Calculate Accuracy of GPS?


by godtripp
Tags: accuracy
godtripp
godtripp is offline
#1
Nov22-11, 12:41 AM
P: 54
Hello,

I need to calculate how accurate a GPS system is using only Special Relativity and a very basic knowledge of GR (without tensors...which is limited).

I'm not sure where to begin however... where does the uncertainty in the measurement come from? How can I calculate the size of the uncertainty of a GPS position?

Any references or insight would be GREATLY APPRECIATED.

Thanks PF,

J
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stevebd1
stevebd1 is offline
#2
Nov24-11, 03:53 AM
P: 604
You can pretty much calculate the discrepancy using the following equations and quantities-

Time dilation due to gravity (GR)-

[tex]d\tau=dt\sqrt{1-\frac{2M}{r}}[/tex]

where [itex]M=Gm/c^2[/itex]

Time dilation due to velocity (SR)-

[tex]d\tau=dt\sqrt{1-\frac{v^2}{c^2}}[/tex]

Quantities required-
Earth's mass
Earth's (mean) radius
satellite's altitude
satellite's velocity


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