Nonlinear regression not working

I want to find the parameters of a nonlinear function based on experimental data. The function involves an integral whose upper limit is the independent variable I'm passing in. I'm trying the nlinfit and lsqcurvefit functions, but both functions don't seem to optimize the guess for some reason. If anyone could help me trying to figure out why it isn't working properly I would really appreciate it. Thanks a lot in advance!

My function

Below is my code.

clc;
clear all;

input0= [160	159	158	157	156	155	154	153	152	151	150	149	148	147	146	145	144	143	142	141	140	139	138	137	136	135	134	133	132	131	130	129	128	127	126	125	124	123	122	121
    0	0.00077053	0.0030894	0.006968	0.012418	0.019451	0.028057	0.038074	0.049486	0.062734	0.078769	0.098834	0.12418	0.15593	0.19477	0.2407	0.29315	0.35117	0.41346	0.47835	0.5437	0.60717	0.6667	0.72101	0.76954	0.81205	0.84846	0.87886	0.90338	0.92262	0.93791	0.95072	0.96188	0.97165	0.98013	0.98719	0.99274	0.99674	0.99918	1
    ];
input0=input0';
T= input0(:,1);
t = zeros(length(input0),1);
for i=1:length(input0)
    t(i)=(T(1)-T(i))./50;
end
alp = input0(:,2);

% X, Y data
g = [t alp];

% guess 
x0=[2.4; 140.7; 44.94];

% Fitting the constants
fun12 = @(constant,time) constant(1)*exp((-4*log(2)*((-time*50+ 160)-constant(2)).^2)/constant(3).^2);
fun11 = @(constant,t) 1-exp(-(arrayfun(@(t) integral(@(t)fun12(constant,t),0,t),t)).^3)      ;
constant_new = nlinfit(g(1),g(2),fun11,x0) 

Warning: Rank deficient, rank = 0, tol = 0.000000e+00.

Warning: The model is overparameterized, and model parameters are not identifiable. You will not be able to compute confidence or prediction intervals, and you should use caution in making predictions.

constant_new = 3×1

2.4000 140.7000 44.9400

%constant_new = lsqcurvefit(fun11,x0,g(1),g(2))  % this is not working either

% Plotting experimental data
plot (t,alp,'ko','Linewidth',1.5)
hold on;

% Plotting the fit
plot(t,fun11(constant_new,t),'Linewidth',1.5);
legend('Input data','Fit')
set(gca,'FontSize',14,'FontName', 'Verdana');
grid on;

Answer 1

[Torsten]

clc;
clear all;

input0= [160	159	158	157	156	155	154	153	152	151	150	149	148	147	146	145	144	143	142	141	140	139	138	137	136	135	134	133	132	131	130	129	128	127	126	125	124	123	122	121
    0	0.00077053	0.0030894	0.006968	0.012418	0.019451	0.028057	0.038074	0.049486	0.062734	0.078769	0.098834	0.12418	0.15593	0.19477	0.2407	0.29315	0.35117	0.41346	0.47835	0.5437	0.60717	0.6667	0.72101	0.76954	0.81205	0.84846	0.87886	0.90338	0.92262	0.93791	0.95072	0.96188	0.97165	0.98013	0.98719	0.99274	0.99674	0.99918	1
    ];
input0=input0';
T= input0(:,1);
t = zeros(length(input0),1);
for i=1:length(input0)
    t(i)=(T(1)-T(i))./50;
end
alp = input0(:,2);

% X, Y data
g = [t, alp];

% guess 
x0=[2.4; 140.7; 44.94];

% Fitting the constants
fun12 = @(constant,time) constant(1)*exp((-4*log(2)*((-time*50+ 160)-constant(2)).^2)/constant(3).^2);
fun11 = @(constant,t) 1-exp(-(arrayfun(@(t) integral(@(t)fun12(constant,t),0,t),t)).^3)      ;
constant_new = nlinfit(g(:,1),g(:,2),fun11,x0) 

constant_new = 3×1

2.6316 140.6281 48.6762

%constant_new = lsqcurvefit(fun11,x0,g(1),g(2))  % this is not working either

% Plotting experimental data
plot (t,alp,'ko','Linewidth',1.5)
hold on;

% Plotting the fit
plot(t,fun11(constant_new,t),'Linewidth',1.5);
legend('Input data','Fit')
set(gca,'FontSize',14,'FontName', 'Verdana');
grid on;

[Sameer Kulkarni]

Thank you very much Torsten!