MATLAB: Least Squares fit of model function

Question

Hi guys!

I need help with a least square method fit for the model function a*cosh(b*x)+c but im not sure how to do it without the curve fitting tool (see solution of code below). I am not sure have to split the a and b or the cosh(b*x) to create a matrix and use the A\y backslash command in matlab to get the variables of a b and c. I tried putting b as 1 to solve it but i dont think i get the right answer (se code below the %curve fitting tool)

I was given 15 different points (x,y).

% Curve fitting tool <-- This should be right i guess
% g = fittype('a*cosh(b*x) + c','coeff',{'a','b','c'});
% options = fitoptions(g);
% fitobject = fit(x',y',g,options);
% fit3 = (fitobject.a)*cosh((fitobject.b)*x) + fitobject.c;
% Without the curve fitting tool <-- Probably wrong
x=[ . . . . . . . . . . . . . . .]
y=[ . . . . . . . . . . .. . .  .]
x=cosh(1*x)';
A=[cosh(x) ones(size(x))]
ab=A\y
n2=[]
for i=1:15
    n=ab(1)*x(i)+ab(2);
    n2(i)=n;
end
plot(x,n2,'ro')

Do you have any clues on how to solve this one without the curve fitting tool?

I would be really greatful if you can help me with this one!

Answer 1

Everyong had the fminsearch function, so use it to do nonlinear curve fitting:

f = @(b,x) b(1).*cosh(b(2).*x) + b(3);
x=[ . . . . . . . . . . . . . . .]
y=[ . . . . . . . . . . .. . .  .]
[B,fval] = fminsearch(@(b) norm(y - f(b,x)), [0.5; 0.5; 0.5])
figure
plot(x, y, 'pg', 'MarkerFaceColor','g')
hold on
plot(x, f(B,x), '-r')
hold off
grid
legend('Data', 'Regression')

Nonlinear parameter estimation can be very sensitive to the initial parameter estimates (here [0.5; 0.5; 0.5]), so you may have to experiment with them to get a good fit to your data.