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I am trying to finding the location of the user using mobile tower signal strengths. Scenario is given in the picture


Here, I know the coordinates (latitude and longitude, like x,y) of Tower 1, 2 and 3. Also I know the signal strength (can I consider it as radius? But for nearest towers radius will be high, and for far towers it will be lower, basically the opposite of radius)

If I have these parameters, how could I calculate my Location?

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See Wikipedia on path loss –  Henry Oct 30 '13 at 8:30
Signal strength won't be the radius for sure. But you can investigate empirically if the signal strenght is proportional to $\frac{1}{r^k}$ for some $k$ or something else (Numerical Calculus for the win). –  Victor Chaves Oct 30 '13 at 8:47
Thank you for your reply. I will try to find out a proportion like that. –  Hari Oct 30 '13 at 10:50

1 Answer 1

You can consider the signal strength as a function (decreasing) of the distance.

Let $T_1$, $T_2$ and $T_3$ be the positions of the towers. The signal strength from a point $P$ to the tower j is

$$ ST_j(P)=g(|P-T_j|) $$ where $g$ is a decreasing function.

Note that if $g$ is decreasing, it is one to one. So knowing the signal strength is equivalent to knowing the distance from $P$ to the towers.

Once you have determined the distances, you just have to solve the system: $$ |P-T_j|=d_j,\,\;\; j=1,2,3. $$

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Thank you for your answer. I'm sorry. I am not that much good at mathematics, so if I am wrong please correct me. First of all, I want to find out the Point where I am standing (I suppose you named it as P, which is unknown to me). Also if I got the three distances, can I take them as the radius and find out the point of intersection? –  Hari Oct 30 '13 at 10:42
Yes, you are right. Note that in general the system has no solution. So you might need to find an approximate solution. –  Pocho la pantera Oct 30 '13 at 14:15
Thank you, but how to calculate g(P-Tj) if P is unknown? –  Hari Oct 31 '13 at 4:01
You need to know the function $g$. Say for example that $g(t)=\frac{1}{t}$, then if $ST_j(P)=g(|P-T_j|)=g_j$ (your measurements), you conclude that $|P-T_j|=\frac{1}{g_j}$. –  Pocho la pantera Oct 31 '13 at 11:44

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