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How GPS Works

How GPS Works. NAVSTAR. 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.

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How GPS Works

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  1. How GPS Works

  2. NAVSTAR • 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

  3. Locating Earthquakes

  4. Locating Earthquakes - Depth

  5. 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

  6. The Timing Problem • 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

  7. Signals in GPS

  8. An Early Pseudo-Random Code • 1776 (seed) • 17762 = 3154176 • 15412 = 2374681 • 37462 = 14032516 • 40322 = 16257024 • 62572 = 39150049 • 91502 = 83722500, etc.

  9. 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

  10. 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

  11. Effect of Timing Error

  12. 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

  13. 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

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