To establish an accurate 3D position using GPS, a minimum of how many satellites are necessary?

To establish an accurate 3D position using GPS, a minimum of four satellites is necessary. This is because determining an object's precise location in three dimensions—latitude, longitude, and altitude—requires the intersection of signals from multiple satellites.

The basic principle of GPS involves triangulation: by calculating the distance to each satellite based on the time it takes for the signal to reach the receiver, the receiver can find its position in space. With three satellites, the receiver can determine its position in two dimensions (latitude and longitude), but it cannot resolve altitude. The fourth satellite is essential to add the third dimension, allowing the GPS receiver to compute height and correct for any time discrepancies in the satellite signal.

If only three satellites are available, the position could be determined, but with an error in altitude due to the lack of a fourth reference point. This is why four satellites are considered the minimum requirement for accurate 3D positioning via GPS.