How GPS Works
NAVSTAR
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NAVigation Satellite Timing And Ranging
Operated by Air Force
Launch Weight 1800 kg (4000 lb)
Orbital radius 20,200 km
Orbital Period 12 hours
Inclination 55 degrees
24 active, 4 spare
4 planes, 6 satellites per plane
Locating Earthquakes
Locating Earthquakes - Depth
GPS and Seismology
• GPS is a lot like locating earthquakes
– Use Trilateration
– Locate an unknown point using distances
from three known points
– Unknown point is actually at intersection of
three spheres (in earth, sort of)
• One important difference
– Earthquakes create signals with different
speeds so distance is coded in the signal
The Timing Problem
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Travel time = Radius to satellite
Distance to NAVSTAR: 14,000-20,000 km
Travel time =.05-.07 seconds
Have to measure travel time to sub-ppm
accuracy
• How do you know radius if you don’t know
where you are?
• Synchronized signals in GPS unit and
satellite
Signals in GPS
An Early Pseudo-Random Code
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1776 (seed)
17762 = 3154176
15412 = 2374681
37462 = 14032516
40322 = 16257024
62572 = 39150049
91502 = 83722500, etc.
The Clock Problem
• Atomic clocks costs thousands of dollars
– In the overall budget of a satellite program, that’s
chump change
– In the cost of a hand-held GPS unit, not so much
• GPS units use inexpensive quartz clocks
– Not precise enough
– One microsecond = 300 meters
• Have satellites broadcast time signals?
– How do we know the travel time?
• Unpredictable timing error introduced
Timing Errors
• Satellite positions known precisely and
ephemeris (or almanacs) updated
regularly
• If distances r1, r2, r3 are known, we can
solve for latitude, longitude, and elevation
• 3 variables, 3 unknowns
• If we also have to solve for an unknown
timing error, three radii are insufficient
Effect of Timing Error
Correcting Clock Errors
• We have four unknowns: latitude,
longitude, elevation and error
• Can solve with four satellite fixes
• Once error is known, can reset GPS unit
clock
• This is why the magic number of four for
GPS signals
• Full x,y,z solution = 3D
What About Less Than Four?
• We have four unknowns: latitude,
longitude, elevation and error
• Three satellites aren’t enough
• But we have a fourth sphere: the Earth
• May have to make assumptions about
radius due to oblateness of earth and
topography
• Can get latitude and longitude (2D) and
accuracy limited