The Missile Knows Where it is (Remix)

>The crowning touch, however, was wiring the seeker to aim not where the target was, but where it would be. The missile knows where it is, [this video] , a great song about missile guidance systems and knowing where you are by how much you aren't (there).

predicting trajectory of a projectile is what computers were first made to do, at least if you count ENIAC as the first, and the Apollo Guidance Computer not long after (the missile knows where it is at all times, it knows this because it knows where it isn't... [0]) as it happens the projectiles have minds of their own now so to predict trajectory will require theory-of-mind shooting down fast moving drones might just be the path to self-awareness in the machine world, "if I were a drone, what action would I take in that situation..." [0] [link] [0.b remix] [this video]

I'm curious about how you'd do that, too. I haven't tried doing anything like that, but I'd think you'd start by trying to formalize the usual optimality proof for the Kalman filter, transfer it to actual program logic on the assumption that the program manipulates real numbers, try to get the proof to work on floating-point numbers, and finally extract the program from the proof to run it. [this video] has a different attempt to formalize Kalman filters which I think we can all agree was not a successful formalization.