A satellite navigation system such as GPS has about 30 satellites orbiting about 20,200 km up. Each one carries an atomic clock and keeps broadcasting a signal that says when it was sent and where the satellite was. A GPS receiver (in a phone, a car or a watch) only receives: it never transmits to the satellites.
From time to distance
- The receiver times how long each signal took to arrive. Radio travels at the speed of light, about 300,000 km per second (300 km in every millisecond), so distance = travel time × speed of light.
- One distance puts the receiver somewhere on a circle round that satellite (in 3D, a sphere).
- Two circles cross at two points: the receiver is at one of them.
- A third circle passes through only one of them: that fixes the position. Using distances like this is strictly trilateration; it's often called triangulation.
Why four satellites?
- The satellites' clocks are atomic, but the receiver's is a cheap one. If it's out by just 0.001 s, every distance is about 300 km wrong, and the circles no longer meet.
- The receiver treats its clock error as one more unknown. In 3D there are four unknowns (latitude, longitude, height and the clock), so it needs four satellites. On this flat map there are three (x, y and the clock), so here three satellites can correct the clock: try Solve for the clock.
- Signals are also slowed a little by the atmosphere, and bounce off buildings. Each distance then has an error, each circle becomes a band, and the receiver can be anywhere in the shaded uncertainty area where the bands overlap. Satellites spread across the sky give a smaller area than satellites bunched together. More satellites (phones use GPS, Galileo, GLONASS and BeiDou together) make it smaller again.
How to use it
Drag the satellites and the phone (the receiver) around the map. Choose how many satellites to use in the title bar. Make the receiver's clock wrong, add signal error, and try the presets. The table shows each signal's travel time and the distance it gives. Uses covers what satellite positioning is used for and how it differs from finding a phone by its cell towers; Challenges tests you.
This map is a flat model, to scale for New Zealand, with the "satellites" in the same plane. Real GPS satellites are 20,000 km up, the circles are spheres, and the errors are a few metres, not the kilometres shown here so you can see them.
Common exam mistakes: saying the receiver sends signals to the satellites; saying GPS measures signal strength; saying three satellites are enough in 3D (they are only with a perfect clock); and saying GPS needs mobile data (it doesn't, though a satnav app may download maps and traffic, and assisted GPS uses the network for a faster fix).
Objective: Cambridge International A Level Information Technology (9626), communications technology: satellite communication systems, how GPS and satellite navigation work, their uses (satnav, geotagging, tracking, timing), and how satellites differ from cell towers.
Where this fits
- Cambridge: Cambridge IGCSE Information and Communication Technology (0417); Cambridge A Level Information Technology (9626) Goes beyond Cambridge IGCSE Information and Communication Technology (0417): 0417 asks for GPS's uses, advantages and disadvantages; timing signals and the fourth satellite for the clock go further.
- Pearson Edexcel International: Edexcel International GCSE ICT (4IT1); Edexcel International A Level Information Technology Goes beyond Edexcel International GCSE ICT (4IT1): 4IT1 asks how navigation aids are used; how GPS fixes a position from signal times goes further.