Anti-missile missiles aren't anything new, as you can see from this film from 1963 (that's '63 dang it, not '64, didn't your mama teach you no Roman Numerals?). Anyway, we've got a fine example of high speed photography run amuck, along with a host of mystery RF equipment and signals, including a 1,000 ton radar unit.
One thing I have wondered about was how the cameras track a missile on take off. I thought about it a couple of times, but I never came up with a sure fire way of doing it without a lot of expensive and complicated equipment. Or software, which amounts to the same thing. There are probably some image processing software libraries that would enable you to cobble together some kind of computerized solution, but I imagine it would take some trial and error to get the kinks worked out.
Or we could just do it like they did it in 1963 (at the 4:50 mark), which is to do it by hand. See the two guys on opposite sides of the telescope/camera? The guy on the left turning the crank? He controls the elevation. The guy on the right also has a crank, but he doesn't start turning it right away, and when he does, he's turning it slower. He's controlling the azimuth (which compass direction it's pointing). I suspect that is still how it's being done.
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