Sedjeel (Hawk) A-A missile Testing Phase.

Yeah, if you want a beam rider to pull lead you need a separate system to continue to track the actual target while doings so
Well, there are several methods how you could do it on single radar - as far as I understood it, the idea is to "offcet target tracking", by adding a calculated error into radar tracking loop, so the boresight would be offset and leading the target. While missile is moving along the beam, the added error would be steadily decreased - so at the end of the trajectory the beam would be aimed directly on target. Not sure, how efficiently such concepts were implemented, though.
 

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