How GPS works

"Koobee Wublee" wrote in message
oups.com...
| From moortel's link, we have
|
| http://www.gpsinformation.org/dale/theory.htm
|
| The distance to satellite i from the receiver is
|
| Ri = c (Ti - t)
|
| Where
|
| ** Ri = This distance
| ** Ti = Time reading from this satellite
| ** t = Time reading from the receiver plus offset
|
| We really don't care about the receiver time t because with the
| fourth satellite it can be calculated. However, all satellites should
| have their time synchronized with each other. The distance from the
| satellite to the receiver is also the following.
|
| Ri^2 = (x - Xi - Vxi (Ti - t))^2 + (y - Yi - Vxi (Ti - t))^2 +
| (z - Zi - Vxi (Ti - t))^2
|
| Where
|
| ** x, y, z = Coordinate of the receiver
| ** Vxi, Vyi, Vzi = Velocity of the satellite at time = Ti
|
| The velocity of the satellite can be embedded in the almanac
| information sent down from the satellite.
|
| So, we have
|
| c^2 (Ti - t)^2 = (x - Xi - Vxi (Ti - t))^2 + (y - Yi - Vxi (Ti
| - t))^2 + (z - Zi - Vxi (Ti - t))^2
|
| Since these satellites are very close to ground, we have
|
| ** abs(x - Xi) Vxi (Ti - t)
| ** abs(y - Yi) Vyi (Ti - t)
| ** abs(z - Zi) Vzi (Ti - t)
|
| With the above simplification, we have a cheaper algorithm as follows.
|
| c^2 (Ti - t)^2 = (x - Xi)^2 + (y - Yi)^2 + (z - Zi)^2
|
| Collecting the information from four satellites at the same time, we
| have the following four equations.
|
| ** c^2 (T1 - t)^2 = (x - X1)^2 + (y - Y1)^2 + (z - Z1)^2
| ** c^2 (T2 - t)^2 = (x - X2)^2 + (y - Y2)^2 + (z - Z2)^2
| ** c^2 (T3 - t)^2 = (x - X3)^2 + (y - Y3)^2 + (z - Z3)^2
| ** c^2 (T4 - t)^2 = (x - X4)^2 + (y - Y4)^2 + (z - Z4)^2
|
| Or you can use polar coordinate. Anyhow, solve for the four unknowns
| (t, x, y, z). You get your position. Again, the time of all
| satellites have to be synchronized.
|
| ** No GR
| ** No SR
| ** Sagnac lack of effect
|
| Androcles is correct after all. This should make moortel extremely
| happy.
|
Thank you, good sir. I've added a mention to your sagacity on the page
immediately following Roberts' idiotic hocus pocus.
http://www.androcles01.pwp.blueyonder.co.uk/GPS.htm

See
http://www.garmin.com/aboutGPS/waas.html

" This correction accounts for GPS satellite orbit and
*** clock drift ***
plus signal delays caused by the atmosphere and ionosphere. "

GPS satellite clock DRIFT has been recognised by the FAA and is a
danger to landing aircraft.
Under no circumstances should a "theoretical physicist" be allowed to
interfere with engineering, they can cause loss of life.
Androcles