Finding Your Place from Space
Every time your phone shows a blue dot on a map, it is performing a remarkable feat of physics and mathematics. GPS satellites orbiting at 20,200 km altitude broadcast precise timing signals that travel at the speed of light. Your receiver measures the arrival time of signals from multiple satellites, calculates the distance to each, and finds the unique point in space where all those distance spheres intersect. This is trilateration — and it works to within a few meters.
The Geometry of Intersection
With one satellite, you know you are somewhere on a sphere of known radius centered on that satellite. Two satellites narrow your position to the circle where two spheres intersect. Three satellites reduce this to two points (one of which is usually in space and discarded). A fourth satellite is needed not for geometric reasons but to solve for the receiver's clock error — since even a one-microsecond timing error translates to 300 meters of range error.
Dilution of Precision
Not all satellite configurations are equal. If four satellites are clustered in one part of the sky, small measurement errors amplify into large position errors — like trying to pinpoint a location from nearly parallel sight lines. This effect is quantified by the Dilution of Precision (DOP). The ideal geometry has satellites spread evenly across the sky, with one directly overhead. This simulation lets you adjust satellite spread to see its dramatic effect on accuracy.
Error Sources and Mitigation
GPS errors come from several sources: atmospheric delays (ionosphere and troposphere bend and slow signals), multipath reflections off buildings, satellite orbit and clock errors, and receiver noise. Modern techniques like dual-frequency receivers, differential GPS, and satellite-based augmentation systems reduce these errors from meters to centimeters. This simulation models noise and clock error to show their impact on the final position fix.