How to best-fit a rational function approximation to Theodorsen's function using the lsqcurvefit function in Matlab?

Question

I am using a rational function (polynomial ratio) to approximate Theodorsen's function. I am having issues in guessing the correct (most optimal) initial guess parameters using the lsqcurvefit function in Matlab. Is there a way to know what would be the best initial guess parameters to get the best fit result?

My code is the following:

k = logspace(-10,1,300);

% Exact Theodorsen's Function C(k) in terms of Bessel Function
Ck= @(k)(besselh(1,2,k))./(besselh(1,2,k)+1i*besselh(0,2,k));

% Ckget function used to extract real and imaginary numbers and stacks the result
Ckget= @(k)[real(Ck(k)); imag(Ck(k))]; 

% Define 3rd order approximation function 
x0= [.1,.1,.1,1,.1,.1,.1,.1]; % Create initial guess
U = 200;
b = 3;
s = 1i*k*(U/b);
Ck2 = @(x,k)((x(1)*s.^3 + x(2)*s.^2 + x(3)*s + x(4))./(x(5)*s.^3 + x(6)*s.^2 + x(7)*s + x(8)));
Ck2get= @(x,k)[real(Ck2(x,k)); imag(Ck2(x,k))]; %extract real & imaginary values

% Use curve fit function for best fit approximation
x2= lsqcurvefit(Ck2get,x0,k,Ckget(k))