Mobile Target Search with Imperfect Perception: A Partially Observable Stochastic Game Theoretical Approach

Abstract: This paper investigates mobile target search under imperfect perceptions caused by sensor limitations, malicious jamming, or communication noise. Searchers and targets operate in a grid-shaped area with bounded mobility, leading to a dynamic interplay between search and evasion. To capture this adversarial interaction under imperfect perceptions, we adopt the partially observable stochastic game (POSG) approach, which generalizes partially observable Markov decision processes (POMDPs) by incorporating target intelligence. To handle false alarms and missed detections caused by perceptual uncertainties, we propose a novel detectability concept to determine whether a search strategy guarantees eventual detection, and provide sufficient detectability criteria based on stochastic recurrence analysis. We further develop a server-assisted distributed algorithm that utilizes the aggregative potential game structure for searchers and a KL-divergence-based reduction for target prediction. Numerical simulations validate the effectiveness of the proposed algorithm and support the detectability analysis.

• The paper introduces a POSG framework that ensures eventual target detection under sensor noise via the novel concept of α-detectability.
• It proposes a server-assisted distributed algorithm leveraging aggregative potential games to overcome the curse of dimensionality.
• Empirical validations show significant improvements in detection times and reliability compared to traditional heuristic strategies.

Partially Observable Stochastic Games for Mobile Target Search with Imperfect Perceptions

Introduction and Motivation

The paper "Mobile Target Search with Imperfect Perception: A Partially Observable Stochastic Game Theoretical Approach" (2606.20232) addresses the search and detection problem for mobile targets by searcher agents operating under imperfect sensing conditions—specifically, sensor limitations, false alarms, missed detections, jamming, and communication noise. The adversarial nature of the target, combined with uncertainty in the observations, motivates the adoption of a multi-agent POSG (Partially Observable Stochastic Game) framework. Previous literature on pursuit-evasion and search games frequently assumes perfect sensing, limiting their applicability in real-world scenarios characterized by substantial perceptual noise.

Problem Formulation and Modeling

The target search is posed on a discrete grid, with both searchers and the target exhibiting bounded mobility. The sensing model incorporates binary-valued observations, with detection probability $p_d$ and false alarm probability $p_f$, both of which critically influence the Signal-to-Noise Ratio (SNR) of search outcomes. Searchers maintain per-area, independent Bernoulli beliefs and update using Bayes' rule, bypassing global normalization which would otherwise couple all areas through false alarm-induced noise.

The core modeling innovation is the explicit consideration of α-detectability: the probability that a search strategy can ensure eventual detection (with detection defined via both an entropy threshold and a unique confidence peak). This concept fills a gap in prior work, which lacked detection guarantees under false alarms, missed detections, and mobile evaders.

Game-Theoretic Framework and Detectability Analysis

The problem is formalized as a POSG, with the searchers minimizing the posterior information entropy and the target maximizing it through evasive maneuvers. The paper leverages the Borel-Cantelli lemma for the detectability proof: detection is formulated as a hitting property in the belief stochastic process, and sufficient conditions are established for α-detectability based on probability recurrence.

For homogeneous agents, the average belief dynamic is analyzed, yielding explicit sufficient conditions on coverage probability $\rho$, detection/false alarm rates, and grid dimensions for achieving α-detectability. The theoretical results contrast sharply with standard search game formulations that ignore false alarms, demonstrating that detectability cannot be reliably guaranteed unless the searchers maintain a uniform lower bound on covering the target and the SNR is above a critical threshold.

Algorithmic Contributions

To address the exponential state-action space (curse of dimensionality) in POSGs, a server-assisted distributed algorithm is proposed. The approach exploits aggregative potential game structure for the searchers, enabling decentralized 1-step lookahead greedy updates, aligned with a global utility objective. The target's prediction is efficiently approximated via a KL-divergence-based reduction, focusing on the scalar average belief instead of the full high-dimensional vector, which remains computationally tractable.

Greedy and inertia-based updates are employed with $\epsilon$-exploration to avoid cycling and ensure convergence to equilibrium. The central server aggregates observations and broadcasts global beliefs, while each searcher optimizes its action locally based on these beliefs and neighborhood information.

Numerical Results and Empirical Validation

Comprehensive numerical simulations validate the theoretical detectability analysis and algorithmic efficacy. Key empirical findings:

• The proposed algorithm reliably achieves α-detectability under moderate-to-high $p_d$ and low $p_f$.
• Under hard regimes (low $p_d$, high $p_f$, limited number of searchers), detection becomes improbable within reasonable time horizons, empirically confirming the sharpness of the theoretical detectability criterion.
• Strong numerical evidence is presented: the distributed algorithm outperforms heuristic strategies (greedy, max-coverage) by attaining lower median detection times and tighter variance, especially against adversarial targets employing NE policies.
• The requirement of maintaining a uniform positive coverage probability is highlighted as critical. When violated (e.g., with only two agents or high noise), the target often escapes detection indefinitely.

Implications, Theoretical Impact, and Future Directions

The paper substantiates that achieving reliable detection of mobile targets under imperfect perception is fundamentally constrained by information-theoretic and game-theoretic bounds. The explicit analysis and algorithmic framework provide a practical tool for robust robotic search applications, with immediate relevance to surveillance, search-and-rescue, and autonomous exploration under adversarial interference.

Theoretically, the work advances the understanding of POSGs by linking recurrence properties of belief processes to guaranteed detection. Future research avenues include:

• Extending algorithmic techniques to heterogeneous agent teams, complex mobility constraints, and dynamic environments.
• Developing scalable approximation strategies for high-dimensional, non-homogeneous POSG instances.
• Exploring real-time adaptive methods for dynamically tuning sensing policies when environmental statistics fluctuate.
• Investigating generalizations of detectability metrics that incorporate longer-term uncertainty minimization or multi-objective optimization.
• Integrating continual learning and online belief adaptation in distributed multi-agent systems.

Conclusion

This paper formalizes and analyzes mobile search games with perceptual imperfections, introducing α-detectability as a rigorous detection criterion under adversarial and noisy conditions. Through conditional recurrence theory and distributed algorithmic design grounded in potential games and information-theoretic principles, it offers both qualitative and quantitative guarantees for target detection. Empirical validation underscores the necessity of sufficient sensing quality and team coordination, delineating the operational limits of target search in stochastic, adversarial environments (2606.20232).