Home in is correct. It bears resemblance to the concept of "home" in that the projectile (or a figurative counterpart) involved is getting to where it is meant to go. However, the variation "hone in" has increasingly been accepted to mean the same thing.

Also see definition #21 here of home, and this very helpful study on the two commonly confused expressions.

This reports the following:

Traditionally, a missile homes in (not hones in) on a target. Hone means "to sharpen." The verb home means "to move toward a goal" or "to be guided to a target." But some usage guides (see notes below) now recognize hone in on as an acceptable alternative to home in on.

An Ngram illustrates the wider usage of "home in on" than "hone in on", at least in current literature.