Question about how GPS works.

sylvie369

I am reading what seems to be a generally fine book, but I'm bothered by this line:

"For example, a GPS receiver determines its position on the surface of the planet by measuring the strength of received radio signals from several geosynchronous satellites".

By contrast, Wikipedia (which I believe to be correct) says:

"A GPS receiver calculates its position by precisely timing the signals sent by the GPS satellites high above the Earth. Each satellite continually transmits messages which include

• the time the message was sent
• precise orbital information (the ephemeris)
• the general system health and rough orbits of all GPS satellites (the almanac).

The receiver measures the transit time of each message and computes the distance to each satellite. Geometric trilateration is used to combine these distances with the satellites' locations to obtain the position of the receiver. "

GPS position isn't really computed from relative signal strength, is it? I was very surprised to see that line in the book, but I suppose it's possible that I'm the one who is misunderstanding this. What do you think?

xanatos

The book quote would appear to be either patently wrong or out of context. The satellites all transmit an incredibly precisely synchronized signal, and the GPS receiver measures the phase and delay from the received signals to compute your position. If signal strength played any role other than allowing the GPS unit to know which signals to pay attention to, then every tree you passed under would change your location!

Dave

sylvie369

xanatos said...
The book quote would appear to be either patently wrong or out of context. The satellites all transmit an incredibly precisely synchronized signal, and the GPS receiver measures the phase and delay from the received signals to compute your position. If signal strength played any role other than allowing the GPS unit to know which signals to pay attention to, then every tree you passed under would change your location!

Dave

Thanks, Dave. That's what I thought. Had it just been on an internet page somewhere I'd have just dismissed it, but I saw it in a book that's pretty technical, and as far as I can see, generally very well-informed. I'm very surprised to see it.

Timmoore

said...

The receiver measures the transit time of each message and computes the distance to each satellite. Geometric trilateration is used to combine these distances with the satellites' locations to obtain the position of the receiver. "

This isn't quite correct either. A GPS receiver doesn't have a good enough clock to measure the transit time that accuracly. What is does is get signals from 4 GPS satellites. Then it has 4 unknowns, 3 coordinates and time. With 4 signals it can solve for 4 unknowns. Thats why GPS receives need 4 satellites to get a lock. When they run with less than 4 satellites its because they have had a lock and assume something doesn't change - often altitude.

Franklin

Timmoore said...
What is does is get signals from 4 GPS satellites. Then it has 4 unknowns, 3 coordinates and time. With 4 signals it can solve for 4 unknowns

Just what does it get and how does it solve the 'unknowns'?

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- Stephen

Timmoore

The position of the satellites is known - it is downloaded from the satellites. The distance from 3 satellites can be calculated from speed of light and time difference but time difference is not known because time difference is smaller than receiver clock accuracy.

(pd-ps1) = c (tr-ts1), (pd-ps2) = c (tr-ts2), (pd-ps3) = c (tr-ts3), (pd-ps4) = c (tr-ts4)

now the start position (ps1-4) are known - satellite position so geometry says there are 2 possible positions - one inside the satellites and one outside. So we assume the position is inside - unlikely you are more than 12000 (thanks sylvie369 for correcting me) miles above earth [noparse]:)[/noparse]. Now you are told ts1-4 (part of signal), you know the ps1-4. So you are solving for pd and tr, the receiver position pd (which is long, lat and altitude) and the receiver time tr. Algebra says if you have 4 equations and 4 unknowns you can solve the equations.

The c above is the speed of light in vacuum, this is a simplification since radio signal from satellites doesn't travel at c through the earths atmosphere. Receivers have a model of the atmosphere to caculate c for different times of day etc. but this is where some of the gps inaccuracy comes from.

Post Edited (Timmoore) : 9/14/2009 4:20:14 PM GMT

sylvie369

Timmoore said...
now the start position (ps1-4) are known - satellite position so geometry says there are 2 possible positions - one inside the satellites and one outside. So we assume the position is inside - unlikely you are more than 22500 miles above earth [noparse]:)[/noparse].

Minor correction there: the GPS satellites are not in geosynchronous orbit at 22,500 miles. They're only about half that high, and orbit the Earth roughly twice per day.

Edit: Oh, I failed to notice that the quote from the book at the start of the thread contains that same mistake. It's an understandable one, though. I used to assume they were in geosynchronous orbit myself, until someone corrected me in an online forum. Nonetheless, two mistakes in one sentence about GPS makes me wonder a bit about how dependable that book is going to be.



Post Edited (sylvie369) : 9/14/2009 4:29:53 PM GMT

Franklin

Thanks, I'll have to read that more than once for it to sink in but it gives me something to do tonight.

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- Stephen

Timmoore

This is the same explanation but may be clearer https://www.courses.psu.edu/aersp/aersp055_r81/satellites/gps_details.html