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Wow. Does anyone know what sort of control they have during the final burn? Do they modulate it in closed loop to track the landing profile or is the control via some other actuators? It just blows your mind that you can get this sort of accuracy with these speeds/distance/time. I also wonder how they get real-time accurate positioning. GPS?

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It's mostly GPS and inertial navigation. Probably integrated together with some kind of Kalman filter.

The very last few seconds add in data from a radar altimeter. Per the post-launch press conference, this time they added some special paint to the landing pad to give a better radar return. I imagine the steel deck of the ASDS already gives a pretty good radar return.

There are cold gas thrusters, grid fins, and the main engines are gimballed.

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