Understanding GPS Fundamentals
Global Positioning System (GPS) is a satellite-based navigation system that provides location, velocity, and time information to receivers on Earth. In self-driving cars, GPS plays a crucial role in global localization, helping the vehicle determine its position relative to a global coordinate system.
GPS works by triangulating signals from at least four satellites. Each satellite broadcasts its position and the time the signal was sent. The receiver calculates the distance to each satellite using the speed of light $c$ and the time delay $\Delta t$:
$$ d = c \cdot \Delta t $$
With distances $d_1, d_2, d_3, d_4$ to four satellites, the receiver solves for its 3D position $(x, y, z)$ and clock bias.
Example: A self-driving car uses GPS to estimate its latitude and longitude, achieving accuracy of about 5-10 meters under ideal conditions. This initial position estimate is fused with other sensors like IMUs for better localization.