A Sequential Game Framework for Target Tracking

Abstract

This paper investigates the application of game-theoretic principles combined with advanced Kalman filtering techniques to enhance maritime target tracking systems. Specifically, the paper presents a two-player, imperfect information, non-cooperative, sequential game framework for optimal decision making for a tracker and an evader. The paper also investigates the effectiveness of this game-theoretic decision making framework by comparing it with single-objective optimisation methods based on minimising tracking uncertainty. The paper assumes that both the tracker and the evader are intelligent operators capable of complex decision making, and use passive sensors to get noisy bearing information about each other. Rather than modelling a zero-sum game between the tracker and the evader, which presupposes the availability of perfect information, and therefore unrealistic, in this paper we model both the tracker and the evader as playing separate zero-sum games at each time step with an internal (and imperfect) model of the other player, which each player constructs based on the imperfect state information they have about the other player. The study defines complex multi-faceted winning criteria for both tracker and evader, and computes winning percentages for both by simulating their interaction for a range of speed ratios. The results indicate that game theoretic decision making improves the win percentage of the tracker compared to traditional covariance minimization procedures in all cases, regardless of the speed ratios and the actions of the evader. In the case of the evader, we find that a simpler linear escape action is most effective for the evader in most scenarios, though the effectiveness of game-theoretic decision making improves when the evader has a more significant speed disadvantage. Overall, the results indicate that the presented sequential-game based decision making framework significantly improves win percentages for a player in scenarios where that player does not have inherent advantages in terms of starting position, speed ratio, or available time (to track/escape), highlighting that game theoretic decision making is particularly useful in scenarios where winning by using more traditional decision making procedures is highly unlikely.

Keywords

• Game theory
• target tracking
• sequential games
• cubature Kalman filter
• maritime surveillance
• strategic interaction