MATLAB: Best fit of ellipse equation to given data

Question

Hello everyone,

For the given ellipse equation denoted as follows:

with additional parameters of mc and PIc to include a rotation of the ellipse:

I need to find

1. a and b (semi-major and semi-minor axes),
2. y0 and x0 (center coordinates), and
3. theta(rotation angle)

to have best fitted ellipse into my data which is give in the form of PI = f(m) with around 5-8 test points per dataset.

Given the fact that my data has various shapes I do not expect the ellipse to be very precise, but still I would like the best I can get out of this method. I have tried to achieve that with Curve Fitting app, using Custom Equation option, but the equation I have put into it was too complex (some errors occurred).

Can you please advice, what would be the most convenient way to achieve my goal?

Kind Regards

Answer 1

There is one implementation I posted here

https://www.mathworks.com/matlabcentral/answers/471640-how-to-fit-ellipse-equation-through-segment-of-ellipse?s_tid=srchtitle