Anyone want to know how GPS works?

[piscator]

i have a degree in geodesy, so chances are i can answer your questions or bullshit my way through them.

[Ayaan]

Since GPS is my good friend, I would like to know how it works.

[cowiz]

I'm more interested how magnets work

[Gawdzilla Sama]

Serious forum.

[piscator]

Since GPS is my good friend, I would like to know how it works.

it triangulates (actually trilaterates) between the GPS satellites (SVs) and your unit


(trilateration means to solve the angles in a triangle using the lengths of the sides and the Law of Cosines (spherical and hyperbolic cosines in this case))


the SVs know where they are (very precisely)
your GPS figures the distances to the SVs it can 'see', and comps some triangles to tell you where you are on a reference ellipsoid (a simplified model of Mother Earth), then roughs in where you are on a geoid (a gravity surface model of Mother Earth, nonlinear and incommensurable with the ellipsoid)

it then spits out your approximate Lat/Long/Elev based on whatever particular datum (earthshape) you've selected (World Geodetic System of 1984 "WGS84" is the "native language/earthshape" of GPS)


so, in short, your GPS measures distances to the GPS satellites, then comps some triangles to figure where you are horizontally, then uses that horizontal position to compute your distance above an average sea level for your particular Geospot

[Ayaan]

Cool. Thanks.

[Gawdzilla Sama]

I've always pictured GPS as where three circles intersect.

[piscator]

I've always pictured GPS as where three circles intersect.

what 3 circles?

i've seen the "intersecting spheres" thing, but i never dug it for a simple explanation
it's easier to visualize a few triangle apexes coming together at your unit



old school celestial navigation (like with a sextant) created an intersection of 2 circles, the edges of which created 2 solutions - one was your position on earth, and the other was likely in the wrong hemisphere and couldn't possibly be where you were, so you rejected it

land surveying and mapping uses a "3 point resection", where a surveyor measures distances to 3 known points to compute his position, but it's generally not used if a direct measurement is available as all measurements are necessarily approximations and the result of 3 imprecise distance measurements (3 circles) is a "Zone of Ambiguity" shaped like a parabolic triangle

Mr surveyor would have to measure to the known point a lot of times and with a device more accurate than he usually carries to get past the statistics and resolve his position to within a given order of accuracy using a simple resection.

this is actually related to something that may come up later, which is why i'm trying to bring it up now, on edit.

[maiforpeace]

Someone showed me a 3d model of how it works, it's really quite interesting. I have a Garmin ETrex and lately I've been doing a bit of mapping of hikes and uploading them to Every Trail, it's great to see what I am walking on a contour map.

[piscator]

moreover Mai, you are walking over a geoid, an equipotential gravity surface normalized to an idealized sea level and square at all times with the local plumb

and those contour lines you are following and crossing are representations of gravity strata
they connect points of equal elevation and thus, equal gravity, just like the shore of a lake would if the water was up to there

but that is a little off point...the basic model of triangulation i want to get across is the triangle formed by the GPS receiver in your hand and 2 SVs 20000+ kilometers above the earth

of course the SVs are moving, so are you, and so is the earth



but that's all good as long as you have the concept of triangulation/trilateration well fixed


then i can move on to just how your unit can measure the distances to the SVs

[Trolldor]

You mean it's not a sexy woman keeping direction for me!?


...why bother living anymore...

[Rum]

I knew all this actually. So there.

[Gawdzilla Sama]

I've always pictured GPS as where three circles intersect.

what 3 circles?

The three circles where the spheres met the Earth. This is for ground/water navigation of course. Aerial navigation, spheres are fine.

[piscator]

3 circles/spheres formed by what?

i did an image search, and came up with this



but that's flawed, as there will never be a point where all 3 circles intersect outside of a perfect world
(if you want to see what i'm talking about, try to draw 3 circles intersecting at a point. even with CAD or something, you have to start with the point and make it a node of at least one of the circles)

2 overlapping circles will intersect at 2 points, but 3 circles demand perfection (and 5 intersection points)

now figure that most GPS receivers can pick up 18 channels (SVs) at once, and typically work with an average of 8-9 SVs at a time
so now you'd have a little computer trying to intersect 9 circles/spheres, each with a different error factor (Dilution of Precision)...





fuck that

triangles are easier

[Gawdzilla Sama]

If you put the satellite on a pole, there are concentric circles on the ground where the signal strikes, each circle larger than the next the signal's lag time. So each satellite creates a "circle of probabilities" for a given distance from it. And just as it takes two lines intersecting to define a point, it takes two circles intersecting to define the two points of probability for a pair of satellites. The third satellite narrows the choice of points down to one spot.