Optimal Guidance Laws with Uncertain Time-of-Flight Against Maneuvering Target and Noisy Measurements

The existing optimal guidance laws assume that the time-to-go is known exactly. The time-to-go is usually estimated and thus is a random variable. This paper deals with the issue of optimal guidance with uncertain time-to-go against maneuvering target with noisy measurements. A problem of control of linear stochastic systems with unknown time-to-go is formulated and solved. The solution is applied to derive guidance laws. The solution depends on the probability density function of the time-of-flight. In this case the resulting guidance law does not have the structure of product of a guidance gain and the zero effort miss. It has the structure of a rendezvous guidance law where the gains are time-dependent and depend on the distribution of the time-to-go. Examples that demonstrate these dependencies are presented. Simulations show that the guidance law that inherently assumes time-to-go uncertainty achieves smaller miss-distance relative to guidance laws that are derived as if the time-to-go is exactly known.