Find coefficients for a unified model for fitting negative and positive output

Hello everyone,

well, I'm trying to fit my data corresponding to points of the contour of a circle to a model. the problem I have is, as I have data for a circle, I have negative and positive values for the radius. So the model has to fit for both values. I want from this fitting data process to find out the coefficients of my model the permit to approach the max possible to the true values of the radius.

I've tried two methods: I used the function "leasqr" from the Octave package "optim", and I used the function "fmin" to search the min of the sum of the squared errors.

the problem with the two methods is that I have to separate my data into two sets: negative and positive, which cause different values of coefficients (which is not what I'm seeking).

Another problem is that I want to calculate the best coefficients so my data be the nearest possible to the nominal value, which I don't know how to do it; when I use "leasqr" it gives me the number of iterations and the final parameters, but I want to know the parameters calculated at each iteration and continue until having the best ones.

please find attached two plots to understand the problem (the fitted plot is far from the nominal value 10)

I'll appreciate any help you could provide me