How GPS actually works

The blue dot

The receiver in your phone is a tiny radio that does nothing but listen. It has no map of the sky, no almanac of where the satellites are, no high-precision clock of its own. It is, in itself, a fairly dumb chip. The reason it knows where it is on Earth to within a few metres is that the satellites it is listening to are doing all of the work in advance, broadcasting precisely calibrated signals on a known frequency and giving the receiver enough information that the geometry of fixing a position becomes a straightforward calculation.

The honest way to understand GPS is to start with what the phone is doing, which is essentially nothing, and then to walk back through the system that puts it in a position to do that nothing usefully. The story goes outward, from the phone in your pocket to the satellites overhead, to the timing precision they need to deliver an answer, to the relativity correction that keeps the timing precision intact.

A constellation overhead

There are about 31 GPS satellites in orbit at any given time. They sit in medium Earth orbit at an altitude of 20,200 kilometres, arranged across six orbital planes inclined at 55 degrees to the equator. Each satellite circles the Earth twice a day, completing one orbit in eleven hours and 58 minutes. The constellation is deliberately overprovisioned, because the design specification is that from anywhere on the surface of the Earth, at any time, with a reasonable view of the sky, at least four satellites are above the horizon. Most of the time, more than four are visible, which is what gives modern receivers their few-metre accuracy.

Each satellite broadcasts continuously on a small set of microwave frequencies. The signal carries two pieces of information that matter to your phone: where the satellite is (an ephemeris, accurate to a few centimetres, updated every few hours from the ground control network) and what time the satellite sent the message, stamped from an onboard atomic clock. Everything else the system needs is derived from those two facts and the speed of light.

One satellite, one sphere

If your phone hears a signal from one satellite, and knows where that satellite was when the signal was sent and what time it was sent, it can calculate how long the signal took to arrive. Multiply that travel time by the speed of light and you have your distance from the satellite. But knowing a distance from one satellite tells you only that you are somewhere on the surface of a sphere centred on that satellite. You could be anywhere on that sphere. With one satellite, the answer is a shell of possibilities, not a position.

Three spheres, one point

A second satellite gives you a second sphere, and the intersection of two spheres is a circle. A third satellite cuts the circle to two points. One of those two points is usually obviously wrong — out in space, or thousands of kilometres into the Earth — so in practice the third satellite is enough to fix you to a single position on the surface of the planet. This is trilateration: distance from three known points pins you to one place. People often call it triangulation, but triangulation uses angles. GPS uses distances, and the geometry is fundamentally different.

Distance is just timing light

The distance calculation rests entirely on timing. The satellite signals travel at the speed of light, which is 299,792 kilometres per second, or roughly thirty centimetres every nanosecond. To pin your position to a few metres, the receiver needs to know how long the signal took to arrive to a few nanoseconds. To know that, the satellite has to send a signal stamped with the time it was sent, and the receiver has to compare it to the time the signal arrived, both accurate to billionths of a second.

The numbers are unforgiving. A clock error of one microsecond — one millionth of a second — works out to a position error of three hundred metres. A clock error of one millisecond would put you three hundred kilometres off. This is why each GPS satellite carries multiple atomic clocks — usually a mixture of caesium and rubidium standards — accurate enough that they drift by less than a billionth of a second a day. They are the most precise clocks ever launched into space at scale, and they are the part of the system that makes everything else possible.

The fourth satellite

The problem is that your phone’s clock is not accurate to billionths of a second. It is a cheap quartz oscillator, accurate to perhaps a millisecond a day, which by satellite standards is hopeless. If the receiver simply trusted its own clock, the position fix would be hundreds of kilometres wrong. The elegant solution is to treat the receiver’s clock error as a fourth unknown and solve for it at the same time as solving for position.

There are four unknowns — x, y, z and the receiver’s time offset — so you need four independent measurements to solve for them. Four satellites, four range equations, four unknowns. The mathematics resolves to a single point in three-dimensional space and a single time correction for the receiver’s clock. That is why a GPS fix requires four satellites in view, not three. The fourth satellite is doing the work of giving the receiver a usable clock without the receiver ever having to own a usable clock of its own. It is one of the most economical pieces of engineering in the system, and it is the reason your phone’s three-dollar timing chip can carry a free atomic-clock-equivalent reading whenever it is outside.

The Einstein correction

This is where the system stops being merely clever and starts being slightly miraculous. The clocks on the satellites do not tick at the same rate as the clocks on the ground, and the reason is Einstein’s relativity. There are two effects, pulling in opposite directions.

The first is general relativity. A clock higher up in a gravitational field ticks faster than one deeper in. The satellites are 20,200 kilometres above the Earth’s surface, in a much weaker part of the Earth’s gravitational potential than we are, so their clocks tick faster than ours. The effect comes out at about +45 microseconds a day.

The second is special relativity. A clock that is moving fast, relative to an observer, ticks slower from the observer’s point of view. GPS satellites orbit at about 14,000 kilometres an hour, which is fast enough for special-relativistic time dilation to matter. The effect runs to about −7 microseconds a day.

The net effect, adding the two together, is that the satellite clocks tick faster than identical ground clocks by about +38 microseconds a day. If you ignored this, the system would still work for a few minutes and then start producing position fixes that drifted by roughly ten kilometres a day and got steadily worse. To prevent that, the satellite clocks are deliberately tuned, before launch, to tick at the rate that will read correctly to ground observers once the relativistic effects are added. The frequency is pre-adjusted so that, in orbit, the satellites’ ticks match the ground’s ticks exactly. The first GPS satellite launched in 1977 carried a switch that could disable the relativity correction; the engineers ran the satellite for twenty days without it before turning it on, watched the predicted error accumulate exactly as Einstein had said it would, and then turned the correction on permanently.

This is the part of the system that is genuinely strange. Every blue dot on every phone on the planet, every commercial flight tracked, every container ship navigated and every harvester driven in a straight line up a paddock by a guidance system depends, in a way that cannot be engineered around, on the fact that Einstein was right about how time behaves in a gravitational field. If general relativity were wrong by even a small amount, GPS as a usable system would not exist.

The blue dot, resolved

Stack the layers and the system reads cleanly. The receiver picks up the signals from four or more satellites overhead. Each signal carries a position and a timestamp from an onboard atomic clock, pre-tuned to compensate for general and special relativity. The receiver compares the timestamps to its own arrival times, solves the four-equation, four-unknown system, and resolves a position in three dimensions plus a corrected time for itself. It does this several times a second. The dot snaps onto your street.

Modern phones do better than the bare GPS minimum — they also use signals from the Russian GLONASS, European Galileo and Chinese BeiDou constellations, and corrections from cellular networks and wifi positioning, which is why a typical phone fix in a city is more like three metres than the ten-metre minimum specification of GPS alone. But the underlying architecture is the same. Atomic clocks in orbit. Light-speed timing. Trilateration in four dimensions. An Einstein correction built into the hardware.

About the system