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Consider the following setup (in a simple 2D world):

There are three receivers A, B and C with known positions (A.x, A.y, B.x, B.y, C.x and C.y). Now meteor goes down at a point H (H.x, H.y) somewhere in the triangle created by these receivers. It produces a shockwave that is detected by each of the receivers. So each receiver will report a time stamp (ta, tb and tc) when it detects the shock wave.

Now what I would like to do is to compute the point of impact H from the receivers positions and time stamps.

I know that multilateration/trilateration can be used to compute the point of impact from the distances between H to each of the receivers (there are plenty of implementations available on github). But what I don't know is how I get these distances out of the time stamps. Because all the time stamps give me are relative information (e.g. the signal arrived n seconds later at receiver B than receiver A). But they don't give me the absolute distances to each receiver.

Could anyone point me in the right direction? I assume this problem has been solved many times before, so I might just be missing the right keywords to find a solution.

Boris
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    If you take two receivers, you know the time difference between them which translates to the difference of distances from the impact to the receivers is constant. The location of points fulfilling this constraint is a branch of a hyperbola. Taking another pair of receivers you get a second hyperbola and now you have to determine the intersection. – Henry Oct 31 '18 at 07:15
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    @Henry i think for this to be true you need to know speed of the shock wave. Otherwise you don't know the difference. – Yola Oct 31 '18 at 08:24
  • @Yola yes, for this you have to know the speed. I don't think you can solve this with only three receivers if the speed is also unknown. – Henry Oct 31 '18 at 08:28
  • I would assume the speed of the shock wave is known and constant. – Boris Oct 31 '18 at 08:46
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    Look at my answer [`here`](https://stackoverflow.com/questions/36176167/) – MBo Oct 31 '18 at 11:17
  • BTW, this is how LORAN worked – Walter Tross Oct 31 '18 at 17:32
  • Possible duplicate of [Trilateration of a signal using Time Difference(TDOA)](https://stackoverflow.com/questions/36176167/trilateration-of-a-signal-using-time-differencetdoa) – Reblochon Masque Nov 01 '18 at 02:01

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