GPS

For now consider only the XY plane, with not height dimension. Consider a satellite above the plane somehere which is constantly transmitting its onboard time and position. We can use this data to find the time take for the signal to reach us. On the surface, this will give us a set of points, which are in a circle as possible solutions.

Now consider the situation where we have two satellites. Upon receiving the signals from them that contain onboard times, and comparing with a local clock to calculate the transmission time, we can come up with a circle for each satellite, where the receiver could possibly be.

These circles intersect at 2 points, and we can just pick any one point and call it a day. For a 3D location description, we will need 3 satellites. After the transmission delay has been used to calculate the distance to the satellite, we can come up with a sphere for each satellite . The spheres will intersect at a set of points. These set of points is where the GPS receiver is located.

We have 4 unknowns that we are trying to find out -

1. Latitutde
2. Longitude
3. Height
4. Time error
   We will make use of the fact that all of the GNSS satellites have their clocks synchronized always. This means that all of the satellites will result in the same time error for a receiver on the ground.

Now, while 3 satellites can get us the data we need (the first three), having 4 satellites means that we can also calculate the time error and get accurate position (approximately 5 - 10 m)