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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

Scenario

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?

Community
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Hari
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2 Answers2

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In open space the signal strength is a function of distance that is a function of $\frac{1}{Distance^2}$. If you are not in open space there are too many variables and you practically can not determine accurately location for such cases.

The idea of the GPS was to support exactly the need for location using "open space" and even this solution may suffer from in accuracies.

If you insist, having a distance you solve equations of the three circles (one for each tower) intersection - you really use only two that are more accurate and the third will be used to determine which of the two solution is the better one.

Moti
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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: $$ |P-T_j|=d_j,\,\;\; j=1,2,3. $$

Pocho la pantera
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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 04:01
  • 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