Dilution of precision (DOP) measures how satellite geometry amplifies GNSS errors: satellites spread across the sky give low DOP and crisp fixes; satellites clustered together multiply every ranging error into position error. Below 2 is excellent; above 6, treat fixes warily.
Understanding DOP
The mathematics in one breath
DOP falls out of the least-squares solution: from the unit vectors receiver→satellite, form the design matrix, invert its normal matrix, and the diagonal's square roots are the DOP components. The recipe makes DOP purely predictive — computable from almanac data for any place and time without any measurements — which is why planning tools have published DOP forecasts since GPS's earliest surveying days.
DOP in the wild
Canyon streets funnel visible satellites into a strip overhead: cross-street position stays decent, along-street smears — DOP anisotropy you can watch in a phone's wandering dot. Polar users see constellations designed for mid-latitudes cluster toward the horizon, inflating VDOP. And safety-critical aviation approaches specify DOP-linked integrity limits, with receivers autonomously excluding satellites whose geometry contribution masks fault detection.