A Unified Estimation--Guidance Framework Based on Bayesian Decision Theory

Using Bayesian decision theory, we modify the perfect-information, differential game-based guidance law (DGL1) to address the inevitable estimation error occurring when driving this guidance law with a separately-designed state estimator. This yields a stochastic guidance law complying with the generalized separation theorem, as opposed to the common approach, that implicitly, but unjustifiably, assumes the validity of the regular separation theorem. The required posterior probability density function of the game's state is derived from the available noisy measurements using an interacting multiple model particle filter. When the resulting optimal decision turns out to be nonunique, this feature is harnessed to appropriately shape the trajectory of the pursuer so as to enhance its estimator's performance. In addition, certain properties of the particle-based computation of the Bayesian cost are exploited to render the algorithm amenable to real-time implementation. The performance of the entire estimation-decision-guidance scheme is demonstrated using an extensive Monte Carlo simulation study.