Clocks, ranges and four unknowns

A navigation signal carries timing and orbital information. Comparing its transmission time with reception time provides a range estimate when combined with the signal’s propagation speed. The receiver uses several such measurements together; a single range does not uniquely locate it in three-dimensional space.

Try an original approximation: use 300 million metres per second for light speed. A timing difference of 10 nanoseconds corresponds to about 3 metres of signal travel. This is a range-error illustration, not a prediction that a receiver’s final position will be wrong by exactly 3 metres. Geometry and other errors also affect the solution.

In the usual unconstrained three-dimensional solution, the receiver estimates three position coordinates and its clock offset. At least four suitable satellite measurements are therefore needed. They constrain the solution together; it is misleading to imagine one satellite independently reporting latitude, another longitude and another altitude.

An original analogy is trying to locate a sound using several arrival times while your stopwatch has an unknown offset. Every measurement carries that shared clock contribution. More observations can help check a solution, but extra copies of the same measurement do not supply independent geometric information.

A timing difference becomes a range difference

Signals can be delayed by the atmosphere or reflected by nearby buildings. Reflected paths can introduce multipath errors. Satellite geometry, blockage and receiver quality also affect the position a user sees. A signal-performance figure is not automatically a guarantee for every receiver in every environment.

In a teaching comparison, the same receiver is used first in an open field and then beside tall reflective buildings. If the position becomes less stable, the constellation has not necessarily changed. Examine visibility and signal paths before assigning the difference entirely to satellite hardware. The GPS accuracy source explains these general receiver-environment distinctions; its numerical service commitments are not Galileo commitments.