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For Students · GPS Trilateration

GPS Trilateration for a great-circle route

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a great-circle route live below — adjust the inputs and watch it respond, right in your browser.

GPS TrilaterationLive

position from distances

Controls

Presets

Ranging noise (m)

A GPS receiver knows its distance to several satellites from signal travel time. Each distance places it on a circle (a sphere in 3D); where three circles intersect is the fix. With perfect ranges they meet at one point, but timing noise blurs the intersection into a small region — which is why GPS uses many satellites and least-squares to pin down position.

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Data Inspector

Satellites3

Ranging noise0 m

Position error0.0 m

Governing equation

(x - x_{i})^{2} + (y - y_{i})^{2} = r_{i}^{2}, σ_{r} = 0 m

Reading this result: With zero ranging noise the three distance circles meet at exactly one point, so the computed fix lands on the true position.

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Frequently asked questions

Is this good for students?: Yes — this version of "GPS Trilateration for a great-circle route" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.