IP GEOLOCATION ALGORITHM
6.1 The Location Algorithm
minRTT = propagation delay + extra delay (due to extra circular routes)
∆T measured= ∆t + ∆t0
(Pseudo -distance)
PD = ∆Tmeasured.α
(Actual distance)
D = ∆t.α
PD = (∆t+∆t0).α
PD = ∆t. α + ∆t0.α
PD = D+∆t0. α
D = actual distance from the landmark.
C = speed of light
a = X(c) i.e. Speed of digital info in fiber optic cable
X = factor of c with which digital info travels in fiber optic cable.
∆T = actual propagation delay along the greater circle router/paths.
∆t0 = the extra delay causing overestimation.
PD = pseudo distance
GRAPHICALLY
Figure 14: Solving the system in 2D plane
H: host
L1: Landmark 1
L2: landmark 2
L3: landmark 3
D1= (XL1 - Xh)
2
 (YL1 - Yh)
2
……………………………………… (2)
FROM (1) & (2)
PD1= (XL1 - Xh)
2
 (YL1 - Yh)
2
+   T0
……………….. (A)
Similarly for other 2 landmarks:
PD2 =
(XL2 - Xh) 2  (YL2 - Yh)
2
   t 0
……………….. (B)
PD3 =
(XL3 - Xh)
 (YL3 - Yh)
2
   t 0
………………...(C)
2
We need to linearize (A), (B) & (C) to solve them
USE TAYLOR SERIES:

n 0
f ( n ) (a)( x  a) n
n!
f  x 0    x  x 0  f ''  x 0    x  x 0 
f  x   f  x0  

1!
2!
Considering the simplified first part
f x   f x0   f x0 x  x0 
Put x  x0  x 
f x   f x0   f ' x0 x
………………………… (3)
Hence to compute the original value of X an arbitrary value x0 is required, this is done by
simple Trilateration.
We know that
H x  X est  X
……………. (D)
H Y  Yest  Y
…………….. (D)
Also
E st Di 
Hx  X est 2  H y  Yest 2
………………………….. (4)
From (3) & (4)
PDi  Est Di 
d Est Di   X d Est Di   Y

 a.t 0
dX
dY
After carrying out partial differentiation
PDi  Est Di 
 X Est  X li 
dX
 X  
YEst  Yli 
dY
Now we need to solve for X , Y , T0 
 Y  a  t 0
  X Est  X l1 

 PD1  E st D1   E st D1
 PD  E D     X Est  X l 2 
st 2 
 2
 E D
st 2
 PD3  E st D3  

X
 X l3 
Est

 E st D3
YEst  Yli 
E st D1
YEst  Y12 
E st D2
YEst  Y13 
E st D3

c
 X 
c    Y 

  t 
c

Solution from (4) is put in eq (D) to get new estimations.
Hx, HY becomes the new estimated position.