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Robust Sensor Placement for Poisson Arrivals with False Alarm Aware Spatiotemporal Sensing

Mingyu Kim, Pronoy Sarker, Seungmo Kim, Daniel J. Stilwell, Jorge Jimenez

TL;DR

The paper tackles robust sensor placement under spatiotemporal environmental variability and false alarms by developing a unified framework that couples detection, filtering, and false-alarm effects through an availability function. It uses a log-Gaussian Cox process to model targets, and derives a tractable, greedy placement approach backed by a Jensen-based lower bound and theoretical guarantees, including a sufficient condition for filtering benefit and a coverage-based void-probability bound that can dominate traditional bounds in certain regimes. Finite-sample robustness is established, showing how estimation error propagates and how near-oracle performance can be maintained with practical data sizes. Numerical experiments with AIS vessel data and synthetic scenarios validate the framework and demonstrate improved void-probability performance when accounting for false alarms and filtering.

Abstract

This paper studies sensor placement when detection performance varies stochastically due to environmental factors over space and time and false alarms are present, but a filter is used to attenuate the effect. We introduce a unified model that couples detection and false alarms through an availability function, which captures how false alarms reduce effective sensing and filtering responses to the disturbance. Building on this model, we give a sufficient condition under which filtering improves detection. In addition, we derive a coverage-based lower bound on the void probability. Furthermore, we prove robustness guarantees showing that performance remains stable when detection probabilities are learned from limited data. We validate the approach with numerical studies using AIS vessel-traffic data and synthetic maritime scenarios. Together, these results provide theory and practical guidance for deploying sensors in dynamic, uncertain environments.

Robust Sensor Placement for Poisson Arrivals with False Alarm Aware Spatiotemporal Sensing

TL;DR

The paper tackles robust sensor placement under spatiotemporal environmental variability and false alarms by developing a unified framework that couples detection, filtering, and false-alarm effects through an availability function. It uses a log-Gaussian Cox process to model targets, and derives a tractable, greedy placement approach backed by a Jensen-based lower bound and theoretical guarantees, including a sufficient condition for filtering benefit and a coverage-based void-probability bound that can dominate traditional bounds in certain regimes. Finite-sample robustness is established, showing how estimation error propagates and how near-oracle performance can be maintained with practical data sizes. Numerical experiments with AIS vessel data and synthetic scenarios validate the framework and demonstrate improved void-probability performance when accounting for false alarms and filtering.

Abstract

This paper studies sensor placement when detection performance varies stochastically due to environmental factors over space and time and false alarms are present, but a filter is used to attenuate the effect. We introduce a unified model that couples detection and false alarms through an availability function, which captures how false alarms reduce effective sensing and filtering responses to the disturbance. Building on this model, we give a sufficient condition under which filtering improves detection. In addition, we derive a coverage-based lower bound on the void probability. Furthermore, we prove robustness guarantees showing that performance remains stable when detection probabilities are learned from limited data. We validate the approach with numerical studies using AIS vessel-traffic data and synthetic maritime scenarios. Together, these results provide theory and practical guidance for deploying sensors in dynamic, uncertain environments.

Paper Structure

This paper contains 17 sections, 6 theorems, 44 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Spatio-Temporal Stochastic Target Model
  4. Sensor Model with Stochastic Performance and Filtering
  5. False-Alarm–Aware Availability
  6. Undetected Targets and Void Probability
  7. Near-Optimal Sensor Placement
  8. Analysis and Guarantees under Stochastic Sensing and False Alarms
  9. Filtering Benefit Considering False Alarms
  10. Coverage–Oriented Void Probability
  11. Finite–Sample Robustness
  12. Numerical Results
  13. Sensing and False–Alarm Models
  14. Filtering Benefit Under False Alarms
  15. Coverage–Oriented Void Probability
  16. ...and 2 more sections

Key Result

Theorem 1

Assume $p_i>0$ and $\alpha(\chi)>0$. For a sensor $i\in\{1,\dots,m\}$, if $\tilde{p}_i$ is differentiable in $\theta_i$, then If, pointwise on $(s,t)$, then increasing $\theta_i$ improves effective detection $\tilde{p}_i$, decreases the expected number of undetected targets $\bar{U}(\mathbf{a})$, and increases the void probability $\nu(\mathbf{a})$.

Figures (6)

  • Figure 1: Ship traffic heatmap near Hilton Head Island, Georgia, USA MarineCadastreAIS. The dashed line denotes line segment $O$, used as the area of interest.
  • Figure 2: (Left) Posterior mean of target intensity $\lambda(s,t)$. (Right) Representative realization of the environment factor $\omega(s,t)$.
  • Figure 3: Filtering diagnostics: (A) margin $m(s,t)$, (B) scatter validation, (C) margin distribution, and (D) mission–level gains versus fraction of cells with $m>0$.
  • Figure 4: Void probability with number of sensors $K$ for NF, NFilt, Random, and FA–Aware with error bars $\pm 1$ std across 30 realizations.
  • Figure 5: Void Probability varying the number of sensors: Greedy, and lower bounds from \ref{['eq:lower-bound-coverage-void']} and \ref{['eq:approx-obj-access']}.
  • ...and 1 more figures

Theorems & Definitions (10)

  • Theorem 1: Sufficient Local Condition
  • Lemma 1: Dominance Threshold of Coverage-Based Bound
  • Corollary 1: Strictly greater than $(1-1/e)\nu(\mathbf{a^{\star}})$
  • Theorem 2: Uniform Concentration
  • Lemma 2: Error in Undetected Targets
  • Theorem 3: Greedy Stability with Estimates
  • proof
  • proof
  • proof
  • proof