Separate static echos from acoustic signal (ICA?) I am using acoustic waves to measure the thickness of material. My problem is that the acoustical lens produces static echos in the signal. I try to separate both because there is a short interference between both.

The frequency of the material echo and the static echo has nearly the same frequency. So spectral subtraction is not a valid method to separate the signals.

I will try the following: 
The first measurement is without any object. So I am able to measure the static echo of the acoustic system. The second measurement I collect the signal with the object to measure.

My idea:
So I got two signals from different signal sources. Maybe I can separate both with Independent Component Analysis (ICA). 

Do you think that this solution will work? Or is there a better method to separate static and echo signals (with noise) out the measured data.

Thanks for your help.
This probably should be a comment, but I didn't earn that option yet. You can try measuring instrument impulse response. If I understand correctly, your system is essentially one-dimensional. Then if you use thin plate or plate of known thickness instead of thick object/material, your output signal will be an approximation of impulse response. Using it as deconvolution kernel will allow you to measure response specific to material, or object.