Symbiotic Positioning, Navigation, and Timing via Game Theory and Reinforcement Learning

Precise positioning, navigation, and timing (PNT) capabilities are essential for numerous critical infrastructure systems and advanced location-dependent applications. The challenges related to the reliability and accuracy of traditional Global Navigation Satellite Systems (GNSS) have driven the pursuit of innovative alternative PNT methodologies. This paper presents a novel approach inspired by the concept of biological symbiosis and leveraging the advanced capabilities of Reconfigurable Intelligent Surfaces (RISs). The proposed framework establishes a cooperative interaction between targets with unknown positions and collaborator nodes with approximate location estimates. These interactions are supported by the RISs and the anchor nodes with known positions. The objective is to minimize errors in positioning and timing for both the targets and the collaborators. This challenge is modeled as a non-cooperative game, and the existence of a Nash Equilibrium is demonstrated using potential game theory. To solve the game, Best Response Dynamics and a log-linear Reinforcement Learning (RL)-based approach are developed to identify the equilibrium state. The proposed system is thoroughly evaluated through simulations, in order to demonstrate its performance and the key trade-offs between game-theoretic strategies and the RL-based solutions.