← INDEX — FIG. 00 — 10.229 999 995 43 MHz
24 SATS · 6 PLANES · 55°
NAVIGATOR
GPS AND SATELLITE NAVIGATION
GPS is really a set of clocks.
BEGIN — CHAPTER 01 →CH.01 / 06 — CLOCKS IN ORBIT
Twenty-four satellites, each broadcasting the time
24 satellites in 6 planes at 55°.
Four satellites: three for position, one for the clock.
CH.02 / 06 — CIRCLES THAT DON'T MEET
Solve for the clock, and the circles close
Pseudoranges all share the same clock error.
The clock error becomes one more unknown.
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Flat, noise-free illustration.
CH.03 / 06 — EINSTEIN IN YOUR POCKET
Satellite clocks run 38 microseconds a day fast
Net 4.4647 × 10⁻¹⁰.
Clocks are set slow before launch.
CLOCK RATE IN A CIRCULAR ORBIT, RELATIVE TO THE GEOID
Δf/f = −Φ₀/c² − GM/(ac²) − GM/(2ac²) = 6.9693 × 10⁻¹⁰ − 3GM/(2ac²)
Ashby, eq. 35.
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CH.04 / 06 — WHERE THE SATELLITES ARE MATTERS
Spread out is precise; bunched up is not
User range error ≤ 2.0 m; actual 0.643 m.
4.9 m under open sky.
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Flat-sky DOP.
CH.05 / 06 — FROM A MILITARY SYSTEM TO EVERY PHONE
The day accuracy improved overnight
Selective Availability off, May 2000.
GLONASS and Galileo.
Every blue dot is a measurement of time.
CH.06 / 06 — REFERENCES