How GPS works

GPS satellite

Lost in a strange city

Suppose we stand in an unknown city. Half a block away, we see a tall monument in the middle of a traffic circle. "Where are we?" I ask a passerby. She happens to be a science teacher who has devised a puzzle for her class and wants to test it out on us. She answers, "I'll give you three clues. You're 432 miles from Atlanta, 818 miles from Boston, and 977 miles from Denver. Figure out where you are." I pull out my map of the USA and a compass for drawing circles. I know from her clues that we are simulataneously on three circles with radii of 432, 818, and 977 miles centered respectively on these three cities. I draw the circles and see that there is only one point where all three intersect. "Ah," I say, "That traffic circle we see must be Monument Circle in Indianapolis."

The principle of trilateration

This story illustrates the principle of trilateration, which is at the core of how GPS works. GPS stands for the Global Positioning System, which is one of several satellite constellations that support navigation and location services. Each satellite transmits one of the "clues" needed for the GPS receiver in a person's mobile device or in a pilot's instrument panel to figure out its location.

What does a GPS satellite transmit?

GPS satellites are equipped with precision atomic clocks that are synchronized with each other. They also have precise data on their orbital motions. Each satellite transmits messages saying, "The time is such and such, I'm at this latitude, this longitude, and this altitude." The receiver gets such a message and compares the time on its own clock to the time of transmission reported by the satellite. The difference between these two times tells the receiver how long it took for the message to travel to it. Knowing the speed of light, this travel time tells it how far away the satellite is. If the receiver has a clear line-of-sight view of three satellites, than it can perform a three-dimensional version of the Indianapolis calculation. It finds its location by mathematically "drawing" three spheres centered respectively on the three satellites and finding out where they all intersect. Mathematically speaking, by combining the three pieces of information from the satellites, it figures out the three numbers that describe its location, namely, latitude, longitude, and elevation.

Correcting for receiver clock inaccuracy

The problem with this is that the receiver is often a cheap and portable device. Its clock will be off. Let's suppose that the receiver's clock runs slightly behind the correct time. When it receives a signal from a satellite, this error will cause it to think that the signal arrived a bit earlier than it acually did. So, it will underestimate the distance to the satellite. Using the map of the Indianapolis calculation as an analogy, we can visualize how this messes things up.

Trilateration with receiver clock error

Suppose my receiver clock error causes the distance to each of the three cities to be underestimed by some amount. The radius of each circle I draw gets shrunk by that amount. The size of the little white disk shows this shrinkage. We can see that now there is no point where all three circles intersect. In the three-dimensional scenario of GPS, the receiver needs to determine four unknown things, its latitude, longitude, elevation, and its clock error. A basic math principle is that one needs four pieces of information to figure out four unknowns. In the GPS system, the receiver gets the fourth piece of information by receiving data from a fourth satellite. This allows it to both locate itself and correct its clock.

GPS works in concert with other things

Many smartphones have GPS, but can also use signals from cell towers to get location information, provided they are within range. Airplane navigation relies on many location methods, including visual navigation by following rivers, coastlines, or other visible landmarks, and ground-based radio navaids such as VOR and DME. These radio navaids, however, have a range of about 200 nautical miles. In remote areas or over oceans, GPS becomes a important navigational tool. This Aviation Theory video explains the many ways that air navigation is done.