Admittance estimation from Admittance measurement

Hi. Here's my problem: I need to identify the admittance of an electronic device given its measured admittance; I have two vectors of data: w and dataY, where w is frequency [rad/s] and dataY is the measured admittance modulus (dataY = Y) measured per each frequency w.

I know (from theory), that the admittance of my device must be:

Y(s) = V(s)/I(s) = s*C_DC + s/(1/C_eq+s^2*L_eq+s*R_eq).

Y(jw) = V(jw)/I(jw) = jw*C_DC + jw/(1/C_eq-w^2*L_eq+jw*R_eq).

The problem is to find the 4 parameters (C_DC, C_eq, L_eq, R_eq) that best identify the admittance that I have measured.

I started with a "standard" least squares method:

err = intmax;
for ind_C_DC = C_DC
    for ind_R_eq = R_eq
        for ind_L_eq = L_eq
            for ind_C_eq = C_eq
                fittingY = 1i*w*ind_C_DC + 1i*w./(1/ind_C_eq-w.^2*ind_L_eq+1i*w*ind_R_eq);
                curr_err = mean((dataY-abs(fittingY)).^2);
                if curr_err < err
                    C_DC_fit = ind_C_DC;
                    R_eq_fit = ind_R_eq;
                    L_eq_fit = ind_L_eq;
                    C_eq_fit = ind_C_eq;
                    err = curr_err;
                end
            end
        end
    end
end

where C_DC, R_eq, L_eq, C_eq are 4 vectors of length N with a number N of possible parameters and C_DC_fit, R_eq_fit, L_eq_fit, C_eq_fit are the best fitting parameters.

Unfortunately, this doesn't work. Or better, it works (quite good) only if I let the simulation run for hours and hours (with N very very big).

Can you please suggest a smarter solution?

Thank you! Paolo