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Correction to my post above:

I used the word "parallax" poorly to refer to the offset between the detectors - localization is most definitely not done via parallax. It's arrival time + some signal processing, so with two detectors, resolution is limited.

Additional details and an image depicting the improvements made by adding a third, properly positioned detector are available at: https://www.ligo.caltech.edu/news/ligo20160404

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