Estimation-Based Guidance Using Optimal Bayesian Decision

Most modern guidance laws are developed assuming perfect information about the target state, implicitly assuming the validity of the separation theorem. However, this theorem has never been proven to be valid in realistic scenarios, involving nonlinearities and non-Gaussian noises. Instead, in such scenarios, Witsenhausen's generalized separation theorem (GST) holds and should be obeyed. We use this approach to modify the acclaimed, perfect-information, differential game-based guidance law (DGLl). An interacting multiple model particle filter is used to obtain the posterior probability distribution function of the game's state. A non-homogeneous Markov model is assumed for the target acceleration commandmode, to cope with an optimally maneuvering smart target. Based on the game space of the perfect information pursuit-evasion problem, four hypotheses are defined, concerning the state of the game. Using a Bayesian decision criterion, an optimal decision regarding the game's state is made under uncertainty. This decision is then used to derive a GST-compliant guidance law that extends the perfect information DGL1 law into the stochastic realm. An extensive Monte-Carlo simulation study is used to demonstrate the performance of the new guidance law in a stochastic interception scenario, showing that following the generalized separation theorem yields significant interception performance improvement.