Fit two data sets with 3 fit parameters, one parameter is the same

I have 2 data sets: x1,y1 & x2,y2 (different lengths).

% k is a constant

I want to fit:

f1 = @ (p,x1) p(1)./sqrt((x1-k).^2+p(2)^2)+p(3);
f2 =@ (p, x2) p(4)./sqrt((x2-k).^2+p(5)^2)+p(3);

Both data sets should be fit to the same p(3). I would like the fitting to return [p(1) p(2) p(3) p(4) p(5)]

Can I do this with lsqcurvefit?

I hope this makes sense,

Luke

Answer 1

[Rik]

As far as I'm aware, you can only fit a single function at once, so you can try something like this:

f1 = @ (p,x1) p(1)./sqrt((x1-k).^2+p(2)^2)+p(3);
f2 =@ (p, x2) p(4)./sqrt((x2-k).^2+p(5)^2)+p(3);

cost_function=@(p) sum((f1(p,x1) - y1).^2) + sum((f2(p,x2) - y2).^2);

Now you can minimize cost_function, which will find the optimal values of p.

Alternatively (and that is probably a better idea), you can just concatenate the two:

L=[true(numel(x1),1);false(numel(x2),1)]
f_=@(p,x)[f1(p,x(L));f2(p,x(~L))];

[Luke Smith]

Thank you! I concatenated the two and it works really well, thank you for such a quick reply.