## Tuesday, 14 May 2013

### How our GPS coordinate is determined

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
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Source taken from :

FauSham @ Malaysia & Singapore Free Maps - MalFreeMaps