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Global positioning systems

Dr. Huidae Cho
Institute for Environmental and Spatial Analysis...University of North Georgia

1   How is a global positioning system (GPS) used in civil applications?

Land, sea, air, and space navigation

Intelligent Vehicle Highway System (IVHS)

Search and rescue

Mapping and GIS

Recreation

Surveying

2   Three main components of GPS

Space segment: GPS satellites

Control segment: Ground controls and monitoring stations

User segment: Owned receivers

2.1   Space segment

Constellation of 24 operational satellites

Run by the Department of Defense

  • U.S. Air Force Space Command (AFSPC)

First satellite launched in 1978

Cost $10 billion

Triangulation-based technology

2.1.1   Operation

Fully operational on April 27, 1995

24 hours a day

All weather conditions

Orbit Earth every 12 hours

Altitude approximately at 20,200 km (12,600 nautical miles)

2.1.2   How many satellites?

Approximately 1,886!

many-satellites.png

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Images courtesy of Analytical Graphics, Inc. (www.agi.com)

2.2   Control segment

control-segment.png

  • 1 master control station
  • 1 alternate master control station
  • 11 command and control antennas
  • 16 monitoring sites

2.3   User segment

Your smartphone with a GPS!

Remember you have an inaccurate time.

3   How does it work?

how-gps-works.png

3.1   Five steps

Accurate timing

Satellite positioning

Satellite ranging

Trilateration

Error correction

3.1.1   Accurate timing

GPS determines its location by measuring time.

It ensures the accurate calculation of a distance.

Atomic clocks on GPS satellites are accurate to the nanosecond (10-9 second).

3.1.2   Satellite positioning

The satellites must know where themselves are.

Radars from ground stations constantly check each satellite to monitor changes in orbit.

3.1.3   Satellite ranging

Measures the distance from the satellite to the receiver

\[ D=S\times T \]

  • $D$: Distance between the satellite and receiver
  • $S$: Speed of signal = 186,000 m/s in vacuum
  • $T$: Time it takes for signal to be sent and received

satellite-ranging.png

3.1.4   Trilateration

Basis of GPS

Measurements are made to calculate the distance from your location to a number of GPS satellites that are at different known locations.

Three variables

  • How far is the point from the satellite?
  • How long does it take for the radio signal to travel that distance?
  • Where exactly are the satellites?

3.1.5   Error correction

$D=S\times T$ works only when $T$ is accurate.

Ideally, $T$ = GPS receiving time – Satellite sending time.

Satellite clocks are very accurate, but GPS clocks are not!

Now, $D=S\times T=S\times(\hat{T} + e)$

  • $D$: Accurate distance
  • $\hat{T}$: Inaccurate travel time
  • $e$: Unknown constant error

How many unknowns? $x$, $y$, $z$, and $e$ ⇒ We need four satellites!

3.2   System of equations

\begin{align*} (x-X_1)^2+(y-Y_1)^2+(z-Z_1)^2&=D(\hat{T}_1,e)^2\\ (x-X_2)^2+(y-Y_2)^2+(z-Z_2)^2&=D(\hat{T}_2,e)^2\\ (x-X_3)^2+(y-Y_3)^2+(z-Z_3)^2&=D(\hat{T}_3,e)^2\\ (x-X_4)^2+(y-Y_4)^2+(z-Z_4)^2&=D(\hat{T}_4,e)^2 \end{align*}

3.3   Why do we need four satellites again?

Why does GPS positioning require four satellites? Four unknown variables!

A typical misleading explanation

one-satellite.png

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