How Does GPS work?

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How Does GPS work?
Justin Chi Martin Chi Elizabeth Tom
2
What is GPS?
GPS Global Positioning System Satellite
Navigation System 27 Satellites (24 in use, 3 for
emergency)
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Applications

• Military
• Navigation
• Surveying
• Visually Impaired
• Geocaching
• Airplanes
• Time

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Types

• Differential GPS (DGPS)
• Wide Area Augmentation System (WAAS)
• Local Area Augmentation System (LAAS)
• Exploitation of DGPS for Guidance Enhancement
  (EDGE)
• Carrier Phase Enhancement (CPGPS)
• Wide Area GPS Enhancement (WAGE)
• Relative Kinematic Position (RKP)

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Geometry
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Simplified GPS

• Using 4 satellites
• (actual GPS uses 4 satellites and least
  squares method)

• xyz-coordinate system
• Earth is the origin
• A position can be expressed as (x, y, z) ? can
  be translated into longitude and latitude
• In this system, a point at sea level is x2
  y2 z2 1
• Speed of light is about .047 (units of earth
  radii per millisecond)

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Ship Example
Satellite Position Time
1 (1,2,0) 19.9
2 (2,0,2) 2.4
3 (1,1,1) 32.6
4 (2,1,0) 19.9
Let (x, y, z) ships position t time when
signals arrive
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Calculating distance for Satellite 1
Satellite Position Time
1 (1,2,0) 19.9
d .047(t 19.9)
AND
d
(x 1)2 (y 2)2 z2 .0472(t 19.9)2
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(x 1)2 (y 2)2 z2 .0472(t 19.9)2
2x 4y 2(.0472)(19.9)t 12 22 -
.0472(19.9)2 x2 y2 z2 - .0472t2
We can do this for the rest of the satellites
2x 4y 0z 2(.0472)(19.9)t 12 22 02 -
.0472(19.9)2 x2 y2 z2 - .0472t2
4x 0y 4z 2(.0472)(2.4)t 22 02 22 -
.0472(2.4)2 x2 y2 z2 - .0472t2
2x 2y 2z 2(.0472)(32.6)t 12 12 12 -
.0472(32.6)2 x2 y2 z2 - .0472t2
4x 2y 0z 2(.0472)(19.9)t 22 12 02 -
.0472(19.9)2 x2 y2 z2 - .0472t2
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2x 4y 4z 2(.0472)(17.5)t 8 5
.0472(19.92 - 2.42) 0x 2y 2z -
2(.0472)(12.7)t 3 5 .0472(19.92 - 2.42) 2x
2y 0z 2(.0472)(0)t 5 5 .0472(19.92
19.92)
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(No Transcript)
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x 5.41 - .095t, y 5.41 - .095t, z 3.67 -
.067t t is free
(5.41 - .095t 1)2 (5.41 - .095t 2)2 (3.67
- .067t)2 .0472(t 19.9)2 .02t2 - 1.88t
43.56 0
2 answers t 43.1 t 50.0
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t 43.1
(x, y, z) (1.317, 1.317, .790) d is about
2 Since the units are Earth radii this means that
the point is about 4000 miles above the surface
of the Earth
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t 50.0
(x, y, z) (.667, .667, .332) d is about
.9997 Since the units are Earth radii this means
the point is on the surface of the Earth. We
can convert this into longitude and latitude
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Wide Area Augmentation System

• Improves upon GPS
• Uses a combination of satellites and ground
  based stations to send correction signals to the
  receiver
• Can improve accuracy up to 5 times