As Simple As Possible — Why does GPS need at least 4 satellite signals?

GPS stands for “Global Positioning System”. It was invented by the U.S. for military use in the 1978 and was globally available since 1994. After around 30 years, almost all smart phones nowadays have a GPS chip to locate user’s location. But how many user knows the underlying theory behind the scene? It is not as difficult as you think!

6 orbital planes & 24-Slot satellite constellation

The U.S. has launched 31 GPS satellites to the space and they are constantly emitting encoded radio signal to the earth. Device with GPS chip can decode the signal and obtain the critical information, such as the position of the satellite and the time of emitting signal.

A 24-slot arrangement is designed by the U.S. It categorise the GPS satellites into 6 different groups. Each group of satellites are orbiting the earth in an equally-spaced plane. There are totally 4 slots in each plane. By this special arrangement, the U.S. can ensure every point on the earth can receive at least “4” satellite signals at the same time. Are you now curious why “4” but not “3” or “5”? Don’t worry. It does not involve any high-level mathematics and can be understood easily with several graphs.

Let’s GO!

Simple explanation of GPS theory

Part 1 of 5: Basic distance formula

As mentioned above, radio signal emitted from GPS satellite contains encoded satellite coordinates and the time of emitting signal. Device with GPS chip can decode the signal and measure the time difference between emitting and receiving signal.

Radio wave is a kind of electromagnetic wave which is transmitted at the speed of light (299,792,458 m/s) that is a universal constant.

With these two information, the distance between user and specific satellite can be calculated.

Part 2 of 5: Sphere with radius = distance

Illustration of sphere with core in 3D space

Imaging that the core of sphere above is one of the GPS satellites. With the calculated distance in the previous part, a sphere with radius distance can be drawn. In other words, all possible user positions are now located at the surface of the sphere.

Part 3 of 5: Merge signals from 2 satellites

Illustration of the common solution (black circle) from 2 satellites

When device manipulates the signal from the second satellite, the overall result can be represented by the two green spheres as shown above, one for each satellite.

As mentioned in previous section, the surface of each sphere represents all the possible user locations. Therefore the common points of the two spheres are the remaining possible solutions. The result is represented as the black circle shown in the above graph.

Part 4 of 5: Manipulate with 3rd satellite signal

Similarly, when the 3rd satellite signal is manipulated, the number of intersection between a 2D circle and a 3D sphere is 2. Therefore, the overall possible solution will be reduced to 2 points. The result is shown as the red dots at the above image.

Part 5 of 5: Handling the final 4th satellite signal

Trivially, the signal from the 4th satellite can further reduce the possible user location from 2 to 1. Finally, device location can be confirmed!

Limitation of GPS

  1. Imperfect penetration power to building or mountain. Radio wave cannot effectively pass through cement and rock. Part of the radio wave is reflected away when hitting a building. The accuracy can drop from ~50m to ~300m when device is moved from outdoor to indoor. The followings are the GPS accuracy data captured from my Android device (Samsung Galaxy Note 5 SM-N9200):
Indoor GPS signal accuracy is 45.51m
Outdoor GPS signal accuracy is 281.71m

2. Interference from the space, such as the solar flare. It is a kind of electromagnetic wave which is the same as radio wave emitted from the GPS satellite. Therefore, solar flare can greatly affect the signal strength by destructive wave interference.

Example of GPS alternatives

No only the U.S. has developed satellite-based navigation system. Several more countries or unions have already developed their own one, see the below list:

  1. China: BeiDou Navigation Satellite System
BeiDou logo

2. India: Indian Regional Navigation Satellite System

Indian Regional Navigation Satellite System logo

3. Japan: Quasi-Zenith Satellite System

Quasi-Zenith Satellite System logo

4. European Union: Galileo

Galileo logo

5. Russia: GLONASS

GLONASS logo

Summary

  1. GPS is a satellite-based navigation system and contains totally 31 satellites.
  2. Radio wave with encoded information is constantly emitted from GPS satellite and contains the satellite coordinates and the time of emitting signal.
  3. The U.S. has ensured user at any point of the earth can receive at least 4 GPS satellite signals to identify his / her own location.
  4. Receiver position can be calculated by manipulating its distances from at least 4 GPS satellites. The position can be confirmed by reducing the possible solution from “a sphere” to “a circle” to “2 points” and finally to “a single point”.
  5. GPS signal is weaker in indoor and is affected by astronomical phenomenon such as solar flare.
  6. At least 5 countries or economic bodies have already developed their own satellite-based navigation system.

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