Science · 6 pages · 12 min
Why four satellites are the usual GPS minimum
Three distances would locate you if your clock were perfect, so a fourth solves the clock.
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From the opening
Four satellites are the usual minimum because the receiver must solve for three coordinates of position and for one more unknown, the error in its own clock. Each satellite supplies one equation, and three would suffice only if the receiver already knew the exact time. The opening covers three coordinates plus a clock, why the clock error is shared, and when three satellites are enough.
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Inside
- Three coordinates plus a clock
- Why the clock error is shared
- When three satellites are enough
- Why a bad four can still solve
- Where the idea stops applying
- A distinction worth keeping
Sources
- GPS pseudorange and receiver clock bias
- The four-satellite solution for position and time