In terms of GPI, the bottleneck is not in the missile booster itself but rather there isn't a high performance DACS that can work within the atmosphere, so the interceptor can't close quarters with the glider reliably. You'd have to wait for the glider to get uncomfortably close (such as when its coming in during its terminal dive) to intercept it, which is not ideal.
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You need extreme accuracy in the last few seconds of the intercept because at those speeds, 1s means you miss by a huge distance.
This is the device that does the pitch, yaw and roll control for SM-3 KV but it's only designed to work in space. It rely on cold-gas thrusters and solid divert systems optimized for vacuum. It's useless when fighting aerodynamic forces during atmospheric flight.
So the challenge is actually in very sophisticated, miniaturized, propulsion and sensor/targeting technologies.
