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(Pseudo-distance)
PD = ?T measured . ?
(Actual distance)
D = ?T . ?
PD = (?T + ?T0). ?
PD = D + ?T0 .c .................................(1)
D = actual distance from the landmark.
C = speed of light
? = X(c) i.e. Speed of digital info in fiber optic cable
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Graphically,
H: host
L1: Landmark 1
L2: landmark 2
L3: landmark 3
Using distance farmula:
D1= ?sqrt(XL1- Xh)^2 + (YL1 - YH)^2 ............................................. (2)
FROM (1) & (2)
PD1= (?sqrt(XL1 - XH )^2 + (YL1 - YH)^2) + ?T0 . ? .................... (A)
Similarly for other 2 landmarks:
PD2= (?sqrt(XL2 - XH )^2 + (YL2 - YH)^2) + ?t0 . ? .................... (B)
PD3= (?sqrt(XL3 - XH )^2 + (YL3 - YH)^2) + ?t0 . ? .....................(C)
We need to linearize (A), (B) & (C) to solve them
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f(x0) . ( x- x0) f ' (x0) . (x - x0)
f( x ) = f (x0) + - ------------ + - --------------------
1! 2!
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PDi = Est Di + ------------- + ------------------
dX dY
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ODi = Est Di + -----------. delta ( x ) + - ---------------- delta ( y) + c. delta(To)
dX dY
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