• Idea: model Global Navigation Satellite System
• Aim: define an object’s position using satellites

Assumptions:

• Earth:
  • flat
  • motionless
  • perfect circle
• Satelites:
  • motionless
  • known position
  • synchronized (i.e. they all have the same “time”)

For given distances between the object’s position and setelites, it is possible to define the postions.

Question: how to define distances?

Answer: Measuring the time between the moment when a signal is emitted by a satellite and the time at which it is received.

Use optim function to maximize:

\[f(x, y) = x ^ 2 + y ^ 2 + 2x + 8y,\] with initial values

\[(x_0, y_0) = (4, 4)\]