Optimal Estimation and Decision in Stochastic Guidance

Perfect-information guidance laws have been known to deliver outstanding performance in simulations complying with their underlying assumptions. However, as is well known, realistic guidance of an intercepting missile towards a highly maneuverable target, using noisy and imperfect measurements, constitutes a hybrid, short-horizon, nonlinear, and non-Gaussian stochastic control problem, and the implementation of the guidance law requires an appropriate target state estimator. In such scenarios, the performance of perfect-information laws can degrade gracelessly. We present a novel design paradigm, which enables the use of perfect-information guidance laws in realistic scenarios by using Bayesian decision theory.

We first modify the DGL1 guidance law to address estimation errors, by using Bayesian decision to statistically rank the costs of all possible guidance decisions. When a unique control cannot be decided, this nonuniqueness is harnessed to shape the pursuer’s trajectory to enhance its estimator’s performance. We next present an overarching tracking and interception strategy, which is robust against sudden changes in the target’s evasion maneuver resulting in inevitable estimation time delays. Whereas the methods presented up to this point follow the standard, miss-distance-minimizing approach, we next propose an inverse paradigm whereby, for a given warhead, the guidance law maximizes the interceptor’s kill probability against any target. Although the aforementioned methods exhibit significant interception performance improvements, they are still based on deterministic guidance strategies, providing no optimality guarantees. We address this point by presenting a real-time optimal interception strategy for stochastic scenarios based on terminal sets for the linear-Gaussian case with bounded controls.