GPS Dilution of Precision — Satellite Geometry & Position Accuracy

Every GNSS receiver — the same navigation chip inside a phone, a car, or a ship — solves the same small linear-algebra problem dozens of times a second: given ranges to several satellites scattered across the sky, back out its own 3D position and clock error. This simulator builds the receiver's geometry matrix live from the satellites you place in the sky, inverts it, and reads off GDOP, HDOP and VDOP exactly as real hardware does. Spread the constellation across the whole sky and the position-error ellipsoid collapses to a tight sphere; cluster the satellites together — or raise the elevation mask until only a handful remain overhead — and the same ranging noise balloons into a large, flattened error ellipsoid. It is the same geometry that makes a GPS fix drift in a dense urban canyon and lock down tight under open sky.