Global Positioning System (GPS)

Global Positioning System (GPS)

The Global Positioning System (GPS) is a space-based navigation system that provides location and time information.

GPS Segments

1. Space Segment: A constellation of at least 24 satellites (NAVSTAR) orbiting the Earth.
2. Control Segment: Ground stations worldwide that monitor and control the satellites.
3. User Segment: Receivers (civilian and military) that process signals to determine position.

How GPS Works

GPS receivers calculate their position by timing the signals sent by GPS satellites.

Trilateration

The receiver measures the distance to at least four satellites to determine its 3D position (Latitude, Longitude, Altitude).

$D = c \Delta t$ Where:

• $c$: Speed of light ($299,792,458$ m/s)
• $\Delta t$: Time taken for the signal to travel.

GPS Surveying Methods

1. Static Surveying: Used for high-accuracy control points. Receivers occupy stations for long periods (hours).
2. Fast Static: Shorter observation times (minutes) but requires specialized post-processing.
3. Real-Time Kinematic (RTK):
   • Uses a base station and a rover.
   • Provides centimeter-level accuracy in real-time.
   • Requires a radio link between base and rover.

Sources of Error

1. Clock Errors: Satellites and receivers may not be perfectly synchronized.
2. Ephemeris Errors: Orbital position errors.
3. Ionospheric and Tropospheric Delays: Signal slows down passing through the atmosphere.
4. Multipath: Signal bounces off surfaces (buildings, trees) before reaching the receiver.
5. Dilution of Precision (DOP): Geometric arrangement of satellites.
   • GDOP: Geometric Dilution of Precision.
   • PDOP: Position Dilution of Precision.
   • HDOP: Horizontal Dilution of Precision.
   • VDOP: Vertical Dilution of Precision.

Low DOP values indicate better geometry and accuracy.

Solved Problems