Signals from Space
The Global Positioning System consists of 31 satellites orbiting at 20,200 km altitude, each broadcasting its precise position and atomic clock time. A GPS receiver on the ground measures the time delay of each satellite's signal, converting it to a pseudorange — the apparent distance corrupted by clock bias and atmospheric delays. With four or more pseudoranges, the receiver solves for its three position coordinates plus its clock error.
Trilateration Geometry
Each pseudorange defines a sphere centered on a satellite. The receiver's position lies at the intersection of these spheres. With exactly four satellites, the system is determined (4 equations, 4 unknowns). Additional satellites overdetermine the system, enabling least-squares estimation that averages out noise. The simulation visualizes these range spheres projected onto a 2D plane, showing how they intersect to pinpoint position.
Dilution of Precision
Not all satellite configurations are equal. When satellites are spread evenly across the sky, the range-sphere intersections form a tight cluster — low GDOP, high accuracy. When satellites are bunched together, the intersections become elongated — high GDOP, degraded accuracy. The simulation lets you drag satellite positions and watch the GDOP value and position uncertainty ellipse change in real time. Urban canyons and mountainous terrain often restrict visible sky, increasing GDOP.
Error Sources and Mitigation
GPS errors come from satellite clock drift (~2 m), ephemeris errors (~2 m), ionospheric delay (2-15 m), tropospheric delay (~0.5 m), multipath reflections (~1 m), and receiver noise (~0.5 m). Dual-frequency receivers eliminate ionospheric delay. Differential GPS (DGPS) uses a nearby reference station to cancel common errors, achieving sub-meter accuracy. The simulator lets you tune each error source and observe the combined effect on position accuracy.