How The Heck Does GPS Work? (An Interactive Exploration)

My notes

Summary

GPS converts time into distance: satellites broadcast radio signals, and the delay between transmission and reception tells your phone exactly how far away each satellite is. Three satellites triangulate position via trilateration; a fourth is required to correct your phone’s imprecise quartz clock. Without relativistic corrections baked directly into satellite hardware, GPS would drift ~11 km per day.

Key Insight

The core GPS mechanism is elegant: each satellite solves one equation in a system. With 3 satellites you get 3 equations for 3 unknowns (x, y, z). The catch is a 4th unknown, clock error (Δt), from your phone’s cheap quartz oscillator, which can drift microseconds. Since 1 microsecond of error = ~300 m of position error, this matters enormously. The 4th satellite adds the 4th equation to solve for Δt simultaneously. There is only one clock correction value where all four spheres intersect at a single point, so the receiver iterates until convergence.

The relativity correction is genuinely surprising engineering: GPS satellite clocks are deliberately manufactured to tick slightly slow on the ground (at a rate offset by ~38.4 μs/day net), so that once in orbit, where special relativity slows them (~7 μs/day loss) and general relativity speeds them (~45 μs/day gain), they end up running at exactly the correct rate. Without this, position error would accumulate at ~11 km/day.

Practical degradation sources:

• Geometric Dilution of Precision (GDOP): satellites clustered in one sky sector = shallow ring intersections = large uncertainty zone. Receivers select satellite combinations to minimise GDOP.
• Multipath error: urban canyons cause signals to bounce off buildings, making the stopwatch think you’re further away. Hardest unsolved problem in consumer GPS.
• Modern phones listen to GLONASS (Russia), Galileo (EU), and BeiDou (China) simultaneously, typically locking 8-12 satellites, averaging out errors.