How does GPS determine elevation?
lardom
Posts: 1,659
This is just to satisfy my curiosity. While stuck in traffic yesterday my thoughts drifted back to something that's puzzled me for a while: I kept wondering how the minimum three satellites could find a GPS location because you could have a large triangular area where three circles intersect. Geometry doesn't answer the question. Then the light goes on in my head...The GPS reciever is located on the circumferences of those three circles. (Traffic jams are a good thing.)
This is what I understand so far: The satellites have synchronised atomic clocks. The GPS reciever has a quartz clock that is synchronised to the atomic clocks. The reciever measures the lag time when the satellite transmits the current time and its location.
OK, from circles to spheres and from a spot on the map to elevation on the planet. How does the reciever do this?
This is what I understand so far: The satellites have synchronised atomic clocks. The GPS reciever has a quartz clock that is synchronised to the atomic clocks. The reciever measures the lag time when the satellite transmits the current time and its location.
OK, from circles to spheres and from a spot on the map to elevation on the planet. How does the reciever do this?
Comments
http://edu-observatory.org/gps/height.html
from each of three or more satellites. Using your precise time
on the ground and the data from the sats your gps calculates
your exact location in 3 dimensions since it knows how far each sat
was from you when the readings were made. If you know your exact
distance from 3 objects then you can calculate where you are
in 3 dimensional space. (There is a special mathematical case where 3 objects
cannot be used to determine your location in space but this does not happen
with gps)
Special Relativity must be taken into account. The clocks on the satellites
slow down due to their speed. The clocks on the ground slow down even
more due to the Earths gravity well. The end result is that the clocks in orbit
must be slowed down just a tiny bit more to match the gps clocks on the
ground. The processor in your gps device takes all these things into account
when it makes its calculations.
The reason I ask is that sea level isn't really level as it varies based upon the density of the rock that underlies the ocean.
-Phil
Your daughters sure have a fun dad to play with :-)
I attached a graphic that shows what 'clicked' in my head.
Two three-D spheres intersect in a two-D circle; the third sphere intersects that circle at two points, and usually by knowing that your location is near the surface of the Earth gives enough info to eliminate one of those two points, yielding your GPS location.
A fourth satellite is usually needed to be able to mathematically deduce the receiver clock time offset as well as the location from the collection of data values, allowing GPS receivers to work with just a relatively cheap clock.
Now, let's just consider two of those. Take two of those rods and fasten them together at the far end -- the receiver end. Now that composite point can only swing in a circle, because it's constrained by two satellite fixes. Your receiver must be somewhere on that circle.
Now, hook up the third rod. There are only two places you can do that -- one point above the table, and one underneath it if you can swing the rods down there. Your receiver knows it's at one of those point locations, and since one of them is probably near the surface of the Earth and the other far out in space it usually guesses lucky.
The GPS receiver does need to know the shape of the Earth too, since it's not exactly spherical, but there is a standard geoid model used for that. It's not exact though which is why altitude information isn't considered as accurate for GPS as position.