The Hyperbola depiction of how the GPS equations are solved:
From several psuedoranges measured at the same time, we can calculate the (absolute) difference in the distances between us and these GPS satellites. 2 satellites gives us 1 known difference in distance, and we can plot our position along the surface of a hyperboloid where all points at the surface have the same (absolute) diff in distance to the 2 satellites. From there we can add an other or several other additional satellites to make more hyperboloids which will create an intersection point at our (receiver) position. We will need 3 hyperboloids to make one point of intersection.
Why will 3 satellites give us only 2 hyperboloids as opposed to 3? (hyperboloids between satellites 1 + 2, 2 + 3, AND 1 + 3?)
And why will 4 satellites give us only 3 hyperboloids as opposed to 6? (hyperboloids between satellites 1 + 2, 2 + 3, AND 3 + 4 AND 1 + 3, 2 + 4, 1 + 4 ?)
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From several psuedoranges measured at the same time, we can calculate the (absolute) difference in the distances between us and these GPS satellites. 2 satellites gives us 1 known difference in distance, and we can plot our position along the surface of a hyperboloid where all points at the surface have the same (absolute) diff in distance to the 2 satellites. From there we can add an other or several other additional satellites to make more hyperboloids which will create an intersection point at our (receiver) position. We will need 3 hyperboloids to make one point of intersection.
Why will 3 satellites give us only 2 hyperboloids as opposed to 3? (hyperboloids between satellites 1 + 2, 2 + 3, AND 1 + 3?)
And why will 4 satellites give us only 3 hyperboloids as opposed to 6? (hyperboloids between satellites 1 + 2, 2 + 3, AND 3 + 4 AND 1 + 3, 2 + 4, 1 + 4 ?)
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