Maths in physics and engineering · Solid · Dissertation

How satellites locate your phone: a maths EPQ idea

Why it works as an EPQ

Distances from known points become equations of spheres; solving them and studying the errors is a real problem.

Scope and difficulty

Solid. Solid. Solve in two dimensions first, then three; describe relativity corrections without deriving them.

The maths

Builds on these A Level topics: Vectors · Coordinate geometry · Algebra and functions.

You would learn:

• Trilateration
• Simultaneous non-linear equations
• Error and dilution of precision

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Locate a point from distances to three known points in 2D.
2. Extend to 3D and add the receiver's clock error as an unknown.
3. Show how timing errors become position errors.
4. Judge the main sources of error from reliable sources.

Pitfalls

• Ignoring the clock-error unknown.
• Claims about relativity you cannot support.

Where to start reading

• Search for: GPS trilateration clock bias four satellites
• Search for: dilution of precision explained

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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All maths in physics and engineering ideas · all 93 ideas

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