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.
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.