How to get best fitting Parameters for a function for all datapoints

syms lh lo r

U_in = 10;
w = 2*pi*[111452 131857 142436 157777 195689 230000 260000 347213 400000];
u_ll = [9.015 9.25 9.37 9.53 9.765 10 10 10 10];

b1_ll = w(1) * (lh +lo);
b2_ll = w(2) * (lh +lo);
b3_ll = w(3) * (lh +lo);

eqn1 = (u_ll(1) == abs((r+1i*b1_ll)*U_in/(50+r+1i*b1_ll)));
eqn2 = (u_ll(2) == abs((r+1i*b2_ll)*U_in/(50+r+1i*b2_ll)));
eqn3 = (u_ll(3) == abs((r+1i*b3_ll)*U_in/(50+r+1i*b3_ll)));
eqns = [eqn1, eqn2, eqn3];
[s_lh, s_lo, s_r] = solve(eqns,[lh lo r]);

Warning: Unable to find explicit solution. For options, see help.

Answer 1

[Torsten]

You cannot estimate lh and lo separately in your approximating model, only their sum (lh+lo).

But your model seems to return constant values - independent of your fitting parameters.

U_in = 3;
w = 2*pi*[111452 131857 142436 157777 195689 230000 260000 347213 400000];
u_ll = [9.015 9.25 9.37 9.53 9.765 10 10 10 10];
fun = @(x) u_ll-abs((x(1)+1i*w*x(2))*U_in./(50+x(1)+1i*w*x(2)));
sol = lsqnonlin(fun,[2 -5])

Initial point is a local minimum.

Optimization completed because the size of the gradient at the initial point 
is less than the value of the optimality tolerance.

sol = 1×2

2 -5

r = sol(1)

r = 2

lho = sol(2)

lho = -5