How Many GPS Satellites Are Needed for Accurate Location Fixing?

When you think about using GPS to determine your location, it's important to understand how the technology works. Contrary to what some might assume, just four GPS satellites are needed to calculate the precise location of a GPS receiver on Earth. Understanding why this is the case can help demystify the technology further.

Conceptual Overview

The mathematics behind GPS location fixing is actually quite similar to the concept of triangulation in older methods of navigation, such as using church bells to determine one's position in a town. Let's dive deeper into how this works.

The Basics of Triangulation

Imagine you are in a town where you hear church bells ring. At noon, the bells start ringing, but that doesn't help you determine where you are because you have two unknowns: your distance (x and y) from the bells, and one piece of information (the bells rang at noon).

Adding Time: The Solution

Now, imagine you are wearing a very accurate watch. When the bells ring, you time it: the bells ring at 12:00:00, and your watch shows 12:00:01.0000. You know the sound takes one second to travel, so you are 331 meters away from the bells. This still doesn't pinpoint your location, but you now have additional information to refine it.

Adding Another Point of Reference

Imagine you add another church with a clock. When you hear the bell at the second church, the time on your stopwatch is 12:00:02.0000. Combining this with the first church, you can plot circles around each church at distances corresponding to the time it took for the sound to reach you. You'll find that the circles intersect, and the point of intersection narrows down your location to a line. However, you still don't know which specific point on that line is your exact location.

Adding a Third Reference Point

Now, imagine you have a third church with a clock, and you hear the bells at 12:00:03.0000. By combining the information from all three churches, the circles intersect in two points. You are at one of these two points, but not knowing which one without additional information makes it difficult to pinpoint your exact location.

The Importance of Time and Extra Satellites

In the case of the GPS system, instead of using church bells, the satellites send out a signal at a very precise time. In the same way, your GPS receiver can't carry an atomic clock due to its size and power constraints. Therefore, an extra signal is required to make up for this lack of knowledge of the time. This is why four satellites are needed to fix your position to one of these two points. Your phone returns the solution that is somewhere near the Earth's surface, the other solution is always far above the satellites.

Why Four Satellites?

The reason four satellites are needed is based on the principles of geometry. With three satellites, the signals intersect in a plane, leaving ambiguity about your exact location within that plane. Adding a fourth satellite narrows this down to a single point. This solution is most likely the one closest to the Earth's surface, which is the one used for practical navigation purposes.

Practical Implications

While GPS receivers don't return both solutions, the system is designed to ensure that the solution is valid and useful. In cases where the ephemeris (the satellite's orbit information) is poor, the system may return both potential locations, but the error in determining which one is correct is generally significant, leading to rejection of the second solution.

Conclusion

In conclusion, the GPS system requires four satellites to fix your position, ensuring that you get an accurate location. This process involves triangulating the signals from multiple satellites, taking advantage of precise timing to solve for your exact coordinates.