Significance Of Antenna Sizes

[peter]

It doesn't seem to be a "different mathematical principle" to me. Whether you construct a triangle using three sides or one side and two angles is not really that different.

But the receiver doesn't have the information to directly know any three sides of a triangle, nor would that be sufficient since it would not specify the orientation of that triangle. All the receiver has to work with are time differences in the signals from the various satellites and the ephemeris information that lets it know where the satellites are located.

 

Even if the receiver had a synchronized atomic clock which would let it calculate distances to the satellites directly the model would be of a pyramid rather than a single triangle. I.e. distances to three known points from an unknown location would define a pyramid shape in space that would let you determine your location (the 4th vertex of the pyramid). So instead of the single triangle used in triangulation you have a pyramid with 4 triangular sides.

 

But in practice the receiver doesn't have a precise clock so must instead simultaneously solve for the time as well as the three space coordinates which further complicates things compared to triangulation.

[+as77]

It doesn't seem to be a "different mathematical principle" to me. Whether you construct a triangle using three sides or one side and two angles is not really that different.

But the receiver doesn't have the information to directly know any three sides of a triangle, nor would that be sufficient since it would not specify the orientation of that triangle.

Even if the receiver had a synchronized atomic clock which would let it calculate distances to the satellites directly the model would be of a pyramid rather than a single triangle. I.e. distances to three known points from an unknown location would define a pyramid shape in space that would let you determine your location (the 4th vertex of the pyramid). So instead of the single triangle used in triangulation you have a pyramid with 4 triangular sides.

That's exactly my understanding of the basic principle of how GPS works.

[+NightPilot]

Then how does NurseDave's GPS work so well with only 2 sats?

 

It doesn't. It doesn't work at all with only 2 satellites. It may still give an indication of position, but it's only guessing, and the guess may be very inaccurate. Believing doesn't make it so.