This paper proposes a novel time-to-go estimation filter necessary for implementing the precise vertical homing guidance law of an anti-ship missiles with a RF seeker. By investigating the behavior of a pure proportional navigation guidance, it is shown that the time-to-go can be expressed as a Gauss hypergeometric function of the relative range, closing velocity and heading error. As an effective way to solve the time-to-go estimation problem, a recursive time-to-go estimation scheme with two-stage filter structure is taken into account. The suggested approach is able to not only consider the length of the curved homing trajectory caused by the heading error but also mitigate the unwanted time-to-go estimation errors due to the correlations among seeker measurement noises. Through the simulations for typical anti-ship missile homing scenarios, it is demonstrated that our method could provide superior time-to-go estimation performance compared to the previous ones.
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