How GPS Works: Trilateration, Atomic Clocks & Relativity

Trilateration: finding a point in 3D

Trilateration — not triangulation, which uses angles — is how GPS fixes position. Each satellite broadcasts its exact location and the exact time it sent the signal. The receiver notes the arrival time and computes the travel time, and since the signal moves at the speed of light:

distance = c × (arrival time − transmission time)

1 satellite → a sphere of possible positions
2 satellites → a circle (sphere ∩ sphere)
3 satellites → narrows to 2 points
4th satellite → resolves ambiguity AND clock bias

A phone's clock is only accurate to about 1 millisecond — enough to cause a 300 km position error on its own. The fourth satellite lets the receiver solve for its 3D position and its clock bias simultaneously: four unknowns from four equations.

live demo · satellite range circles pinning down a receiver position● LIVE

Nanosecond timing and atomic clocks

Light travels 30 cm in 1 nanosecond, so 1-metre accuracy demands timing correct to better than 3 nanoseconds. Each GPS satellite carries multiple caesium and rubidium atomic clocks, accurate to about 20-30 nanoseconds per day — roughly 1 part in 10¹³ — monitored and corrected by ground stations whose offset values are uploaded and transmitted to receivers.

The relativity correction: two effects, opposite directions

Special relativity says a moving clock ticks slower: at ~3.9 km/s orbital speed, satellite clocks lose 7.2 μs/day relative to the ground. General relativity says clocks tick faster in weaker gravity: at 20,200 km altitude, satellite clocks gain 45.9 μs/day. The two effects don't cancel — general relativity dominates.

Special relativity (velocity):  −7.2 μs/day   (−2.16 km/day)
General relativity (gravity):  +45.9 μs/day   (+13.77 km/day)
Net effect:                    +38.7 μs/day   (+11.6 km/day if uncorrected)

Engineers solve this by manufacturing satellite clocks to tick slightly slower than their nominal frequency on the ground — so once in orbit, combining both relativistic effects, they run at exactly the right rate. Physicist Neil Ashby summed it up: "GPS is a practical application of general relativity," arguably the most convincing real-world test of the theory that exists.

Other error sources and GNSS beyond GPS

Ionospheric delay (20-30 ns, up to 150 ns during solar storms) is corrected with dual-frequency receivers; tropospheric delay (~7 ns) is corrected with weather models; multipath reflections off buildings are suppressed with phased-array antennas. GPS geometry quality is quantified by PDOP — Position Dilution of Precision — with values under 2 considered excellent. GPS is just one of four global systems: GLONASS (Russia), Galileo (EU) and BeiDou (China) all operate similarly, and modern phones combine signals from all four for faster, more accurate fixes.

Frequently asked questions

Why does GPS need at least 4 satellites?

A receiver's clock is only accurate to about 1 millisecond, which alone would cause a 300 km position error. Three satellites fix a 3D position given a perfect clock, but a fourth satellite lets the receiver solve for both its 3D position and its own clock bias simultaneously — four unknowns from four equations.

How much would GPS drift without relativistic corrections?

Special relativity makes satellite clocks run about 7.2 microseconds per day slower due to their orbital velocity, while general relativity makes them run about 45.9 microseconds per day faster due to weaker gravity at altitude. The net effect is +38.7 microseconds per day, which uncorrected would cause position errors to accumulate at roughly 11.6 km per day.

What is trilateration and how is it different from triangulation?

Trilateration determines position from distances (ranges) to known points, while triangulation uses angles. GPS measures the travel time of each satellite signal, converts it to a distance via c×time, and finds the position where circles (or spheres) of those radii around each satellite intersect.

Try it live

Everything above runs in your browser — open GPS Trilateration and watch a Gauss-Newton least-squares solver fix a receiver position from noisy satellite ranges, with a live GDOP error ellipse.

▶ Open GPS Trilateration simulation