Given: The data from Lab 5. Specifically, you have signals from three GPS "satellites." These satellites live in a two-dimensional world and they transmit from these X,Y coordinates (in ambiguous units) :

• Satellite 1: position [ 2.3, 2.3], Range 3.0
• Satellite 2: position [-3.0, 2.0], Range 3.5
• Satellite 3: position [ 2.4, -1.8], Range 3.0

My answer from Lab 5 (i.e the minimum of the contours).

Now we'll use least squares. Unlike the polynomial case, the observations in this example (the ranges) are not linearly related to what we want to know - where the GPS receiver is. We'll need to linearize the equations. This is directly analogous to the GPS case, without the complications (like clocks).

Steps to follow:

1. Make a guess of the receiver location. I'll call its coordinates X_ro and Y_ro.
2. Linearize the measurement equations

   where

   

3. Calculate prefit residual l, i.e. observed range (radius of the circle) minus model range ()

4. Define your A matrix (superscripts are satellites, subscripts are receivers):

   

5. is defined as (A^TA)^-1A^Tl.
6. Your receiver location is X_ro+ and Y_ro+ .
7. Use this new location as your new nominal coordinates and iterate until your position solution converges.

Turn in:

Your receiver location and code.