how does gps work? justin chi martin chi elizabeth tom
TRANSCRIPT
How Does GPS work?
Justin Chi
Martin Chi
Elizabeth Tom
What is GPS?
GPS = Global Positioning System
Satellite Navigation System
27 Satellites (24 in use, 3 for emergency)
Applications:
• Military
• Navigation
• Surveying
• Visually Impaired
• Geocaching
• Airplanes
• Time
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)
Geometry:
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)
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) = ship’s position
t = time when signals arrive
d = 222 )0()2()1( zyx
(x – 1)2 + (y – 2)2 + z2 = .0472(t – 19.9)2
Satellite Position Time
1 (1,2,0) 19.9
Calculating distance for Satellite 1:
d = .047(t – 19.9)
AND
(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
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)
00022
47.3056.220
86.3077.442
00022
47.3056.220
86.3077.442
67.3067.100
41.5095.010
41.5095.001
67.3067.100
41.5095.010
41.5095.001
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
(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
t = 43.1
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
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