Having only a few data points to work with is a little worrisome, but something like this may work:
function estimates = fitsinewave(xdata, ydata, start_point)
% Call fminsearch with a starting point.
model = @sinefun;
options = optimset('MaxFunEvals',3000);
estimates = fminsearch(model, start_point, options);
% sinefun accepts curve parameters as inputs, and outputs sse,
% the sum of squares error for A*sin(2*pi/365*xdata-B)+C-ydata.
function sse = sinefun(params)
A = params(1);
B = params(2);
C = params(3);
ErrorVector = A*sin(2*pi/365*xdata-B)+C - ydata;
sse = sum(ErrorVector .^ 2);
return
end
return
end
Here is an example to test it out:
A = 3;
B = 3*pi/4;
C = -1.5;
xdata = sort(rand(1,5)*365);
ydata = A*sin(2*pi/365*xdata-B)+C;
start_point = [0, 0, 0]; % Zeros unless you have a good guess for A, B, and C
ABCestimates = fitsinewave(xdata, ydata, starting_point)
ABCestimates =
3.0001 2.3562 -1.5000
