nlinfit returns same values

Hi, I am having an issue with the nlinfit function in Matlab. I am given some experimental data and trying to fit a curve that I solve for in another file and extract some parameters (ng, Kg) but the nlinfit always returns the same initial guesses. If anybody can help me, I would greatly appreciate it. Below are the files/functions that I used:

This is the main file:

global ng Kg
% exp data
ti=[0;.5;1;1.5;2;2.5;3;3.5;4;4.5;5];% min
Sup=[9.02;7.95;7.24;6.37;5.79;5.42;4.70;4.38;3.91;3.60;3.33]; 
yi=Sup*10^-3;
% fit estimated parameter to exp data
plot(ti,yi)
Beta=[ng Kg];    
Beta0 = [2 .0004 ];
[Beta,resid,J,Sigma] = nlinfit(ti,yi,@esti_j,Beta0);
CI = nlparci(Beta,resid,'jacobian',J)
Beta

This is the file that calls the other 2 functions:(mom_j)

function dudt = mom_j(t,u)
global ng  Kg
C_eq = 10^-3;  
po = 1277; 
sf = 1; 
xin = 106*10^-6;          

Gode = Kg*(u(4)-C_eq).^ng;      
dudt = zeros (4,1);
dudt(1) = 0;
dudt(2) = u(1)*Gode;
dudt(3) = 2*Gode*u(2);
dudt(4) = -po*sf*(3*Gode*u(3));

end

the other function(est_j):

function [t Cf] = esti_j(Beta,ti)
global ng Kg
ng=Beta(1);
Kg=Beta(2);

po = 1277;                
sf = 1;            
C_eq = 10^-3;             
Min = 20*10^-6;           
xin = 106*10^-6;          
V = 50*10^-6;             
c_0 = 9.02*10^-3;          

%set of equations describing initial conditions

u0_0 = Min/((xin^3)*po*sf*V);
u1_0 = Min/((xin^2)*po*sf*V);
u2_0 = Min/(xin*po*sf*V);
[t,u] = ode15s(@mom_j,ti,[u0_0 u1_0 u2_0 c_0 ]);

Answer 1

[Robert Cumming]

do you get any warning messages? If your problem is not solvable - then nlinfit can appear to return the same values, do this and you should see that nlinfit is attempting to change the parameters:

format long
disp ( Beta ) % in your esti_j function

[kate oucherif]

Hi Robert,

Thank you for taking a look at his. I get the following warnings:

Warning: Rank deficient, rank = 0, tol = 0.0000e+000.

Warning: Some columns of the Jacobian are effectively zero at the solution, indicating that the model is insensitive to some of its parameters...

Warning: Matrix is singular to working precision.

I tried displaying the values of beta as you suggested and they almost don't vary at all:

1.600000000000000 0.000800000000000

1.600000000000000 0.000800000000000

1.600009688727124 0.000800000000000

1.600000000000000 0.000800004844364

I wonder if there are any error in the code itself.Any further suggestions would be extremely helpful! thanks again!

[Robert Cumming]

nlinfit starts by incrementing the value in small steps (as its showing above) - so that is working, the size of the following increments depends on what the results you get back are.

The warning message is telling you that there is a problem with your data and/or equation - in that it cannot be "fit"