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### How our GPS coordinate is determined: Trilateration

Posted: 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? 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. huerm....... my gps device so brilliant... math-power.....

See this diagram.....   and 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: 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: Substituting : into the formula for the third sphere and solving for y there results: 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: All this calculation has been made and use by our GPS to do tracking  Diagram credit: Wikipedia