Introduction
In our first lesson, we introduced GNSS as a network of "sky lighthouses." But how exactly do those lighthouses help your phone know where you are? The answer lies in a clever geometric principle called trilateration.
The Basic Idea: Finding Yourself with Landmarks
Imagine you're blindfolded in a large, empty field. Someone tells you that you are exactly 100 meters from a specific tree. Where could you be? You could be anywhere on a circle with a 100-meter radius, centered on that tree.
Now, someone tells you that you're also 150 meters from a large rock. Where could you be now? You're at one of the two points where the circles intersect.
A third distance measurement pinpoints your exact location.
2D Trilateration: The Folding Chair Analogy
Have you ever sat in a folding chair?
- One leg down: The chair can rotate anywhere
- Two legs down: The chair can still swing back and forth
- Three legs down: The chair is fixed firmly in place
Trilateration works the same way. In a 2D plane, you need three distance measurements for a unique location.
Moving to 3D: Adding Satellites
In 3D space, the "circles" become spheres:
- One satellite: You're on a sphere around that satellite
- Two satellites: You're on the circle where two spheres intersect
- Three satellites: Two possible points (one usually discarded)
- Four satellites: Single precise point in 3D space
Why Four Satellites?
Mathematically, three satellites should be enough. So why four? The answer is time, specifically, the clock in your receiver.
GPS satellites have precise atomic clocks. Your phone has a cheap quartz clock. The fourth satellite measurement allows the receiver to solve for this timing error.
Summary
- Measure Distance: Receiver calculates distance to each satellite
- Draw Spheres: Each distance creates an imaginary sphere
- Find Intersection: Position is where spheres intersect
- Correct Time: Fourth satellite fixes clock error