Optimal guidance laws with uncertain time-of-flight

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. The issue of optimal guidance with uncertain time-to-go is dealt with here. A problem of the control of linear discrete 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. This guidance law has the structure of a rendezvous guidance law where the guidance gains are time-dependent and depend on the distribution of the time-to-go. Examples that demonstrate these dependencies are presented