Question about how GPS works.

Comments

• xanatos Posts: 1,120

  2009-09-13 16:11 edited 2009-09-13 16:11

  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 Posts: 1,622

  2009-09-13 18:08 edited 2009-09-13 18:08

  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 Posts: 1,031

  2009-09-13 19:11 edited 2009-09-13 19:11

  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 Posts: 4,747

  2009-09-14 00:18 edited 2009-09-14 00:18

  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'?
  
  ▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔
  - Stephen
• Timmoore Posts: 1,031

  2009-09-14 04:14 edited 2009-09-14 04:14

  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 Posts: 1,622

  2009-09-14 09:35 edited 2009-09-14 09:35

  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 Posts: 4,747

  2009-09-14 17:58 edited 2009-09-14 17:58

  Thanks, I'll have to read that more than once for it to sink in but it gives me something to do tonight.
  
  ▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔
  - Stephen
• Timmoore Posts: 1,031

  2009-09-15 05:20 edited 2009-09-15 05:20

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