MATLAB: 3-term exponential fit

Question

Hi, I want to fit a 3-term exponential function i.e.

y = a*exp(-b*x) + c*exp(-d*x) + e*exp(-f*x)

to get coefficients b,d,f.

Matlab's curvefitting toolbox is great for 2 term fitting, but that is it's limit. Tried log fits, polyfit fit but had no luck. Any ideas?

Thanks, Will

Answer 1

I don’t have the Curve Fitting Toolbox (Optimization and Statistics instead). This uses fminsearch:

y = @(b,x) b(1).*exp(-b(2).*x) + b(3).*exp(-b(4).*x) + b(5).*exp(-b(6).*x);
p = [3; 5; 7; 11; 13; 17]*1E-1;             % Create data
x  = linspace(1, 10);
yx = y(p,x) + 0.1*(rand(size(x))-0.5);
OLS = @(b) sum((y(b,x) - yx).^2);           % Ordinary Least Squares cost function
opts = optimset('MaxFunEvals',50000, 'MaxIter',10000);
B = fminsearch(OLS, rand(6,1), opts);       % Use ‘fminsearch’ to minimise the ‘OLS’ function
fcnfit = y(B,x);                            % Calculate function with estimated parameters
figure(1)
plot(x, yx, '*b')
hold on
plot(x, fcnfit, '-r')
hold off
grid