My Math Forum stance Error Caused by GPS Receiver Error

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 September 30th, 2018, 11:03 AM #1 Newbie   Joined: Sep 2018 From: Portland Posts: 2 Thanks: 0 stance Error Caused by GPS Receiver Error Not sure how to categorize this, and I feel like this should be pretty simple but I'm a little confused. GPS uses satellites to find the position of a receiver. Now the satellite clocks all have synchronized atomic time; however, the receiver clock is fast by 0.05 microseconds. How much error in distance measurement between satellite and receiver is induced by receiver clock that's fast by 0.05 microseconds? No measurements are given besides the 0.05 microseconds. So, assuming I can make an arbitrary distance (13,000 meters) per time (let's say a minute) for the equation, wouldn't it be: 13,000 m/min= 216.67 m/s 216.67 m/s X 1 sec/1,000,000 microseconds X 0.05 microseconds=1.083 X 10^-5 m so it the distance error would be 1.083 X 10^-5 m for the receiver clock error of 0.05 microseconds Thanks for the help!
 September 30th, 2018, 02:04 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,208 Thanks: 1164 this is a tremendously complicated problem. Essentially the 0.05 microsecond error causes estimated distances to the satellites to be short by 0.5 usec x the speed of light. How that error then enters into the triangulation calculations is going to be utterly dependent on the individual satellite positions at the time. I don't believe there is any simple answer.
 September 30th, 2018, 02:17 PM #3 Newbie   Joined: Sep 2018 From: Portland Posts: 2 Thanks: 0 Ha, that's good then. I think that helped. As far as I've learned from this class, we've been taught that the satellites creates a sphere of possibilities-there's no directional information being presented-that narrow down the field considerably per satellite. Far as I know this is just for one satellite instead of the four, so wouldn't the distance error be 0.05 microseconds X speed of light? Actual location doesn't matter for me here (yet), just the distance error. Thanks for the input

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