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I need to go back 25 years to school and pay more attention to simultaneous equations.
I'm going to remove speed (speed = 1) and make the distance unitless.
Ah, fantastic. Looks like exactly what I need. And a frighteningly similar example of why ...!
Let me work that through a few times.
Thanks.
Do you think you could do it again, please?
That does look like exactly the same problem. OKay, the solution assumes the sensors are colinear. That;s not a big issue. Will read this more thoroughly after a few hours Zzz..
I have some calculated data. One thing I can do, based on knowing the co-ordinates of the event is calculate the delta time (assuming speed = 1) between the first sensor and the other three. Now, how do I attach a spreadsheet?
x y tB tC tD tA
4 4 10.84 16.97 10.84 0.00
4 8 3.70 11.06 8.94 0.00
8 4 8.94 11.06 3.70 0.00
8 8 3.11 5.66 3.11 0.00
3 12 0.00 10.24 12.26 3.83
3 16 0.00 12.46 18.35 11.28
6 18 0.00 7.82 16.48 12.65
9 12 0.00 1.56 4.24 2.96
9 16 0.00 1.86 9.57 8.51
10 10 0.00 0.00 0.00 0.00
11 2 11.88 10.91 0.00 1.96
14 5 12.71 8.35 0.00 7.06
16 3 18.35 12.46 0.00 11.28
17 2 21.15 14.64 0.00 13.51
18 6 16.48 7.82 0.00 12.65
14 14 6.75 0.00 6.75 11.31
14 18 7.82 0.00 12.65 16.48
16 16 10.84 0.00 10.84 16.97
18 14 12.65 0.00 7.82 16.48
18 18 15.28 0.00 15.28 22.63Oh, just to help, I changed it to a 20x20 universe instead of 10x10. :-(
Thanks. I know it can be done. I'm pretty sure I've seen ultrasound used to triangulate swarm robots without knowing an angle: just time deltas. I just can't find it again!! But, don't you hate when someone else swoops in with an answer? Heh heh. I feel your pain!
Hi.
First post. Hope it's worthy.
I need to calculate the position in 2D space of an "event" using four sensors positioned at the corners of the rectangular "universe".
Let's say the event is a sound which might occur somewhere inside the rectangle and the sensors are microphones.
Is it possible to calculate the co-ordinates for the epicentre based on the time for the sound to reach each of the four sensors?
At first sight, it seems straightforward enough. Until you realise that you don't know what time the event happened at, so you don't actually know the time for the event to travel to any of the sensors. You only know the time delta between the sound hitting each of the sensors.
So, the event happens at time S (but we don't know when that was). Then (in the shown example) the soundwave hits B A C and D. We can see that the timestamp registered at point C is going to be the time SC minus the time SB, etc:
tC = SC - SB and
tD = SD - SB
tA = SA - SB
But we don't know time SB.
Can anyone help me find the location of S, please?
Rules suggest I should indicate my "level". Well, I didn't sit high school maths, but I'm a masters degree qualified Aerospace engineer. So, I'm a bit irked that I couldn't work this one out for myself...
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