How to optimize experimental data to measured reference signal?

Hello,

I would like to use the optimization toolbox for the following task.

I have a reference signal, lets call it RefSignal which is array of doubles. Moreover, I have an array with experimental data, lets call that ExpSignal. I know from the theory that the sum of two different shifted RefSignal results in ExpSignal. Refsignal and ExpSignal are equally long.

I would like to achieve an optimization alogrithm which minimize an error function:

I thougt of something like this

ErrFunc=ExpSignal-param(1).*(circshift(RefSignal,-param(2))+circshift(RefSignal,param(2)))

Whereas, param includes the optimize parameter namley param(1) the amplitude and param(2) the shift itself.

I achieved results using fminsearch which needs the theoratical function RefSignal. However, the experimental data are not that ideal why I would like to use the measured RefSignal. It is working manually by changing each param individually but I would like to automize the whole process.

How can I minimize the error function when only sampled signals are given ?

EDIT: I have attached the data ExpSignal and RefSignal I working with. In Result.fig is the resutl I could achieve manually.

[dpb]

I'd guess you might get the shift directly with correlation...without signals to see just what you have to work with, it's pretty tough to think of much for a specific problem.

[Pawl]

I added the signals I working with and the result I achieved manually. I had a similar idea with the correlation approach. But therefore I have to guess the amplitude value of the RefSignal before applying correlation. Only the combination of the correct shift and correct amplitude gives an unique solution which might be the right task for an optimization.