Set up a nonlinear least squares minimization and use the Matlab optimization tool lsqnonlin to find the receiver's position and the time correction.

The reason that a minimum of 4 satellites are needed is because in the navigation equation there are 4 unknowns. In this case, the problem is a square problem and no least squares are involved. Assume now that two more satellites are observing the receiver with the following data available: Satellite 5 : position = (17800; 6400; 18660); time interval =0:0732; Satellite 6 : position = (17500; 7590; 18490); time interval =0:0735: (a) (20 pts) Set up a nonlinear least squares minimization and use the Matlab optimization tool lsqnonlin to nd the receiver's position and the time correction.

My function is

function F = myfun(p)
x=p(1);
y=p(2);
z=p(3);
d=p(4);

c = 299792458;

F(1)=sqrt((x-15600).^2 + (y-7540).^2 + (z-20140).^2 )-c.*(0.07074-d);
F(2)=sqrt((x-18760).^2 + (y-2750).^2 + (z-18610).^2 )-c.*(0.07220-d);
F(3)=sqrt((x-17610).^2 + (y-14630).^2 + (z-13480).^2 )-c.*(0.07690-d);
F(4)=sqrt((x-19170).^2 + (y-610).^2 + (z-18390).^2 )-c.*(0.07242-d);
F(5)=sqrt((x-17800).^2 + (y-6400).^2 + (z-18660).^2 )-c.*(0.0732-d);
F(6)=sqrt((x-17500).^2 + (y-7590).^2 + (z-18490).^2 )-c.*(0.0735-d);
end

x0 = [1 2 3 4] % Starting guess
[d,resnorm] = lsqnonlin(@myfun,x0); % Invoke optimizer

options = optimoptions('lsqnonlin', 'Algorithm', 'quasi-newton');
[dfinal, fval, exitflag] = lsqnonlin(@myfun,[-1 -1 2 2],options);

Answer 1

[Alan Weiss]

This is clearly a copied homework problem (you wrote "(a) (20 pts) Set up a ..."). So instead of asking us to do your homework for you, I suggest that you show us what you tried and ask for help on the part where you get stuck.

Alan Weiss

MATLAB mathematical toolbox documentation