There are many ways to solve trilateration problem. This method is based on solving the equations of circle.The Figure below shows the 3 circles drawn from each of 3 landmarks to the target. r1, r2, r3 are the radius of circles.
P1=1st Landmark position in x,y coordinates
P2=2nd Landmark position in x,y coordinates
P3=3rd Landmark position in x,y coordinates
d1= distance from 1st Landmark to target (Calculated using distance=(MinRTT/2)*alpha)
d2=distance from 2nd Landmark to target (Calculated using distance=(MinRTT/2)*alpha)
d3=distance from 3rd Landmark to target (Calculated using distance=(MinRTT/2)*alpha)
i1=P1.x,
i2=P2.x,
i3=P3.x
j1=P1.y,
j2=P2.y,
j3=P3.y
x=target x coordinate
y=target y coordinate
Using Equation for circles and solving the above figure
x =
{ ( [ (d1^2-d2^2) + (i2^2-i1^2) + (j2^2-j1^2) ] * (2*j3-2*j2) - [ (d2^2-d3^2) + (i3^2-i2^2) + (j3^2-j2^2) ] *(2*j2-2*j1) ) /
[ (2*i2-2*i3)(2*j2-2*j1)-(2*i1-2*i2)(2*j3-2*j2 ] }
y = [ (d1^2-d2^2) + (i2^2-i1^2) + (j2^2-j1^2) + x*(2*i1-2*i2)] / (2*j2-2*j1)
x,y are the required coordinates of a Point (Target)
