Radar guided via eletro optic signal, they don't know much but the ground does. The whole point is the missile is very cheap for a missile and all the fun stuff is ground based inside of the protective sphere of influence.
The Iron Dome works wonders for intercepting dumb rockets which are on a calculable set trajectory. They are not guided with electro-optic but using a simple signal to tell the rocket where to be at what time. Dumb rockets are much, much cheaper to produce than guided missiles.
Iron Dome's fatal flaw is when a projectile does not follow the path of the image above but changes trajectory mid-air. E.G another guided missile. It is designed to stop Hamas style fire-and-forget rockets. It cannot deal with projectiles rapidly changing trajectory.
This was so fucking cool to watch, from an engineering perspective observing the secondary propellant ignite to boost its speed to intercept the target, as well as an internet video watcher seeing the camera person capturing the entire scenario with perfect tracking and centering of the subject (rocket)
Huh, hadn't thought about that capability, but it does make a ton of sense if the first target was successfully serviced (or no longer needs servicing). No need to waste an interceptor by launching another for target #2.
Or if the radar and guidance system decides another incoming threat is more important to take out. Like if the tracking system calculates the probable hit location of the new target to be a school/hospital/commandopost etc.