I know how to fit a curve when given some data points in the cartesian coordinate. Recently, I encountered a model that needs to fit a closed curve in the polar coordinate. I'm thinking of deducing a similar formula using Maximum Likelyhood, but the problem is I don't know what kind of hypothesis to choose.
In Cartesian coordinate, we can use the hypothesis of Polynomials $y=a_nx^n+...+a_0$, but this cannot be extended to my model because the "polynomial" in the polar coordinate $r=a_n\theta^n+...+a_0$ may not be closed.
What can I do?