In a real-world, stochastic pursuit-evasion game, a sudden change in the target’s evasion maneuver generates an inevitable time delay at the pursuer’s estimator, due to its inherent reliance on incomplete and noisy measurements. In turn, this time delay might severely degrade the pursuer’s worst-case interception performance. A common approach to address this challenge is to incorporate time delay(s) in the deterministic derivation of the guidance law. However, these solutions unrealistically assume that the delay is constant throughout the game, and, because the value of the delay is unknown, it is generally regarded as a tuning parameter only. Moreover, these solutions feed the delayed-information guidance law with current (filtered) time estimates, thus breaking the assumptions underlying the derivation of this law.
We present a novel tracking and interception strategy that addresses the aforementioned problems in a game involving highly maneuverable targets. We first solve a bounded-control differential game with two time-varying delays, thus extending an already known result. Second, we introduce a novel algorithm for online estimation of these delays using semi-Markov chains, without requiring the standard assumptions of linearity and Gaussian distributions. Finally, as the developed guidance law requires delayed information about two states, we use a fixed-lag particle smoother to provide the best information at the appropriate time. This approach renders an improved framework for intercepting an evasively maneuvering target in a stochastic setting, where a sophisticated target can exploit the inherent estimation delay for evasion. We evaluate the performance of this methodology using a thorough Monte-Carlo simulation study.