How a receiver finds itself by listening to four clocks it cannot see

Both approaches to satellite navigation receivers work. What differs is what they cost you, and the cost is what this sets out.

The satellites do not know where you are

Each satellite broadcasts a description of its own orbit together with the exact time according to an atomic clock it carries. Your receiver listens, works out how long each signal took to arrive, and multiplies by the speed of light to obtain a distance. One distance places you somewhere on a sphere, two spheres intersect in a circle, and three narrow that circle down to two points.

One of those points is absurd, far out in space or moving impossibly fast, so the receiver discards it without any difficulty. Nothing is ever transmitted upward, which is why a receiver behaves identically whether one person or a million are using it simultaneously.

The fourth satellite is fixing your clock

Measuring travel time requires knowing when a signal left and when it arrived, to within a few billionths of a second. Satellites carry atomic clocks, while your receiver carries a cheap crystal oscillator that drifts far too much for that kind of precision. The receiver therefore treats its own clock error as a fourth unknown alongside latitude, longitude and height above the reference surface.

Four satellites provide four equations, which is exactly enough to solve for position and for the clock offset at the same time. A useful side effect is that any receiver holding a fix also has extraordinarily accurate time, which many other systems quietly depend upon.

The signal arrives buried underneath the noise

By the time it reaches the ground the signal is weaker than the background radio noise occupying the same stretch of spectrum. It is recovered because each satellite multiplies its data by a long pseudo-random code that the receiver already knows in advance. The receiver generates the same code and slides its copy in time until the two align, which lifts the signal clear of the noise.

In the datasheet, the alignment producing that match is itself the travel time measurement, so the trick that finds the signal is the trick that measures it. This also explains why the antenna must see sky: the margin is so thin that a roof or dense canopy removes it completely.

Why the first fix takes so long

A cold receiver does not know which satellites are overhead, where they currently are, or how far its own clock has drifted. It must search a two-dimensional space of code alignment and frequency shift for every candidate satellite, and that search takes time.

It then needs orbital data, transmitted slowly inside the signal itself over a period of some tens of seconds per satellite. Assistance data delivered over a network short-circuits all of this by supplying orbits and a rough starting position, cutting a fix to seconds.

That is why positioning feels instant with a data connection and painfully slow on a device switched off for weeks in a new country.

Cities break the geometry

Buildings block satellites, and those that remain visible are often clustered in a narrow strip of sky along the line of the street. Clustered satellites give poor geometric spread, which amplifies small timing errors into large position errors even when the signals are clean.

Worse, signals reflect off glass and stone, so the receiver may end up measuring a path that bounced rather than the direct one. A reflected path is always longer, which biases the distance outward and can place you confidently on the wrong side of a street. Receivers spot some reflections by their weaker, distorted correlation, but discarding them costs satellites the receiver could not really spare.

Firmware updates change this behaviour more often than hardware does.

More constellations and more frequencies

Several independent satellite systems now broadcast compatible signals, and most current receivers listen to all of them at the same time. More satellites mean better geometry in obstructed places, which matters far more in a city than raw accuracy on an open plain.

Receivers that track two frequencies at once can measure and remove the delay that the ionosphere adds to a passing signal. That delay varies with solar activity and is one of the largest remaining error sources for any single-frequency receiver. None of this helps indoors, where the sky is gone entirely and the device falls back on quite different positioning methods.

Side by side

The takeaway

It is a timing instrument first and a map accessory second.

The constraint is almost always physical, and marketing rarely mentions which one.