I think you'd better fix t0 because overparameterization exists between t0 and Ai. You can also apply a constraint between parameters.
If you need 3 or 4 parameters Ai and ti, the fitting function can be defined as follows (4 parameters Ai and ti).
y=y0+A1*(1-exp(-(x-t0)/t1))+A2*(1-exp(-(x-t0)/t2))+A3*(1-exp(-(x-t0)/t3))+A4*(1-exp(-(x-t0)/t4));
Parameter Initialization can be defined,
t0 = min(x_data);
int sign;
t1 = get_exponent(x_data, y_data, &y0, &A1, &sign);
t1 = t2 = t3 = t4 = -1 / t1;
A1 = A2 = A3 = A4 = - sign * exp(A1 - t0/t1) / 4;
y0 = y0 - 4*A1;
Sam
OriginLab Technical Services
