Question

The minimum number of satellites required to determine a 3D position using GPS is:

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

If you only need a 2D position (Latitude and Longitude at a known altitude), a minimum of 3 satellites is required.
For high-precision survey work, often 5 or more satellites are preferred to improve the Dilution of Precision (DOP).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Global Positioning System (GPS) positioning is based on the principle of trilateration, which involves measuring the distance (range) from the receiver to multiple satellites.
Step 2: Detailed Explanation:
To determine a position in three-dimensional space, we have four unknowns:
1. Latitude (\( X \))
2. Longitude (\( Y \))
3. Altitude or Elevation (\( Z \))
4. Receiver Clock Bias (\( t \))
While mathematically, three spheres (from 3 satellites) intersect at two points (one of which can usually be discarded as being in space), a fourth satellite is absolutely necessary to synchronize the receiver's clock with the atomic clocks on the satellites. Without this time synchronization, distance measurements would be highly inaccurate.
Step 3: Final Answer:
Therefore, a minimum of 4 satellites is required to solve for the four variables (\( X, Y, Z, t \)) and provide a 3D position fix.