a wide range of applications, including surveillance of known environments, optimal locations for 5G towers, and placement of missile defense systems. However, few works explore the robustness and efficiency of the resulting sensor network concerning sensor failure or adversarial attacks. This paper addresses this issue by optimizing for the least number of sensors to achieve multiple coverage of non-simply connected domains by a prescribed number of sensors. We introduce a new objective function for the greedy (next-best-view) algorithm to design efficient and robust sensor networks and derive theoretical bounds on the network's optimality. We further introduce a Deep Learning model to accelerate the algorithm for near real-time computations. The Deep Learning model requires the generation of training examples. Correspondingly, we show that understanding the geometric properties of the training data set provides important insights into the performance and training process of deep learning techniques. Finally, we demonstrate that a simple parallel version of the greedy approach using a simpler objective can be highly competitive.
Paper Structure (20 sections, 6 theorems, 54 equations, 11 figures, 2 algorithms)

This paper contains 20 sections, 6 theorems, 54 equations, 11 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. The problem definition
  4. Methods
  5. The greedy algorithm
  6. A submodularity theory
  7. Parallelizing the greedy algorithm
  8. Learning the gain function
  9. The neural network.
  10. The training data sets
  11. Numerical experiments
  12. Results from Algorithm \ref{['alg:eps-greedy']} using $\mathcal{G}_k$
  13. Results from Algorithm \ref{['alg:round_robin']} using $\mathcal{G}_1$ on three parallel runs
  14. Results from Algorithm \ref{['alg:eps-greedy']} using the learned gain functions
  15. Performance statistics and comparisons
  16. ...and 5 more sections

Key Result

Proposition 3.1

(Monotonicity of $f_k$) If $w_i \geq 0$ for all $1\le i\le k$ in eq:f_k, then for all countable sets $A \subseteq B \subseteq \Omega_\text{free}.$

Figures (11)

  • Figure 1: Representations of environments in $\mathbb{R}^2$ and $\mathbb{R}^3.$
  • Figure 2: Illustration of $\phi_{\mathbf{x}}(\mathbf{y})$ in a 2 dimensional environment.
  • Figure 3: Example of $\mathcal{O}_\text{vis}$.
  • Figure 4: Algorithm \ref{['alg:eps-greedy']}. Left: 10 sensors places, 45% order 3 coverage. Right: 24 sensors places, 90% order 3 coverage.
  • Figure 5: Algorithm \ref{['alg:round_robin']} Left: 9 sensors placed, 43% order 3 coverage. Right: 18 sensors places, 90% order 3 coverage.
  • ...and 6 more figures

Theorems & Definitions (9)

  • Proposition 3.1
  • Proposition 3.2
  • Theorem 3.1
  • Proposition A.1
  • proof
  • Proposition A.2
  • proof
  • Theorem A.1
  • proof