GNSS and Coordinate Systems

Each satellite broadcasts its position and transmission time; the delay gives a distance, placing the receiver on a sphere. Three spheres intersect at a point — but the receiver's clock is a cheap crystal drifting by microseconds, and a microsecond is 300 metres.

Treating the clock offset as a fourth unknown and solving four equations simultaneously removes the need for an accurate receiver clock. That is why four satellites are the minimum — and why every receiver is a precise clock as a by-product, which is how telecoms networks and power grids get their timing.

Geometric dilution of precision measures how the satellites' arrangement amplifies range error into position error. Well-spread satellites intersect steeply and give a tight fix; clustered ones intersect at a shallow angle and produce a long thin uncertainty — which is why an urban canyon degrades precision even with a strong signal.

A base station on a known point measures the shared error and broadcasts the correction, turning metres into centimetres — and carrier phase processing then turns centimetres into millimetres.

GNSS reports on WGS84, a global ellipsoid fitted to the whole earth — best on average and best nowhere in particular. National grids use a local ellipsoid fitted to their own region and deliberately displaced. The difference reaches hundreds of metres, and it is a datum error rather than a measurement error.

Height is worse. The geoid — mean sea level extended under the land — is genuinely lumpy because the earth's density is not uniform, while GNSS gives ellipsoidal height above a smooth surface. They differ by up to 100 m globally, so a geoid model is needed, and water still flows downhill according to the geoid.

GNSS made measurement fast and cheap and changed none of the discipline: work from whole to part, check independently, observe redundantly, know your datum. A receiver reporting 10 mm precision on the wrong datum is 200 m out and entirely confident about it.