Adaptive Filtering Algorithms for Ultrasonic NDT applications

Hello
I am doing some work with the LMS, NLMS and RLS adaptive algorithms in the applications of ultrasonic NDT, at this stage; i am intending to do experiments to haracterize the behavior the algorithms in filtering and deconvolution contexts, I mean to determine the excess mean-square-error, misadjustment and evaluate tracking behavior.
To do this; I need to experimentally know the ideal filter coefficients for the specific case, my idea is to use the "system identification" application of the adaptive filter to model my ultrasonic signals and get the ideal coefficients then do the experiments and compare the coefficients which I get with those of the model.
The problem:
how to model the ultrasonic signals and noise in system identification contexts? what will be the input signal and what will be the reference one?
the ultrasonic signal is non-stationary, the noise origin is from the materials grain structure which has power close to other reflectors in the material (edges or defects), so the nature of the signal and noise are not covered by the assumptions in most of adaptive filters literature like the stationary signals and Gaussian noise...

The traditional case for system identification uses white Gaussian noise as input signal, I believe this does not apply for my case!

I am using LABVIEW 2009
I hope i was able to present the idea
Your help is highly appreciated