GPS Triangulation

Imagine you're on a boat in a foggy ocean, and three lighthouses tell you exactly when they flashed. You could work out your position right away. Once you know you're 5 km from the first lighthouse, your position narrows to somewhere on a big circle with a 5 km radius around it.

Add the fact that you're 3 km from a second lighthouse, and the two circles overlap at just two points. Those are your only candidates. Then you check the distance to the third lighthouse, and the three circles meet at one single point. Now you know exactly where your boat is.

Your phone's location feature works the same way. Instead of lighthouses, dozens of GPS satellites orbit about 20,000 kilometers above Earth, sending out signals nonstop. Your phone measures the tiny delay before each satellite's radio signal reaches your hand, and from that it calculates the distance to each satellite.

So the blue dot blinking on your map app isn't your phone wandering around looking for you. It's the result of some clever geometry: circles drawn around the satellites, using the timing data they broadcast, all overlapping at your spot.

On a flat map, three circles are enough to find a position. In 3D space, three spheres meet at two points. One of those points is out in space and the other is on Earth's surface, so it seems like three satellites should do the job. But real navigation needs a signal from at least four satellites.

The reason is the clock inside your phone. Radio waves travel at the speed of light, which is fast enough to circle the Earth seven and a half times in one second. If your phone's clock is off by just one millionth of a second, your calculated distance is off by a whopping 300 meters.

The satellites carry extremely precise atomic clocks. Your phone, though, has an ordinary, cheap electronic clock. So the phone treats its own clock error as one more unknown, just like its position. Latitude, longitude, altitude, and clock error make four unknowns, which is why you need at least four satellites.

With four signals, the phone solves for all four values at once. The clock error gets worked out and cancelled, and that's what makes navigation accurate to within a few meters.

We usually call it triangulation, but the more accurate technical term is trilateration. Traditional triangulation measures the angles between reference points to find distances. GPS instead calculates the distances (the side lengths) to the satellites directly and uses them to find your position.

Real radio waves also don't travel through a vacuum the whole way. They pass through Earth's atmosphere, and their speed changes slightly. The ionosphere and troposphere can bend or slow the signal. Correction data from the satellites and correction algorithms remove much of this distortion.

When your navigation jumps to the wrong place among tall downtown buildings or in an underground parking garage, the cause is different. The direct signal from the satellite may bounce off concrete buildings, which is called multipath error, or the signal may be blocked entirely.

That's why modern smartphones also use nearby Wi-Fi routers and cell towers' signal strength as helpers when the satellite signal is weak. That lets them lock onto your location faster and more smoothly.