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Quickest change detection for UAV-based sensing

Saqib Abbas, Anurag Kumar, Arpan Chattopadhyay

TL;DR

The paper tackles quickest change detection for a UAV surveilling two locations, introducing the Location Switching and Change Detection (LS-CD) algorithm that performs repeated one-sided SPRTs at each location and switches between locations to minimize the worst-case detection delay $\mathrm{WADD}$ under ARL2FA and energy constraints $\bar{E}$. It provides a thorough theoretical analysis, deriving tight ARL2FA bounds and a tight WADD bound $\mathrm{WADD}_l \le \frac{\gamma_l}{D(g_l\|\!f_l)} + C' + O(1)$, with additional results for the symmetric, zero-switching-time case that yield a novel asymptotic ARL2FA bound for standard CUSUM. The analysis leverages random-walk theory and ladder variables to quantify performance, while numerical results demonstrate energy-delay trade-offs and identify practical switching settings (e.g., $n=3$) that balance feasibility and performance. Overall, LS-CD offers an energy-aware, multi-location QCD approach with rigorous performance guarantees and clear avenues for extension to more locations and robustness concerns, potentially impacting UAV-enabled sensing systems in surveillance and environmental monitoring.

Abstract

This paper addresses the problem of quickest change detection (QCD) at two spatially separated locations monitored by a single unmanned aerial vehicle (UAV) equipped with a sensor. At any location, the UAV observes i.i.d. data sequentially in discrete time instants. The distribution of the observation data changes at some unknown, arbitrary time and the UAV has to detect this change in the shortest possible time. Change can occur at most at one location over the entire infinite time horizon. The UAV switches between these two locations in order to quickly detect the change. To this end, we propose Location Switching and Change Detection (LS-CD) algorithm which uses a repeated one-sided sequential probability ratio test (SPRT) based mechanism for observation-driven location switching and change detection. The primary goal is to minimize the worst-case average detection delay (WADD) while meeting constraints on the average run length to false alarm (ARL2FA) and the UAV's time-averaged energy consumption. We provide a rigorous theoretical analysis of the algorithm's performance by using theory of random walk. Specifically, we derive tight upper and lower bounds to its ARL2FA and a tight upper bound to its WADD. In the special case of a symmetrical setting, our analysis leads to a new asymptotic upper bound to the ARL2FA of the standard CUSUM algorithm, a novel contribution not available in the literature, to our knowledge. Numerical simulations demonstrate the efficacy of LS-CD.

Quickest change detection for UAV-based sensing

TL;DR

The paper tackles quickest change detection for a UAV surveilling two locations, introducing the Location Switching and Change Detection (LS-CD) algorithm that performs repeated one-sided SPRTs at each location and switches between locations to minimize the worst-case detection delay under ARL2FA and energy constraints . It provides a thorough theoretical analysis, deriving tight ARL2FA bounds and a tight WADD bound , with additional results for the symmetric, zero-switching-time case that yield a novel asymptotic ARL2FA bound for standard CUSUM. The analysis leverages random-walk theory and ladder variables to quantify performance, while numerical results demonstrate energy-delay trade-offs and identify practical switching settings (e.g., ) that balance feasibility and performance. Overall, LS-CD offers an energy-aware, multi-location QCD approach with rigorous performance guarantees and clear avenues for extension to more locations and robustness concerns, potentially impacting UAV-enabled sensing systems in surveillance and environmental monitoring.

Abstract

This paper addresses the problem of quickest change detection (QCD) at two spatially separated locations monitored by a single unmanned aerial vehicle (UAV) equipped with a sensor. At any location, the UAV observes i.i.d. data sequentially in discrete time instants. The distribution of the observation data changes at some unknown, arbitrary time and the UAV has to detect this change in the shortest possible time. Change can occur at most at one location over the entire infinite time horizon. The UAV switches between these two locations in order to quickly detect the change. To this end, we propose Location Switching and Change Detection (LS-CD) algorithm which uses a repeated one-sided sequential probability ratio test (SPRT) based mechanism for observation-driven location switching and change detection. The primary goal is to minimize the worst-case average detection delay (WADD) while meeting constraints on the average run length to false alarm (ARL2FA) and the UAV's time-averaged energy consumption. We provide a rigorous theoretical analysis of the algorithm's performance by using theory of random walk. Specifically, we derive tight upper and lower bounds to its ARL2FA and a tight upper bound to its WADD. In the special case of a symmetrical setting, our analysis leads to a new asymptotic upper bound to the ARL2FA of the standard CUSUM algorithm, a novel contribution not available in the literature, to our knowledge. Numerical simulations demonstrate the efficacy of LS-CD.

Paper Structure

This paper contains 20 sections, 8 theorems, 80 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Background
  3. System Model
  4. The Location Switching and Change Detection Algorithm: LS-CD
  5. Performance analysis
  6. One-Sided SPRT Analysis
  7. ARL Analysis of LS-CD
  8. WADD Analysis of LS-CD
  9. Numerical Results
  10. Setup and Parameter Choices
  11. Results
  12. Conclusion
  13. Proof of lemma \ref{['lemma:bound_E0_tau_l_w_AND_E0_tau_l']}
  14. Proof of lemma \ref{['lemma:bound_beta']}
  15. Proof of lemma \ref{['lemma:Lower-bound-psi_0l_w']}
  16. ...and 5 more sections

Key Result

Lemma 1

The quantities $\mathbb{E}_{\infty}(T_{l}^{(w)})$ and $\mathbb{E}_{\infty}(T_{l})$ are upper-bounded as: where $Z_{l}=Z_l(t)=\log \Bigl(\tfrac{g_l(Y_{l,t})}{\,f_l(Y_{l,t})}\Bigr)$.

Figures (6)

  • Figure 1: System setup
  • Figure 2: Illustration of the location switching procedure under the LS-CD algorithm with $n_A = n_B = 3$ and $\nu_A = \nu_B = \infty$. The intervals $T_A^{(1)}, T_A^{(2)}, T_A^{(3)}$ are i.i.d. samples from the distribution of $T_A$ under no change.
  • Figure 3: 3D plots of $\max\{\textrm{WADD}_A,\textrm{WADD}_B\}$ vs. $(\gamma_A,\gamma_B)$ for LS-CD ($n=1,3,5$). Points are color-coded by whether they violate energy only (black), ARL (green), both (red), or are feasible (blue). A triangulated surface is drawn over feasible points.
  • Figure 4: $\textrm{WADD}_A$ vs. $\gamma_A$ for different $\gamma_B$ under LS-CD with $n=1$.
  • Figure 5: $\textrm{WADD}_A$ vs. $\gamma_A$ for different $\gamma_B$ under LS-CD with $n=5$.
  • ...and 1 more figures

Theorems & Definitions (20)

  • Remark 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Theorem 1
  • ...and 10 more