Good ol' fashioned archery is closer still.
In fact, archery was the first and oldest form of "artillery" - well, after throwing rocks. Medieval Brit archers were taught to fire in two ways. First, at the butts - basically a target, just like we do now. Second, at distant marked off areas in an open field. The idea in that second was that the archers as a group were trained to fire en masse upward so their arrows would fall down en masse from above into the marked off section. In that way, they learned to bring down accurate indirect fire on distant units of soldiery. The arrows arcing downward would avoid shields to strike shoulders, upper bodies, faces, or arms of distant foes or would strike downward on the backs of horses, injuring them and causing the knight atop to lose control of the horse, breaking up his attack and, with a bit of luck, throwing him from the horse or causing the horse to careen into others in the unit to break up an attack.
I can see some similarities - in learning to judge range, for example. I can see using indirect fire rules to judge the results, even of the archers mentioned above. I can see FO skill helping out. I also see some significant differences: no amount of training in how to judge range and observe for distant gunners is going to teach you the body knowledge needed to hold your own weapon at precisely the right angle needed to achieve that range. I don't know the rules precisely, but I would have substituted skill with the weapon for FO skill if you're the one holding the weapon and you have eyes on the target.