How our GPS coordinate is determined: Trilateration

Guides, FAQs, How-to, etc

Moderators: Moderators, Regional Mappers

Forum rules
1. Be nice to each other and respect the moderators. Post in normal font size, color and weight. Follow Nettiquette
2. NO out of topic. Discuss matters pertaining MFM community and forum only.
3. NO abuse, profanity and insults
4. NO spamming, cross posting and opening of duplicate topics
5. NO advertisement post or link
6. NO post/link to warez, cracks, serials or illegally obtained copyrighted content
7. Each message posted is owned by and is the opinion of the original poster. Neither mfm nor its owner or moderators are legally responsible for anything posted on the forum
User avatar
FauSham
Posts: 104
Joined: Fri Sep 19, 2008 10:13 pm
Location: Kelantan [Legend Cx / Nuvi 200(Damage) / Nuvi 760 / Nuvi 265W(New)]
Contact:

How our GPS coordinate is determined: Trilateration

Postby FauSham » Fri Jan 30, 2009 10:34 pm

Trilateration
Selected and re-edited by FauSham from many resources as Informative sources for MFM Reader.

Did u know that, our GPS use Trilateration geometric equation to calculate our coordinate? :D
But I like to share with all MFM's member.....

What is Trilateration?
The measurement of a series of distances between points on the surface of the earth, for the purpose of establishing relative positions of the points in surveying.

Trilateration is a method for determining the intersections of three sphere surfaces given the centers and radii of the three spheres. :-k huerm....... my gps device so brilliant... math-power.....

See this diagram.....
Image

We start with the equations for the three spheres

Image

Image

and

Image

We need to find a point located at (x, y, z) that satisfies all three equations.

First we subtract the second equation from the first and solve for x:

Image

Substituting this back into the formula for the first sphere produces the formula for a circle, the solution to the intersection of the first two spheres:

Image

Substituting :Image into the formula for the third sphere and solving for y there results:

Image

Now that we have the x- and y-coordinates of the solution point, we can simply rearrange the formula for the first sphere to find the z-coordinate:

Image

All this calculation has been made and use by our GPS to do tracking :thumbsup:

Image
Diagram credit: Wikipedia
FauSham @ Malaysia & Singapore Free Maps - MalFreeMaps
AMATEUR RADIO CALLSIGN: 9W2WFN

Return to “Library”

Who is online

Users browsing this forum: No registered users and 2 guests