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A more practical method is, after identifying a reflection of interest, to repeat the measurement manually or to let the platform automatically repeat it at intervals, and to use a small piece of absorption to block a path to the side of the microphone. And as you move the blocking piece around the mic, you will eventually identify a position where that particular reflection is 'gone' - or blocked. And here you know that you have intercepted it in 'flight'. From this, you can extrapolate the path from the mic capsule through the blocking location to identify the general location of the reflection incident point on a boundary. Further iterations of this process can further refine the location.
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There is a faster more accurate way to do this. Use a kinetic, psycho-acoustically servo controlled unit to generate stimuli which trigger the reflections of interest.
(Move about the room, clapping your hands. Stop at each spot where the slap or flutter is worst.)
Now introduce another kinetic, servo and voice controlled unit, capable of positioning a reflection stopping device in any position or plane.
( A friend! with a panel of 703, wrapped in fabric)
The interaction of the two units plus their combined central processing units results in speedy and certain identification of the best locations for the reflection stopping devices, obviating iteration.
(Friend moves panel to spot, flutter stops, hang the panel there)
:-)
DD