A Sequential Game Framework for Target Tracking

TL;DR

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.

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. Rather than modelling a zero-sum game between the tracker and the evader, which presupposes the availability of perfect information, 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. The study defines 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. 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.

Figures (6)

• Figure 1: Sample simulation run. Here the tracker undertakes the covariance minimisation action and chooses its heading accordingly at each time step, and the evader undertakes the linear escape action. The tracker speed is $v_T = 3$ units per time step, and the evader speed is $v_E = 1$ units per time step. The figure reflects $k=100$.
• Figure 2: Sample simulation run. Here the tracker and evader both undertake game-theoretic decision making at each time step. The tracker speed is $v_T = 3$ units per time step and the evader speed is $v_E = 3$ units per time step. The figure reflects $k=150$.
• Figure 3: Comparing actions by tracker when evader chooses linear escape. Note that for all speed ratios, the tracker is better off making decisions by using game theory.
• Figure 4: Comparing actions by tracker when evader chooses game theoretic decision making. Note that for all speed ratios, the tracker is better off making decisions by using game theory.
• Figure 5: Comparing actions by evader when tracker chooses covariance minimisation. It can be noted that the best action for evader is linear escape for all speed ratios, except when it has a strong speed disadvantage, in which case it is better off undertaking game theoretic decision making.